A small rectangular pyramid­ shaped metal object made of a single metal is found in an archaeological dig. Because of the metals available to the area’s inhabitants at the time, scientists believe the metal could be either iron, lead, nickel, or silver. The weight of the object is 612.4 grams. The rectangular base of the pyramid is 3 cm by 6 cm and the height is 9 cm. The density for each metal is shown below: Iron: 7.874 grams/cm 3 Lead: 11.34 grams/cm 3 Nickel: 8.908 grams/cm 3 Silver: 10.49 grams/cm 3 Select the metal shown below that was used to construct the small rectangular pyramid-shaped metal object found in the archaeological dig. A. Iron C. nickel B. Lead D. silver

Answer:

177 degrees

Step-by-step explanation:

supplementary angles add up to 180 degrees, so if angle one is 3 then angle two is 177

Based on the information in the graph, we can infer that the missing numbers are: 9, 4, 19, 30, 84, 16, 8, 22, and 40.

To complete the table correctly we must identify the columns or rows with more data. These will be the easiest to complete. First of all, we must fill in those that already have a number in the total box because we can add the available numbers and later subtract them from the total to identify the missing number.

We can also find the numbers in the total cells by adding all the numbers in a column or row to find this result. Finally, the boxes that are being completed serve as clues to complete the others.

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Answer:

4(1/2) = 2

2-8 = -6

-6 is your answer

hope this helps!

For finding g(1/2) you need to substitute the value of x= 1/2

Thus , g(1/2):

\( = 4 \times \dfrac{1}{2} - 8\)

\( = 2 - 8\)

= \(\red{\bold{\large{-6}}}\)

In order to solve for x in this equation, we must divide 75 by 9. Dividing 75 by 9 gives us 8.3 as the answer. So, x = 8.3.

An equation is a mathematical statement that expresses the equality of two expressions, usually containing one or more variables. It is used to describe the relationships between different variables, such as the area of a circle or the slope of a line. Equations can be used to describe the behavior of physical systems, calculate the solutions to problems, and make predictions about future events.

This is happening because when we divide 75 by 9, we are essentially asking "how many 9s go into 75?". 75 divided by 9 is equal to 8.3, meaning 8 and 3/9ths of 9 go into 75. Therefore, x = 8.3.

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In order to solve for x the given equation, we must divide 75 by 9. Dividing 75 by 9 gives us 8.3. So, x = 8.3.

An equation is a mathematical statement that expresses the equality of two expressions, usually involving one or more variables. Used to describe relationships between different variables. Area of ​​circle or slope of line. Equations can be used to describe the behavior of physical systems, calculate solutions to problems, and predict future events.

That's because when you divide 75 by 9, you're essentially asking, "How many 9s are there in 75?" 75 divided by 9 is 8.3. So 3/9 of 8 and 9 is 75. So x = 8.3.  

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The complete question is as follows:

Solve for x. Round to the nearest tenth, if necessary.

75 = 9x

a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

you need to take a better picture nobody can see that i not trying be be rude

Step-by-step explanation:

Answer:

upload clear picture, it is very easy

Step-by-step explanation:

To determine the unit rate of pages, that is, the number of pages Leo reads in one hour you can use cross multiplication

1/3h _____14 pages

1h______x pages

Leo reads 42pages/hour

17 1/4 = p - 2 3/4

To solve for p add 2 3/4 to both sides

P = 17 1/4 + 2 3/4

P = 20

The measure of angle A in the isosceles triangle ABC is 62.5 degrees.

In an isosceles triangle ABC, where AB = AC, we are given that angle B (denoted as ∠B) measures 55 degrees. We need to calculate the measure of angle A (denoted as ∠A).

Since AB = AC, we know that angles A and C are congruent (denoted as ∠A ≅ ∠C). In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent.

Therefore, we have:

∠A ≅ ∠C

Also, the sum of the angles in a triangle is always 180 degrees. Hence, we can write:

∠A + ∠B + ∠C = 180

Substituting the given values:

∠A + 55 + ∠A = 180

Combining like terms:

2∠A + 55 = 180

Subtracting 55 from both sides:

2∠A = 180 - 55

2∠A = 125

Dividing by 2:

∠A = 125 / 2

∠A = 62.5

Therefore, the measure of angle A in the isosceles triangle ABC is 62.5 degrees.

