A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches. What is the surface area of the pyramid? Enter your answer in the box. in²

Based on the information, it can be inferred that after one hour Jake and Lisa will have filled 3 socks each.

To find the time necessary for both of them to have filled the same number of socks, we must take into account the speed at which each one fills the socks.

Additionally, when Jake arrives at work, Lisa has already filled two stockings. According to the above, after one hour Lisa will complete all 3 socks and Jake will have filled the first 3 socks for him.

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Answer:

X=-2-y

2(-2-y)+2y=8

-4-2y+2y=8

Step-by-step explanation:

-4-8=0

=-12

Answer:

511 million km²

Step-by-Step Explanation:

Let the total surface area of the Earth be x.

Water covers 70.7% of the total surface area of the Earth, i.e.,

70.7% of x = 3.61 x 10⁸ km²

or, 70.7x /100 = 3.61 x 10⁸ km²

or, 707x/1000 = 3.61 x 10⁸ km²

or, 707x = 3.61 x 10⁸ x 1000km²

or, 707x = 3.61 × 10^11 km²

or, x = 0.0051 × 10^11 km²

or, x = 5.1 × 10⁸ km² = 511 million km²

Hope it helps.

If you have any query, feel free to ask .

Answer:

511 million km²

Step-by-step explanation:

Let x be the approximate total surface area of the Earth.

Given water covers 70.7%, or about 3.61 × 10⁸ km², set up an equivalent ratio of percent (in decimal form) to area:

[tex]\implies 0.707:3.61 \times 10^8=1:x[/tex]

Solve for x:

[tex]\implies\dfrac{0.707}{3.61 \times 10^8}=\dfrac{1}{x}[/tex]

[tex]\implies0.707x=3.61 \times 10^8[/tex]

[tex]\implies x=\dfrac{3.61 \times 10^8}{0.707}[/tex]

[tex]\implies x=\dfrac{3.61 }{0.707}\times 10^8[/tex]

[tex]\implies x=5.10608203...\times 10^8[/tex]

One million has 6 zeros and can be written in scientific notation as:

Therefore, to write x in millions as x × 10⁶, subtract 2 from the exponent and move the decimal point to the right by 2 places:

[tex]\implies x=510.608203...\times 10^6[/tex]

Therefore, the approximate surface area of the Earth is 510.608203... million km², which is 511 million km² to the nearest million.

By rewriting the 3 given systems, we will see that:

1) Independent and consistent.

2) Independent and inconsistent.

3) Dependent.

Let's analyze each system.

Let's look at the first one, we can rewrite it as:

y = 2x + 3

y = -x - 3

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

Now let's look at the second system, we can rewrite it as:

y = 3x - 2

y = 3x + 2

Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.

For the final system, we have:

y = (-1/2)*x + 2

y = (-1/2)*x + 2

So, we have two equal lines, so this system is dependent.

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The amount of money each student will pay, excluding taxes and tip,  $23.534

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

3 Coffee 5.85

1 Diet Bev. – lg. 3.38

1 Sparkling Water 2.50

3 Ranch Chicken Sandwich 44.97

1 Classic Burger 12.95

1 Thai Stir-fry Special 11.50

2 Club Sandwich 22.98

Subtotal 104.13

Tax (13%) 13.54

Total 117.67

The receipt is for lunch for five students. Each student will pay 1/5 of the bill

The amount of money each student will pay = ?

⇒  1/5x117.67

⇒   23.534

Therefore, the amount each student will pay, $23.534

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For given parallelogram, x = 4.

There are six crucial parallelogram characteristics to be aware of:

Congruent sides are those when AB = DC.

Congruent opposite angels are D = B.

(A + D = 180°) Consecutive angles are supplementary.

All angles are correct if just one of them is.

A parallelogram's diagonals cut each other in half.

In Geometry, a parallelogram is a type of quadrilateral. It is a two-dimensional figure with four sides. The most important properties of a parallelogram are that the opposite sides are parallel and congruent and the opposite angles are also equal.

5x-1=19

⇒5x=19+1

⇒5x=20

x=20/5

x=4

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We can use a system of equations to solve x + 8 = 12 and the both equations are true, we can conclude that the number is 4.

What is system of equations ?

