3-99. Determine which similarity conjectures (AA -, SSS-, or SAS -) could be used to establish that the following pairs of triangles are similar. List as many as you can. Homework Help b. DA 30 304 48 800 3.5 3-100.

Martina takes 48/10 minutes per meter to fill the aquarium to a depth of 1 meter.

To find the unit rate in minutes per meter, we need to know the number of minutes it takes Martina to fill the aquarium to a depth of 1 meter.

To do this, we can convert the given depth and time to the same units, and then divide the time by the depth to find the unit rate.

First, let's convert the depth of the aquarium to meters. The depth of the aquarium is given as 7/8 meters, so we don't need to do any further conversion.

Next, let's convert the time to minutes. The time is given as 4 and 1/5 minutes, which is the same as 4 + 1/5 = 4.2 minutes.

Now that we have both the depth and time in the same units, we can divide the time by the depth to find the unit rate:

                       = 4.2 minutes / 0.875 meters

                       = 4.8 minutes/meter

The unit rate in minutes per meter is 4.8. This can be written as a mixed number as 4 8/10 minutes per meter, or as a fraction in simplest form as

48/10 minutes per meter.

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The area of regular hexagon is 166.27688 inch².

The area is the amount of space within the perimeter of a 2D shape.

Given:

side = 8 inch

Using

Area of regular hexagon = 3 √3/2 * a²

= 3 √3/2 * 8*8

=96√3

= 166.27688 inch²

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The distribution is called the binomial distribution, the probability that exactly 15 products satisfy the requirement is 0.0651, the population mean and standard deviation are 21.25 and 1.965 respectively and the probability that the mean number of products satisfying the requirement is at least 16 is 0.998.

Given that 85% of a certain product actually satisfy the requirement, we have 25 of such products and let x be the number of products that satisfy the requirement.

The probability of x number of products satisfying the requirement is given by the binomial distribution formula:

P(X=x) = nCx * p^x * q^(n-x)

Where n = 25, p = 0.85, q = 1 - p = 0.15.

b) To find the probability that exactly 15 products satisfy the requirement, we substitute the values of n, p, q, and x in the binomial distribution formula:

P(X=15) = 25C15 * 0.85¹⁵ * 0.15¹⁰ = 0.0651

c) The population mean is given by:

μ = np = 25 * 0.85 = 21.25

The population standard deviation is given by:

σ = √(npq) = √(25 * 0.85 * 0.15) = 1.965

d) The probability that the mean number of products satisfying the requirement is at least 16 is given as:

P(X ≥ 16) = P(X > 15.5) = P(Z > (15.5 - 21.25) / (1.965/√36)) = P(Z > -2.92) = 1 - P(Z ≤ -2.92) = 1 - 0.002 = 0.998

Thus, the distribution is called the binomial distribution, the probability that exactly 15 products satisfy the requirement is 0.0651, the population mean and standard deviation are 21.25 and 1.965 respectively and the probability that the mean number of products satisfying the requirement is at least 16 is 0.998.

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The reasons why we factor all the polynomials before multiplying rational expressions is;

To reduce a rational expression to its simplest form.

To ensure that the denominators are not 0.

A polynomial expression is defined as an expression having one or more terms in which the variable has non-negative integer powers.

We know that rational expressions usually have a polynomial numerator and a polynomial denominator. Now, in many events, these polynomials can be factored. Therefore, we can conclude that to reduce a rational expression to its simplest form, we have to factor the numerator and denominator, and cancel out any common factors between them. That's the reason why factoring is an important part of simplifying a rational expression.

Finally, we have to mindful about the values the final denominator of a rational expression can take, because such values must not be 0.

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Since triangle DEF is a scale drawing of triangle ABC, the scale factor used is equal to 1/3.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.

Mathematically, the scale factor of a geometric object such as a triangle can be calculated by using this formula:

Scale factor = Dimension of image/Dimension of original figure

Substituting the given parameters into the formula, we have the following;

Scale factor = 3/9

Scale factor = 1/3.