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Options :

A. Each roll has a 0.117 probability of being divisible by 3.

B. Each roll has a 0.333 probability of being divisible by 3.

C. Each roll has a 0.5 probability of being divisible by 3. D. Each roll has a 0.667 probability of being divisible by 3.

Answer: B. Each roll has a 0.333 probability of being divisible by 3.

Step-by-step explanation:

Sample space for a six-sided number cube :

1, 2, 3, 4, 5, 6

Number of outcomes divisible by 3:

(3, 6) = 2

Probability of an event = Number of required outcomes / total number of possible items

Probability (getting a number divisible by 3):

(Number of outcomes divisible by 3 / total outcomes in sample space)

Probability (getting a number divisible by 3):

2 / 6 = 1/3

= 0.333

The reward-to-variability ratio of the best feasible is 0.4221 that is option a.

The proportion of stocks invested in the optimal risky portfolio can be calculated with the use of following formula:

Portfolio Invested in the Stock = [(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 - (Expected Return of the Bond - Risk Free Rate)*Covariance between Bond and Stock]/[(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 + (Expected Return of the Bond - Risk Free Rate)*(Standard Deviation of Stock)^2 - (Expected Return of Stock - Risk Free Rate + Expected Return of Bond - Risk Free Rate)]*Covariance between Bond and Stock

Portfolio Invested in Bond = 1 - Portfolio Invested in the Stock

Here, Risk Free Rate = 4 and Covariance = 32*24*.1250 = 96

Using these values and other information provided in the question, we get,

Portfolio Invested in the Stock = [(10 - 4)*(24)^2 - (7 - 4)*96]/(10 - 4)*(24)^2 + (7 - 4)*(32)^2 - [(10 - 4 + 7 - 4)]*96 = .5593

Portfolio Invested in Bond = 1-.5593 = .4407

Step 2: Calculate Expected Return and Standard Deviation of the Optimal Risky Portfolio

Expected Return = Portfolio Invested in Stock*Expected Return of Stock Portfolio Invested in Bond*Expected Return of Bond = .5593*10% + .4407*7% = 8.68%

Standard Deviation = [(Portfolio Invested in Stock)^2*(Standard Deviation of Stock)^2 + (Portfolio Invested in Bond)^2*(Standard Deviation of Bond)^2 + 2*(Portfolio Invested in Stock)*(Portfolio Invested in Bond)]^(1/2) = [(.5593)^2*(32)^2 + (.4407)^2*(24)^2 + 2*(.5593)*(.4407)*(96)]^(1/2) = 21.90%

Step 3: Calculate Reward-to-Volatility Ratio

The reward-to-volatility ratio can be calculated with the use of following formula:

Reward-to-Volatility Ratio = (Expected Return of the Portfolio - Risk Free Rate)/Standard Deviation of Portfolio = (8.68 - 4)/21.90 = .4221

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Answer:

19

Step-by-step explanation:

The zebra is the 10th fastest, so there are 9 zebras that are faster.

It's also the 10th slowest, so there are 9 zebras that are slower.

The total number of zebras is therefore 9 + 1 + 9 = 19.

Answer:

The answer is B.

Step-by-step explanation:

Points (−6, 3) and (−6, −3) on the coordinate grid below show the positions of two dogs at a park:

A coordinate plane is shown. There is a point at negative 6, 3 labeled Dog 1. There is a point at negative 6, negative 3 labeled Dog 2.

Answer:

im pretty positive its divide  1,000 by 775, correct me if im wrong.

Answer: It is A multiply .775 by 100 to get 77.5

Step-by-step explanation:

Hence, the margin of error for this 95% confidence interval of a population proportion is 5.4%.

The margin of error for a confidence interval is the distance between the sample statistic (in this case, the sample proportion) and the confidence interval limits. To find the margin of error, we can use the formula:

Margin of error = (upper limit - lower limit) / 2

In this case, the lower limit of the 95% confidence interval is 64.5% and the upper limit is 75.3%. So the margin of error is:

Margin of error = (75.3% - 64.5%) / 2

Margin of error = 10.8% / 2

Margin of error = 5.4%

Therefore, the margin of error for this 95% confidence interval of a population proportion is 5.4%.

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If Christina does her due diligence and carefully weighs the costs and potential income, buying and renting out the holiday apartment could be a sound investment. However, she should carefully assess the market demand and legal requirements before making any final decisions.