A system of equations is a collection of two or more equations that are solved simultaneously to find the values of the variables that satisfy all of the equations. Each equation in the system represents a constraint on the variables, and the solution to the system is the set of values for the variables that satisfy all of the constraints.

We can use a system of equations to solve this problem. If the number in question is called "x", we can write:

x + 8 = 12

y

3 * x = 12

Now we can solve for "x". First, we will isolate "x" from the first equation:

x + 8 = 12

x = 12 - 8

x = 4

Now we can check if this result also satisfies the second equation:

3 * x = 12

3 * 4 = 12

Since both equations are true, we can conclude that the number is 4.

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Answer:

4?

Step-by-step explanation:

(143-35)/3^3

108/27

4

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{143 - 35}{3^3}}[/tex]

[tex]\mathsf{= \dfrac{108}{3^3}}[/tex]

[tex]\mathsf{= \dfrac{108}{3 \times 3 \times 3}}[/tex]

[tex]\mathsf{= \dfrac{108}{9 \times3}}[/tex]

[tex]\mathsf{= \dfrac{108}{27}}[/tex]

[tex]\mathsf{= 4}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{4}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex] \frac{36}{9643} = 0.003733278[/tex]

Answer: 34 on both?

Step-by-step explanation:

According to the problem,Therefore, x = 12714.29 and y = 1285.71. Mitchell invested $12714.29 at 6% and $1285.71 at 7%.

Investment is the process of using money to purchase assets in order to generate income or increase in value. Investing involves the purchase of assets such as stocks, bonds, mutual funds, real estate, commodities, or other investments in order to achieve financial goals. It is a long-term strategy that involves setting aside funds for the future, with the expectation of obtaining a return on the investment. The ultimate goal of investing is to maximize the return on an investment while minimizing the risk of loss.

Let x be the amount invested at 6%, and y be the amount invested at 7%.

We know that x + y = 14,000, as this is the total amount of the advance.

We also know that the total interest each year is $930. We can calculate the interest individually using the formula I = Prt, where P is the principal (the amount invested), r is the interest rate and t is the time (1 year in this case).

For the 6% investment: I = (x)(0.06)(1) = 0.06x

For the 7% investment: I = (y)(0.07)(1) = 0.07y

We now have two equations:

0.06x + 0.07y = 930

x + y = 14,000

We can use substitution to solve for x and y.

Substitute x + y = 14,000 into equation 0.06x + 0.07y = 930 to get 0.06(14,000) + 0.07y = 930.

Simplifying, we get 840 + 0.07y = 930.

Subtract 840 from both sides to get 0.07y = 90.

Divide both sides by 0.07 to get y = 1285.71.

We now know that y = 1285.71.

Substitute y = 1285.71 into x + y = 14,000 to get x = 14,000 - 1285.71 = 12714.29.

Therefore, x = 12714.29 and y = 1285.71. Mitchell invested $12714.29 at 6% and $1285.71 at 7%.

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Answer:

Step-by-step explanation:

THIS SOLUTION IS x=15

The minimum quantity that the factory must sell in order to obtain benefits is x is 3.

Assuming that the unit price and unit cost are known, in addition to the fixed costs, the following formulas are proposed to determine the minimum quantity number of units that the factory must sell in order to obtain benefits: Input, cost, total cost, benefit, and utility. This example illustrates these formulas.

Unities sold = x =?

Unitary selling price = [tex]S.(2x-2)[/tex]

Unit cost is [tex]\frac{S}{(x+4)}[/tex]

Fixed costs = [tex]\frac{S}{160}[/tex]

Assumption: I(x) = p*x= x*

[tex](2x-2)[/tex]

Total cost: C(x)=[tex]x*(x+4)+160[/tex]

U(x) = [tex]x*(2x-2)-x*(x+4)+160[/tex]

U(x) = [tex]2x^{2} -2x-x(4)+160[/tex]

U(x)= [tex]x^{2} -6x+160[/tex]

derived from and equal to zero:

U'(x)= [tex]2x-6=0[/tex]

x = 3​.

Therefore, the minimum quantity that the factory must sell in order to obtain benefits is x is 3.

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When 6,132 is divided by the exponent (10 to the 3rd power) it yields the value 6.132.

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The integer value is given as 6132.

