9 yd
9 yd
5 yd
3 yd
Perimeter:
Area:

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

x = -37/32

Step-by-step explanation:

32x + 26 = -11

Subtract 26 from each side

32x + 26-26 = -11-26

32x = -37

Divide each side by 32

32x/32 = -37/32

x = -37/32

Answer:

x= -1 5/32 or x=-1.15625

Step-by-step explanation:

The square root of 169 is indeed 13.When simplifying the square root of a perfect square (a number that has an exact integer square root), we find the square root by identifying the largest perfect square factor of the given number. In this case, 169 is a perfect square because it can be expressed as 13^2.

To simplify the expression √169, we need to find the square root of 169. The square root of a number is a value that, when multiplied by itself, equals the original number.

In this case, we can calculate the square root of 169 as follows:

√169 = 13

So, the simplified form of the expression √169 is 13.

To verify this result, we can square 13 to check if it equals 169:

13^2 = 169

Therefore, the square root of 169 is indeed 13.

In general, when simplifying the square root of a perfect square (a number that has an exact integer square root), we find the square root by identifying the largest perfect square factor of the given number. In this case, 169 is a perfect square because it can be expressed as 13^2.

Taking the square root of a perfect square yields the positive and negative square roots of that number. However, when referring to the principal square root (which is typically denoted by the radical symbol), we consider only the positive square root.Hence, the simplified form of √169 is 13.

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Answer:

A

Step-by-step explanation:

143.6° and x are adjacent angles and sum to 180° , then

x + 143.6° = 180° ( subtract 143.6° from both sides )

x = 36.4° → A

Answer:

i think it is the second one?

Step-by-step explanation:

i hope it helped!

Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.

The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.

To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.

Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.

To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.

Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.

If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.

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Answer:

The nile river is 6690 kilometers long.This is 394 kilometers longer than the Amazon River.How long is the Amazon River?

6690-394=6296 kilometers

Step-by-step explanation:

Answer:

The Amazon river is 6296 kilometers long.

Answer:

10/r x 4

Step-by-step explanation:

The linear equation of Johnny's charges is C(x) = 10 + 7.5x

From the question, we have the following parameters that can be used in our computation:

Initial charge = $10

Hourly rate = $7.50

Let the number of hours be x and the total cost be C(x)

So, we have the following representation

C(x) = Initial charge + Hourly rate * x

Substitute the known values in the above equation, so, we have the following representation

C(x) = 10 + 7.5x

Hence, the function is C(x) = 10 + 7.5x

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Complete question

Johnny charges $10 plus $7.50 per hour to mow lawns.

Determine the linear equation

(a) the expected value of the amount you win 2/9 , (b) the variance of the amount you win 5/18 , c) The expected value of the amount you win is -$0.0667 and d)The variance of the amount you win is 1.2898.

Let's calculate the expected value and variance of the amount you win step by step:

a) Calculate the probability of drawing two marbles of the same color.

First, calculate the probability of drawing two red marbles:

P(RR) = (5/10) * (4/9) = 20/90 = 2/9

Similarly, calculate the probability of drawing two blue marbles:

P(BB) = (5/10) * (4/9) = 20/90 = 2/9

b) Calculate the probability of drawing two marbles of different colors.

P(RB) = (5/10) * (5/9) = 25/90 = 5/18

P(BR) = (5/10) * (5/9) = 25/90 = 5/18

c) Calculate the expected value.

The expected value (EV) is calculated by multiplying each outcome by its probability and summing them up.

EV = (P(RR) * $1.10) + (P(RB) * -$1.00) + (P(BR) * -$1.00) + (P(BB) * $1.10)

= (2/9 * $1.10) + (5/18 * -$1.00) + (5/18 * -$1.00) + (2/9 * $1.10)

= $0.2444 - $0.2778 - $0.2778 + $0.2444

= -$0.0667

Therefore, the expected value of the amount you win is -$0.0667.

d) Calculate the variance.

The variance is a measure of the dispersion of the outcomes around the expected value. It is calculated as the sum of the squared differences between each outcome and the expected value, weighted by their probabilities.