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The null hypothesis and alternative hypothesis for the given data is equal to  H0: μ = 436 and Ha: μ ≠ 436.

Weight of the bag filled with machine works = 436 grams

The null hypotheses for the bag filled with machine work will be the statement of no effect

And it'll be the mean weight of the bag which is equal to 436grams.

Null hypothesis is equal to ,

H0: μ = 436

The alternative hypotheses for the above scenario representing that the bag isn't filled with 436grams.

They are either less filled or that is below 436grams or overfilled that is above 436grams.

Alternative hypothesis is equal to,

Ha: μ ≠ 436

Statistics is the study of surveys and research on numerical data.

Two different kinds of hypotheses.

A null hypothesis is one that holds true.

And an alternate hypothesis is another.

The null hypothesis is a default condition which represents there is nothing happening.

If there is no relationship between two given measured between groups.

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Answer:

6

Step-by-step explanation:

Integers are just whole numbers.

So between 1.25 and 7.1 there is...

2,3,4,5,6,7

These are 6 integers.

\(oOoBrainlyPrincessoOo\)

Integers are positive and negative numbers.

So integers between 1.25 and 7.1 are : 2, 3, 4, 5, 6, and 7.

That's a total of 6 integers.

Hope it helps!

\(GraceRosalia\)

Answer:

1 ft³ of gold will weigh 1209.6 pounds

1 ft³ of copper will weigh 559 pounds.

Step-by-step explanation:

We know the formula for:

Density = Mass/Volume

Hence, making mass the subject of the formula:

Mass = Density × Volume

From the question we are told:Volume of each metal = 1 ft³

1) Metal: Gold

Density of Gold = 0.70 pounds per cubic inch(lb/in³)

We convert the Volume of gold from ft³ to in³

The Volume of gold given in the question = 1 cubic foot = 1 ft³

1 cubic foot = 1728 cubic inches

Hence, the volume of Gold = 1728 in³

Mass of Gold = Density of Gold × Volume of Gold

Mass of Gold = 0.70Ib/in³ × 1728 in³

= 1209.6 lb(pounds)

2) Metal : Copper

Density of copper given in the question = 8.96 grams per cubic centimeter

Ib = pounds

We convert this density in g/cm³ to ib/in³

453.5g = 1 Ib

8.96g = a Ib

Cross Multiply

= 453.5g × a Ib =8.96g × 1 Ib

= a Ib = 8.96g × 1 Ib/453.5g

a Ib = 0.0197574421 Ib

Density of Copper = 0.0197574421 Ib/cm³

28,316.8 cm³ = 1 ft³

1 cm³ = b ft³

b ft³ = 1 cm³ × 1 ft³/28,316.8cm³

b ft³ = 0.0000353147 ft³

1 cm³ = 0.0000353147 ft³

We have to convert the density of Copper from Ib/cm³ to Ib/ft³

0.0197574421 Ib/cm³ = 0.0197574421 Ib/0.0000353147 ft³

559.46793026 Ib/ft³

Volume of copper = 1ft³

Mass = Density × Volume

Mass of copper = 559.46793026 Ib/ft³ × 1 ft³

= 559.46793026 Ib or pounds

≈ 559 pounds

Therefore , the weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.

Answer:

Gold

Density of Gold = 0.70 pounds per cubic inch

1 cubic foot = 1728 cubic inches

Hence, the volume of Gold = 1728 in³

Mass of Gold = Density of Gold × Volume of Gold

Mass of Gold = 0.70Ib/in³ × 1728 in³ = 1209.6 lb(pounds)

2) Metal : Copper

Density of copper given in the question = 8.96 grams per cubic centimeter

We convert this density in g/cm³ to ib/in³

453.5g × a Ib =8.96g × 1 Ib = 8.96g × 1 Ib/453.5g = 0.0197574421 Ib

Density of Copper = 0.0197574421 Ib/cm³

Volume of copper = 1ft³

Mass = Density × Volume

Mass of copper = 559.46793026 Ib/ft³ × 1 ft³ = 559.46793026 Ib or pounds

≈ 559 pounds

The weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.