The exponent value is given as 10³.

Use the arithmetic operation of division -

6132 / 10³

Write the numerator of the expression in the exponent form -

(6.132 × 10³) / 10³

Then use the exponent rule - a^x / a^y = a^(x-y).

6.132 × 10^(3-3)

6.132 × 10^0

Anything raised to the power 0 is 1.

6.132 × 1

6.132

Therefore, the value is obtained as 6.132.

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The reasoning represent by the both of the students for congruent of vertical angle are correct but the reasoning of student 1 is more suitable and cleared than student 2.

The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees.

In this, ∠1 and ∠2 are adjacent angle so the sum of the measure of these two angles are 180°

∠1 + ∠2 = 180 ⇒ ∠1 = 180 -∠2

like this ∠2 and ∠3 are adjacent angle so the sum of the measure of these two angles are 180°

∠2 + ∠3 = 180 ⇒ ∠3 = 180 -∠2

from the above equation;

∠1 = ∠3

or, we can say that the vertically opposite angles are equal in measure.

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The sampling methods here that are not examples of simple random sampling are;

A) Select the first 10 people from a list of members.

B) Ask 10 members in the gym on a Monday morning

E) Select every 20th person from a list of members until she has 10 .

F) Ask all members of the gym

A subset of a certain population chosen at random is referred to as a simple random sample. You'll see that each person in the population has an exact equal probability of getting chosen using this sampling technique.

Simple random sampling is significant because it eliminates all prejudice because each member has an equal probability of being chosen. As a result, it will provide a good illustration of the topic of our investigation.

A) Choose the top 10 individuals from a list of members; this is not a straightforward random sampling because the selection is targeted rather than random.

B) This is not random because it is particular to one day of the week—a Monday morning—and we have no idea who might show up on other days.

C) Pick 10 people at random from a list using a random number generator; this is known as basic random sampling.

D) Without looking, choose the names of 10 members at random from a box; this method is random since each member has an equal chance of being chosen.

E) Choose 10 members at a time from a list of members; this is not a random process because not all members have an equal probability of getting chosen.

F) Consult with every gym patron; this is not a random pick.

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Answer:

= 11.496503

Step-by-step explanation:

Answer:

x=-4.5 y=13.5

Step-by-step explanation:

plug in y=-3x to x+y=9

x+(-3x)=9

distribute

x-3x=9

combine like terms

-2x=9

isolate the variable

-2x/-2=9/-2

x=-4.5

plug in x=4.5 into y=-3x

y=-3(-4.5)

simplify

y=-13.5

done :D

The gravitational force exerted by the spheres on a particle of mass m located at (a)r=a,(b)r=b, and (c)r=c are

    [tex]F=\frac{Gm_1m_a}{R_1^2}\\\\F=\frac{Gm_1m}{b^2}}\\\\F=m(\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2} )[/tex]

Total gravitational Field at r=a

Total gravitational Field at r=a=Field due to solid sphere+ field due to spherical shell

we know the gravitational field inside the spherical shell is zero.

and gravitational field due to the solid sphere inside = [tex]\frac{GMr}{R^2}[/tex]

so here

Total gravitational Field=Field due to solid sphere+ field due to spherical shell

[tex]G=\frac{Gm_1a}{R_1^2} +0\\\\G=\frac{Gm_1a}{R_1^2}[/tex]

Force exerted on particle F=mG

[tex]F=\frac{Gm_1m_a}{R_1^2}[/tex]

when r=b:

we know the gravitational field inside the spherical shell is zero.

and gravitational field due to a solid sphere outside at a distance:

[tex]r=\frac{GM}{r^2}[/tex]

so here

Total gravitational Field=Field due to solid sphere+ field due to spherical shell

[tex]G=\frac{Gm_1}{b^2}}+0\\\\G=\frac{Gm_1}{b^2}}[/tex]

Force exerted on particle F=mG

[tex]F=\frac{Gm_1m}{b^2}}[/tex]

gravitational field due to a hollow sphere outside at a distance:

[tex]r=\frac{GM}{r^2}[/tex]

and gravitational field due to a solid sphere outside at distance:

​[tex]r=\frac{GM}{r^2}[/tex]

so here

Total gravitational Field=Field due to solid sphere+ field due to spherical shell

[tex]G=\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2}[/tex]

Force exerted on particle F=mG

[tex]F=m(\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2} )[/tex]

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The mean commute distance (in miles) for the students in the sample is given as follows:

7.9 miles.