Secondly, Christina needs to consider the costs involved in purchasing and maintaining the holiday apartment. She should factor in the purchase price, any renovation or repair costs, ongoing maintenance costs, and taxes and insurance. She also needs to consider any potential income from renting out the apartment and weigh that against the costs.
Thirdly, Christina should research the legal and regulatory requirements for renting out a holiday apartment in the area. She needs to ensure that she is complying with all relevant laws and regulations, such as obtaining any necessary permits or licenses and adhering to safety standards.

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If Christina is considering buying this holiday apartment for rental purposes, she should do thorough research before making a final decision. The apartment's location, amenities, and rental potential are important factors to consider.

She should also evaluate the cost of purchasing and maintaining the property versus the potential rental income it could generate. It's advisable to speak with a real estate agent or property management company to gain insights on the rental market in the area. Furthermore, Christina should ensure that the apartment meets all legal requirements for rentals in the location she plans to rent it out in. By taking these steps, Christina can make an informed decision on whether to invest in the holiday apartment and earn a steady income from renting it out to holiday guests.

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Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

Answer:

please continue i'm facinated on were this story goes

Step-by-step explanation:

From the graph, the correct options are given as,
B. Mia left her house 10 minutes before Erick left his house.
D. Erick and Mia arrived at the park at the same time.
E. Erick walked the same distances as Mia during the last 10 minutes.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The graphs show their distances from home over the same 30-minute period as they walked to the park.
From the graph,
It can be concluded that,
Both reach the park at the same time, as the termination point of the curve is the same.
The graph of mia starts after 10 minutes Erick, which implies Mia left her house 10 minutes before Erick left his house. And Erick walked the same distances as Mia during the last 10 minutes as the slope of the last segment of both curves is the same.

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Answer:

b. -5

Step-by-step explanation:

\(( - 3) + (5) + ( - 7) \\ - 3 + 5 - 7 \\ - 10 + 5\)

\( \boxed{\bold{Answer:{\boxed{\bold{\green{b.- 5}}}}}}\)

┈➤ . . ⇢ ˗ˏˋ⌦ ..♡ˎˊ˗ ꒰✈꒱   

╭─────────

┊╭─────────

┊✿꒷꒦ ◇♧♡♤

╰─────────

★ . ꜝꜞ ᳝ ࣪ hope that helped!  ʬʬ

Answer:

-5

Step-by-step explanation:

This can be added/subtracted simply. Just take into account the negative symbols.

We'll start with the first two numbers:

(-3)+(5)

We have a negative number, -3. We'll add 5 positive numbers.

-3, -2, -1, 0, 1, 2

(-3)+(5) = 2.

Now that we have this number, we add it to the final number.

(2)+(-7)

We may be adding, but we are adding a negative number, so we are actually subtracting. We adding 7 negative points to the number 2.

2, 1, 0, -1, -2, -3, -4, -5.

Thus, our final answer is -5.

9514 1404 393

Answer:

  2.05 hours

Step-by-step explanation:

Using the given equation with the given time, we have ...

  55x +35(2.5) = 200

  55x = 112.5 . . . . . . . . subtract 87.5

  x = 2.05 . . . . . . . . . . divide by 55

The car spends 2.05 hours at 55 mph.

The distance between the two points from the geometrical formula for that purpose is 6.2.

The distance between two points in geometry is the length of the straight line segment that connects the two points. It is calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Using the formula;

d= √(x2 - x1)^2 + (y2 - y1)^2

d = √(7.5 - 3)^2 + (6.25 - 2)^2

d = √20.25 + 18.06

d = 6.2

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The expression of the integral that quantifies the increase in volume of a sphere as its radius r quadruples from r to 4·r is therefore;

∫dV/dr, r, r, 4·r = 84·π·r³

An integral is a function which when differentiated, yields a specified function.

The volume of the sphere with radius r is V = (4/3) × π × r³

The increase in volume with a change in radius from r to 4·r is the difference between the volume at r and the volume with a radius of 4·r, as follows;

ΔV = ∫dV/dr, r, r, 4·r = \(V_{final}\) - \(V_{initial}\)

Therefore;

ΔV = ∫dV/dr, r, r, 4·r = ∫4·π·r², r, r, 4·r =  (4/3) × π × (4·r)³ - (4/3) × π × r³ = 84·π·r³

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a_e < a_d < a_c < a_b < a_a; due to air resistance, balls moving in the same direction experience a decreasing acceleration.

