Two plastic geometric models shaped like a triangular prism and a triangular pyramid are each 16 cm tall. The base of each model is a triangle with a base of 12 cm and a height of 5 cm. How much greater than the volume of the prism?

Answer:

The function is not one-to-one

Step-by-step explanation:

This is a quadratic function.

\(f(x)=x^2-2\)

A function is one-to-one

\(\text{if } f(x_1)=f(x_2) \Leftrightarrow x_1=x_2\)

The function given is not one-to-one because there are values of the input \(x\), which leads to the same output.

For example.

\(y=f(2)=2^2-2=\boxed{2}\)

\(y=f(-2)=(-2)^2-2=\boxed{2}\)

The endpoint coordinates of the midsegment of ΔBCD that is parallel to BD are (0, 2) and (1, 3).

What is the midpoint of the segment?

In geometry, the midpoint is the point in the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid. It cuts the segment in half.

By using the graph we can find out the coordinates of B, C, and D.

B(-3, 1), C(3, 3) and D(-1, 3).

Then let's suppose PQ is a line segment passing through the midpoint of the side BC and the midpoint of the side CD.

Therefore PQ line will be parallel to BD.

So we have to find the coordinates of points P and Q.

For BC,

      By using the midpoint formula,

            P(x, y) ≡ ((-3 + 3)/2, (1 + 3)/2)

                       ≡ (0/2, 4/2)

            P(x, y) ≡ (0, 2)

For CD,

      By using the midpoint formula,

            Q(x, y) ≡ ((3 - 1)/2, (3 + 3)/2)

                       ≡ (2/2, 6/2)

            Q(x, y) ≡ (1, 3)

Hence the endpoint coordinates of the midsegment of ΔBCD that is parallel to BD are (0, 2) and (1, 3).

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Answer:

g/22.3 = n

Step-by-step explanation:

The value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = 1 - x²

g(x) = √(11 - 4x)

f(-1) = 0

g(-1) = √15

f(2) = -3

g(2) = √3

(f/g)(-1) = f(-1)/g(-1) = 0/√15  = 0

(g . f) (2) = g(2)f(2) = (√3)(-3) = -3√3

(g - f)(-1) = g(-1) - f(-1) = √15 - 0 = √15

(g + f) (2) = g(2) + f(2) = √3 + (-3) = √3 - 3

Thus, the value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

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Answer:

Option C

Step-by-step explanation:

\(( { - 2m}^{3} {p}^{2} ) {}^{4} \)

\( {( { - 2m}^{3}) }^{4} \times ( { {p}^{2} )}^{4} \)

\( {16m}^{12} \times {p}^{8} \)

Answer:

\( {( - 2 {m}^{3} {p}^{2}) }^{4} \\ = { (- 2)}^{4} { {m}^{3} }^{4} { {p}^{2} }^{4} \\ = 16 \times {m}^{12} {p}^{8} \\ c \: is \: ur \: answer \: \\ thank \: you\)

Answer:

  ₹168 per hour

Step-by-step explanation:

The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.

We know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...

  (15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h

Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.

The pay per hour is found by dividing pay by hours.

  ₹1050/(6.25 h) = ₹168/h

Tamara's hourly rate of pay is ₹168 per hour.

the unit rate of the crackers will be $0.233.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

A certain brand of crackers costs $2. 89 for 12. 4 ounces.

So per 1 ounce it will cost = 2.89/12.4 = 0.233

Hence the unit rate of the crackers will be $0.233.

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Answer:

Green

Step-by-step explanation:

The diameter is the length of the line through the center that touches two points on the edge of the circle and only green does that

Answer:

\(y=\frac{3}{4}x\)

Step-by-step explanation:

The graph represents direct variation since it is a line passing through the origin.

The constant of proportionality is \(\frac{18}{24}=\frac{3}{4}\), so \(y=\frac{3}{4}x\).

Answer: c=7

Step-by-step explanation:

8c = 56  Divide both sides by 8

\(\frac{8}{8}c = \frac{56}{8}\)  

c = 7

The time when the food price is most and cheapest is obtained from the extremum value of the function.

The extremum of a function is a maximum or minimum value of the function.

The function that models the food-price is I(t) = 0.00009045·t⁵ + 0.001438·t⁴ - 0.0656·t³ + 0.4598·t² - 0.6270·t + 99.33

Where;

t = The number of years since 1984

I(3) = 100

The time when the food is cheapest or most expensive can be obtained by differentiating the function for food-price and equating the result to 0 as follows;

I'(t) = 0.00009045×5·t⁴ + 0.001438×4·t³ - 0.0656×3·t² + 0.4598×2·t - 0.6270 = 0

Factoring the result, using a graphing calculator, we get;

(t - 0.823)·(t - 5.131)·(t - 11.05)·(t + 29.72) = 0

The values of the minimum and maximum values are therefore';

I(0.823) = 0.00009045×0.823⁵ + 0.001438×0.823⁴ - 0.0656×0.823³ + 0.4598×0.823² - 0.6270×0.823 + 99.33 ≈ 99.08

I(5.131) = 0.00009045×5.131⁵ + 0.001438×5.131⁴ - 0.0656×5.131³ + 0.4598×5.131² - 0.6270×5.131 + 99.33 ≈ 100.67

I(11.05) = 0.00009045×11.05⁵ + 0.001438×11.05⁴ - 0.0656×11.05³ + 0.4598×11.05² - 0.6270×11.05 + 99.33 ≈ 96.38

I(-29.72) = 0.00009045×(-29.72)⁵ + 0.001438×(-29.72)⁴ - 0.0656×(-29.72)³ + 0.4598×(-29.72)² - 0.6270×(-29.72) + 99.33 = 1270.8

Therefore, the food price when the food was cheapest is $99.08

The time when the food is most cheapest where 0 ≤ t ≤ 10 is t = 0.823 years ≈ 1 years

Similarly, the food price when the food was most expensive in a 10 year time frame is $100.67

The time when the food is most expensive is t ≈ 5.131 years ≈ 5 years

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The correct answer is A. Standard deviation measures the dispersion or variability around the expected value or mean of a data set. It is a commonly used statistical measure to quantify the spread of data points.