The translation transformation of the parent function in the graph, indicates that the equation for each of the specified graphs, using the form y = f(x - h) + k, are;

a. y = f(x) + 3

b. y = f(x - 3)

c. y = f(x - 1) + 2

A transformation of a function is a function that takes a specified function or graph and modifies them into another function or graph.

The points on the graph of the specified function f(x) in the diagram are; (0, 0), (1.5, 1), (-1.5, -1)

The graph is the graph of a periodic function, with an amplitude of (1 - (-1))/2 = 1, and a period of about 4.5

Therefore, we get;

a. The graph in part a consists of the parent function shifted up three units. The transformation that can be represented by the vertical shift of a function f(x) is; f(x) + a or f(x) - a

Therefore, the translation of the graph of the parent function is; f(x) + 3

b. The graph of the parent function in the graph in part b is shifted to the right two units, and the vertical translation is zero units, down or up.

The translation of the graph of a function by h units to the right or left can be indicated by an subtraction or addition of h units to the value of the input variable, therefore, the translation of the function in the graph of b is; y = f(x - 3) + 0 = f(x - 3)

c. The translation of the graph in part c are;

A vertical translation 2 units upwards

A horizontal translation 1 unit to the right

The equation representing the graph in part c is therefore; y = f(x - 1) + 2

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Formula to convert milligrams to micrograms: Number of micrograms = Number of milligrams x 1000

To convert milligrams (mg) to micrograms (μg), you need to multiply the number of milligrams by 1000. This is because there are 1000 micrograms in one milligram.

Here is the formula:

Number of micrograms = Number of milligrams x 1000

For example, let's say you want to convert 5 milligrams to micrograms. You would use the formula as follows:

Number of micrograms = 5 mg x 1000 = 5000 μg

Therefore, 5 milligrams is equal to 5000 micrograms.

It's important to pay attention to the units when making conversions, as mixing up units can lead to errors in calculations.

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The angle between AFE is measured (A) 42°.

Since ΔABC is an equilateral triangle, all its angles are 60°. Since CAD-18°,: ∠CAE = ∠CAD + ∠DAE = 18° + 60° = 78°.

Since AC is the angle bisector of ∠BCD,:

∠ACB = ∠ACD = (1/2)∠BCD. Since ΔABC is equilateral, ∠BCA = 60°.

Therefore, ∠BCD = ∠BCA + ∠ACB = 60° + (1/2)∠BCD, which implies that ∠ACB = 30°.

Since BE- CD,:

∠BEC = ∠BCD - ∠CED = ∠ACB - ∠CED = 30° - ∠CED.

Since ∠CAF = 12°,:

∠BAC = ∠CAD + ∠DAF = 18° + 12° = 30°.

Therefore, ∠BCA = 30°, and BC = AC.

Let x = ∠CED. Since BE = CD and BC = AC,: CE = AD = BC = AC.

In ΔCED,: ∠ECD = 180° - ∠CED - ∠CDE = 180° - x - 60° = 120° - x.

In ΔCAD,: ∠CAD + ∠CDA + ∠ACD = 180°, which implies that ∠CDA = 60° - (1/2)∠CAD = 60° - 9° = 51°.

In ΔADF,: ∠ADF = 180° - ∠BAC - ∠DAF = 180° - 30° - 12° = 138°.

In ΔAFE,: ∠AFE = ∠ACB + ∠BEC + ∠CED + ∠ECD + ∠CDA + ∠ADF = 30° + (180° - 30° - x) + x + (120° - x) + 51° + 138° = 489° - x.

Since the angles of a triangle sum to 180°:

∠AFE + ∠EAF + ∠AEF = 180°

∠AFE + 60° + 78° = 180°

∠AFE = 42°.

Therefore, the answer is (A) 42°.

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Answer:

4 times 2+3-1=10

Step-by-step explanation:

Step-by-step explanation:

Here, slope= 4/5 , As y= mx+c

according to formula, y-y1= m(x-x1)

y-6= 4/5(x+6)

5/4 (y-6)= x+6

5/4y - 15/2= x+6

x- 5/4y + 27/2 =0

Answer:

m < 1.4

Step-by-step explanation:

Make \(\frac{8}{5}\) a decimal.