The mean of a data-set is calculated as the sum of all observations in the data-set divided by the number of observations.

The histogram gives the number of observations in each range.

Hence, to obtain the sum of the observations, we consider the midpoint of each range, as follows:

S = 20 x 2 + 20 x 6 + 14 x 10 + 7 x 14 + 4 x 18 + 3 x 22

S = 536.

The number of people is given as follows:

20 + 20 + 14 + 7 + 4 + 3 = 68.

Hence the mean is of:

536/68 = 7.9 miles.

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The inverse Laplace transform of F(s) equals 5 minus 2 t plus fraction numerator 7 e to the power of t over denominator 2 end fraction plus fraction numerator 3 e to the power of minus t end exponent over denominator 2 end fraction.

The function's representation in the time domain is the supplied function's inverse Laplace transform. The function in this problem has the denominator s2 (s2 - 1) and the numerator 5s + 2. The outcome of the inverse Laplace transform is a function of time t with a constant term of -5, a linear term of 2t, two exponential terms (7et and 3e-t) split by 2, and a constant term of 7et.

These words are combined to form the final response, which provides the supplied function's time-domain representation. The answer options' divergent interpretations of the constant and linear terms show that there are several correct ways to calculate the inverse Laplace transform.

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929

Step-by-step explanation:

yes sorry i cant do this

The value of x is 7.5. Each pair of alternate interior angles formed by a transversal cutting two parallel lines are equal. Each pair of interior angles on the same side of a transversal that cuts two parallel lines are supplementary, or they add up to 180 degrees.

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. Any line that crosses two straight lines at two different points is said to be a transversal. Different angles are created when any two parallel lines cross a transversal. Between these pairs of angles, there is a relationship.

Since,

The lines are bisected by parallel lines.

hence,

[tex]\frac{4}{6}=\frac{5}{x} \\\\x=\frac{30}{4} \\\\x=7.5[/tex]

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P(z > -5.233): Not the usual approximation, but the exact binomial computation is used for the computation of the the probability of correctly tossed 63 or more.

For the stated question:

In 63 out of 100 trials inside a blind ESP test, the person accurately determines whether a coin will land on its head or tail.

Thus, P(z > -5.233) is the  normal approximation.

Not the usual approximation, but the exact binomial computation is used for the computation of the the probability of correctly tossed 63 or more.

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The two types of tickets cost $36 and $21.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let x = cost of a crab meal

and, y = cost of a vegetarian meal

So, the system of equations

36x + 16y = 1632.......(1)

21x + 28y = 1344 ...........(2)

Solving equation (1) and (2) we get

36x + 16 ( 1344 - 21x) / 28 = 1632

36x + 768 - 12x = 1632

24x = 864

x= 36

and, y = 1344 - 21(36) / 28

y = 21

Hence, tickets cost are $36 and $21.

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The Probability that an incoming lot contain 36% of imperfect cloths will be acceptable is 0.00957

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,

Given that Cappelli Inc. designs and manufactures women's apparel using material from various mills.

Their acceptance sampling plan states that 10 two inch squares of the incoming material must be carefully checked. If 3 or less squares reveal imperfections, the lot is accepted

Here no of defects in the 10 checked is Binomial because each trial is independent and there are only two outcomes.

X = no of defects is Bin (10, 0.36)

The probability  that an incoming lot from Blufton Mills that contains 36 percent imperfect cloth will be accepted

P (X ≤ 3) = 0.00957.

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The restricted values of x for the given rational expression are all real numbers except for x = −12.

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Tax on hotel room that costs $120 = $11.7

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Function for tax of hotel room

T(x)=0.06x+4.5

where x is the cost in dollars of the room

T(x) = the tax in dollars.

Cost of the room = $120

Tax of the room

= 0.06(120) + 4.5

= 7.2 + 4.5

= $11.7        

Hence, $11.7 is the tax on room that costs $120.

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Answer: √15

Step-by-step explanation:

AB²+BC²=AC²

(√8)²+(√6)²=AC²

AC²=14

AC=√14