Standard deviation is calculated by taking the square root of the variance. The variance is the average of the squared differences between each data point and the mean. By squaring the differences, negative values are eliminated, ensuring that the measure of dispersion is always positive.

A higher standard deviation indicates greater variability or dispersion of data points from the mean, while a lower standard deviation suggests that the data points are closer to the mean.

On the other hand, the mean (option B) is a measure of central tendency that represents the average value of a data set. It does not directly measure the dispersion or variability around the mean.

The coefficient of variation (option C) is a relative measure of dispersion that is calculated by dividing the standard deviation by the mean. It is useful for comparing the relative variability between different data sets with different scales or units.

The chi-square test (option D) is a statistical test used to determine if there is a significant association between categorical variables. It is not a measure of dispersion around the expected value.

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Answer:

1/42 probability

dice = 1/36 probability

spinner = 1/6

Answer:

64 cups

Step-by-step explanation:

1 gallon = 16 cups

Therefore, 4 gallons = 4 x 16 = 64 cups

Answer:

64

Step-by-step explanation:

hope this helps!!! :)

Step-by-step explanation:

They are equal .....

   a transveral across two parallel lines creates equal alternate interior angles

ANSWER: 202.46 if you need all the question answers just ask :D

Answer:

Before heading towards the solution, you need to make sure how multiple and factors are related to each other.

The multiple of a number could be obtained by multiply it with another number.

For example, the first five multiples of 12 are 12, 24, 36, 48 and 60

1 X 12 = 12

2 X 12 = 24

3 X 12 = 36

4 X 12 = 48

5 X 12 = 60

Factors are the numbers that are multiplied to get a given number.

For example,

1 X 12 = 12

2 X 12 = 24

3 X 12 = 36

The factors of 12 are 1, 2, 3, 4, 6 and 12.

As division and multiplication can be used to find factors and multiples.

For example a whole number is a multiple of its factors.

Let w = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} be the set of even wholes numbers from 2 to 20.

As 2 is a factor of 20 because 20 ÷ 2 = 4

20 is a multiple of 2 because 2 X 10 = 20

So, in the same way, the equation 8 X 5 = 40 can be used to determine how factors and multiples are related.

Let the equation be

                                   8 X 5 = 40

8 is a factor of 40 because 8 X 5 = 40

40 is a multiple of 8 because 40 ÷ 5 = 8

So, this is how factors and multiples are related to each other.

The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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The Hardy-Weinberg equation is a mathematical formula used to calculate the frequency of alleles (alternative forms of genes) in a population.

It states that the frequency of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.

The equation is expressed as: p² + 2pq + q² = 1

In this equation, p represents the frequency of the dominant allele in the population, and q represents the frequency of the recessive allele.

The superscripts 2 represent the proportion of individuals in the population that are homozygous for that allele (meaning they have two copies of the same allele), while the 2pq term represents the proportion of individuals that are heterozygous (meaning they have one copy of each allele).

The sum of these terms is always equal to 1, as it represents the entire population.

This equation assumes several conditions: that the population is large, randomly mating, with no mutations, migration, natural selection, or genetic drift.

In reality, these conditions are rarely met, and the Hardy-Weinberg equation serves as a useful model for understanding how allele frequencies can change over time due to various evolutionary influences.

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Given the hypotheses H0: μ ≤ 6 and Ha: μ > 6, this is a right-tailed test. So, the correct answer is B. right-tail.

The hypotheses given are about the population mean μ being either less than or equal to 6 (null hypothesis, H0) or greater than 6 (alternative hypothesis, Ha). The alternative hypothesis Ha indicates a one-sided or directional hypothesis because it specifies a particular direction of change (i.e., increase) in the population mean.

In this case, the test is a right-tailed test because the alternative hypothesis indicates that the population mean is greater than the null hypothesis value of 6. A right-tailed test is used when the alternative hypothesis suggests that the population parameter of interest is greater than the null hypothesis value.

Therefore, the answer is B. right-tail.

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Answer:

100m²

Step-by-step explanation:

Area of trapezoid= ½×h×(a+b)

½×10×(8+12)

=5×20

=100m²

Answer:

100m²

Step-by-step explanation:

Answer:

less than

Step-by-step explanation:

it's a fraction, so it will be a fraction of the original number.

100 times.

It's basically just asking you how many 2 dollars reach to 200 dollar. Ignore the 94 dollar ( prize) since it's not entirely useful in this question.

When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. When you add the standard deviation to the mean and also subtract the standard deviation from the mean, you get the upper and lower bounds of the range that contains about 68% of the data. This range is called one standard deviation.The value of the standard deviation indicates how much the data varies around the mean. If the standard deviation is high, then the data is widely spread out and vice versa. Additionally, when you write a measurement as the mean ± standard deviation, it is assumed that the data is normally distributed. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

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so we have that to paint 1 door we have to use:

so we have to use 1 1/4 liter to paint one door

Step-by-step explanation:

1st horse time taken = 65 min/job; invert to get rate = 1/65 job/min

2nd horse time taken = 35 min/job ; invert to get rate = 1/35 job/min

Together Time taken = n min/job ; invert to get rate = 1/n job/min

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

Equation :-

Rate + Rate = together rate

1/65 + 1/35 = 1/n

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

35n + 65n = 35*65

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

100n = 2275

n = 22.75 minutes = 22 minutes 45 seconds

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