1.6

3 > m + 1.6

m < 1.4

The following equation-definition will be consider to solve the problem:

Where the base in this case is 120.

The rate is the porcentage, which is the missing part in the problem.

And 48 is the part. Hence, the solution is:

The solution is C. rate

The test hypothesis using 0.05 significance level has the following results:The treatment means differ, The block means do not differ.

A poll or study's findings can be tested using the statistical procedure known as hypothesis testing to see if the findings are significant. By calculating the likelihood that the findings happened by chance, you are basically evaluating if the findings are genuine. If it's possible that your results were a coincidence, the experiment won't be reproducible and won't be of much help.

Hypothesis testing may be one of the most perplexing components for students, mostly because you must first determine what your null is so that you can conduct a test. These challenging word problems that you encounter might sometimes be challenging to understand.

Make a plan for your null hypothesis.

Write down your null hypothesis

Determine the type of test you must do,

How to solve?

Describe the null and alternate treatment hypotheses:

Null hypothesis: No difference in treatment means

Alternative interpretation: The means differ

Indicate the treatment decision-making process:

F(1,2)=18.51 as seen in the table

Reject the null hypothesis if the estimated F exceeds 18.51.

Treatments Calculated F=43.75 > 18.51; hence, the null hypothesis is rejected.

As a result, we find that the treatment means differ.

Write out the null and alternative hypotheses for blocks.

Block means are not different under the null hypothesis.

A different theory There exists at least one pair of distinct meanings.

State the block decision rule as well:

Table F(2,2)=19.0 value

If the estimated F is greater than 19, reject the null hypothesis.

Blocks determined that F=8.14 19.0, thus we did not reject the null hypothesis.

Our conclusion is that the block means are equivalent.

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Answer:

1.) $4.02

2.)$29.95

3.) $31.96

Step-by-step explanation:

Answer:

2 < x < 12

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the interval

difference of 2 sides < x < sum of 2 sides , that is

7 - 5 < x < 7 + 5

2 < x < 12

third side could be 3, 4, 5, 6, 7, 8, 9, 10, 11

Answer:

the answer is 3 option hope that it helps

Functions can be represented with equations, graphs and tables

The value of g(3) is 9

For x = 3, the equation of the function is:

g(x) = 2x + 3

So, we have:

g(3) = 2 * 3 + 3

Evaluate the product

g(3) = 6 + 3

Evaluate the sum

g(3) = 9

Hence, the value of g(3) is 9

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Answer:

Step-by-step explanation:

Hope it helps :D

Answer:

................

Step-by-step explanation:

.................

\(-28=-7(3x+4)+21x\\\\\implies -21x -28 +21x = -28\\\\\implies -28 =-28\\\\\text{The equation is true for all x.}\)

Answer:x=-0.5

Step-by-step explanation:

You would add the 2.5 on both sides of the equal sign

Answer:

I would go with the first car.

Step-by-step explanation:

If you multiply the first cars miles by four because it shows its total distance off of 5 miles, you will get 300 miles in 20 gallons. This is a higher rate than the second car.

Answer:Choose a minimum of two input values.

Evaluate the function at each input value.

Use the resulting output values to identify coordinate pairs.

Plot the coordinate pairs on a grid.

Draw a line through the points.

Step-by-step explanation:

Answer:

Please attach a screenshot of the question and I could answer it. Thank you!

Answer:

a) V = 1000 cm³

b) V = 614.125 cm³

Step-by-step explanation:

a) side length a = 10 cm

face diagonal f = 14.142135623731 cm

solid diagonal d = 17.320508075689 cm

surface area S = 600 cm²

volume V = 1000 cm³

___________________________

b) side length a = 8.5 cm

face diagonal f = 12.020815280171 cm

solid diagonal d = 14.722431864335 cm

surface area S = 433.5 cm²

volume V = 614.125 cm³

_____________________________

Formula: V=a³