Let's begin by calculating the acceleration of each ball in the direction of its motion. First, the acceleration of ball aa is given by the equation of motion: aa = v2/r, where v is the speed and r is the radius of the circular path. For ball ab, the acceleration is given by the equation aab = v2/2r, as it is moving twice as fast as aa. Similarly, for ball ac, the acceleration is ac = v2/3r and for ball ad, the acceleration is ad = v2/4r. Finally, for ball ae, the acceleration is ae = v2/5r. Thus, the accelerations can be expressed in terms of the speed and radius of the circular path. We can then rank the accelerations from largest to smallest as a_e < a_d < a_c < a_b < a_a; due to air resistance, balls moving in the same direction experience a decreasing acceleration.

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Answer:

m∠6 = 90°

Step-by-step explanation:

∠1 and ∠2 are a linear pair.  This means they are supplementary, or their measures sum to 180°.  To find m∠2, we subtract m∠1 from 180:

180-140 = 40°

The measure of ∠2 is 40°.

The sum of the measures of the angles in a triangle is 180°.  We have ∠2 and ∠3; to find the measure of ∠6, we subtract these two from 180:

180-(40+50) = 180-90 = 90°

The solid has a 62.5 cubic unit volume. Finding the volume of a solid with a circular base of radius 5 units is the task at hand.

The following formula can be used to determine how much of the magical potion is left after a specific period of time:

Let h represent the solid's height. The volume can therefore be stated as follows:

V = (12.5 dh from 0 to h)

Combining, we obtain:

V = 12.5h

The height of the solid is equal to the radius of the circle, which is 5 units, because the slices are perpendicular to the base. Therefore:

V=12.5h=12.5(5)=62.50 cubic metres

Thus, the solid has a 62.5 cubic unit volume.

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Answer:

x<-1

Step-by-step explanation:

Answer: 2:3

Step-by-step explanation:

Hallie donated 4 pairs and Mattie 6

the ration is 4:6

simplify that (both can be divided by two) and you get 2:3

So for every two pairs of jeans Hallie Donates, Mattie Donates 3

Hope that helps

The ratio to describe the number of jeans shared by Hallie and Mattie is obtained as 2 : 3.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

The number of jeans donated by Hallie and Mattie are given as 4 and 6 respectively.

It can be written in terms of ratio as 4 : 6.

It can be simplified as,

⇒ 4 : 6

⇒ 4/6

⇒2/3

⇒ 2 : 3

Hence, the number of jeans donated can be written in terms of ratio as 2 : 3.

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Based on the information given the average speed for his trip is 64 miles.

Using this formula

d=rt

r=d/t

Where:

r=rate=?

d=distance=512 miles

t=time=8 hours

Let plug in the formula

r=512/8

r=64 miles

Inconclusion the average speed for his trip is 64 miles.

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Answer:

In order to solve this, we need to transform the equation into R = D/T

Plug in the numbers into this equation

R = 512/8

So after we divide these two numbers, we get an answer of 64 mph as Adam's average speed.

Answer: \(-10,\ 0\)

Step-by-step explanation:

Given

Two graphs are given, one is upward facing parabola and other is downward facing parabola.

From the graph, for downward facing parabola

When \(x=4\), it corresponds to \(y=-10\)

Similarly, If \(g(x)=2\), it corresponds to \(x=0\) because \(g(x)\) cuts the y-axis at only one point.

Step-by-step explanation:

Volume of ice =   10 X 10 X 20 = 2000 cm^3

tank volume increase will be the same

   100 x 40 x HEIGHT = 2000

            Height = 2000/ ( 100 X 40) =  .5 cm height increase

The melting of the ice block would raise the water level in the tank by approximately 0.5 centimeters. This can be answered by the concept of Volume

To calculate the amount of water that would be displaced by the ice block, we need to first find its volume, which is 10 x 10 x 20 = 2000 cubic centimeters. Since 1 cubic centimeter of water has a mass of 1 gram, the mass of the ice block would be 2000 grams or 2 kilograms.

When the ice block melts, it will turn into water and occupy the same volume, which would displace an equal amount of water in the tank. The volume of the tank is 100 x 40 x h, where h is the increase in water level. Setting the volume of the ice block equal to the increase in the water level, we get:

2000 = 100 x 40 x h

h = 0.5 centimeters

Therefore, the melting of the ice block would raise the water level in the tank by approximately 0.5 centimeters.

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