Variance = (P(RR) * ($1.10 - EV)²) + (P(RB) * (-$1.00 - EV)²) + (P(BR) * (-$1.00 - EV)²) + (P(BB) * ($1.10 - EV)²)

Variance = (2/9 * ($1.10 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (2/9 * ($1.10 - (-$0.0667))²)

= (2/9 * $1.1667²) + (5/18 * -$0.9333²) + (5/18 * -$0.9333²) + (2/9 * $1.1667²)

= 1.2898

Therefore, the variance of the amount you win is 1.2898.

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In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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The average rate of return on this investment over the two-year period using the geometric mean is 9.165%.

The geometric mean is given as the nth root of a the product of the “n” number of values.

The formula for the geometric mean is given as \(\sqrt (a*b)\) or \(\sqrt(ab*...n)\).

The returns in one year = 12%

The returns in the next year = 7%

The number of years, n = 2

\(\sqrt(a*b)\)

\(\sqrt0.12 * 0.07\)

= \(\sqrt0.0084\)

= 0.09165

= 9.165%

Thus, the average rate of return of this investment, using the geometric mean, is 9.165%

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The simple interest rate charged is found to be 50%.

In the given question,

the principal (P) is $1,000.00,

the fee (F) is $500.00 and

the time (t) is 7 months.

To calculate the simple interest rate charged, we can use the following formula:

Simple Interest (I) = (P × r × t)/100

where r is the simple interest rate.

Now, we can use the given values to find the value of r.

I = (P × r × t)/100

I = (1000 × r × 7)/100

I = 70r

On adding the fee to the principal, the total amount that Wade has to pay back is $1,500.00.

Therefore, the interest charged is $500.00.

Using the formula,

I = (P × r × t)/100

500 = (1000 × r × 7)/100

5 = 10r

Rearranging the equation, we get:

r = 5/10

r = 0.5 or 50%

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Answer:

12a^2+18ab-6ac+25a-3b+c

Step-by-step explanation:

Answer:

\(\huge\boxed{\bf\:2\left(3x-1\right)\left(3x+2\right) }\)

Step-by-step explanation:

\(18x^{2} + 6x - 4\\\\Factor \: out \: the \: common \: factor = 2\\\\= 2\left(9x^{2}+3x-2\right) \\\\Split\:the\:quadraric\:equation\:inside\:the\:parentheses \\\:using\:the\:splitting-the-middle-term \:method.\\\\= 2\left(9x^{2}-3x\right)+\left(6x-2\right) \\= 2 (3x\left(3x-1\right)+2\left(3x-1\right) )\\= \boxed{\bf\:2 \left(3x-1\right)\left(3x+2\right) }\)

\(\rule{150pt}{2pt}\)

Answer:

2(3x - 1)(3x + 2)

Step-by-step explanation:

18x² + 6x - 4 ← factor out 2 from each term

= 2(9x² + 3x - 2) ← factor the quadratic

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 9 × - 2 = - 18 and sum = + 3

the factors are - 3 and + 6

use these factors to split the x- term

9x² - 3x + 6x - 2 ( factor first/second and third/fourth terms )

= 3x(3x - 1) + 2(3x - 1) ← factor out (3x - 1) from each term

= (3x - 1)(3x + 2) ← in factored form

then

18x² + 6x - 4

= 2(3x - 1)(3x + 2)

Answer: 33

Step-by-step explanation:

Answer:

-0.13157894736

Step-by-step explanation:

In multiple regression analysis, the correlation among the independent variables is termed multicollinearity

Multicollinearity in a multivariate regression model refers to the correlations between two or more independent variables. Multicollinearity can lead to skewed or false results when a researcher or analyst attempts to determine how effectively each independent variable can be used to predict or understand the dependent variable in a specific statistical model.

It is the term which is generally used to describe the situation in which two or more explanatory variables in a multiple regression model have strong linear correlations with one another but not with the dependent variable. Many times, the creation of new dependent variables that are reliant on other variables can also result in multicollinearity.

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The formula for the area of circle is,

Substitute 2 for r in the formula to obtain the area of circle.

So, exact area of circle is 1.56637061 square centimeter.

Substitute 2 for r and 3.14 for

in the formula to obtain the approximate area of circle.

So approximate area of circle is 12.56 square centimeter.

The number of bacteria  in an egg salad that is left out at room temperature is 256 option D.

The bacteria would double 4 times in 2 hours, so the total number of bacteria in the egg salad would be 256.

So we have 4 bacteria after 2 hours we have,

4 x 4 x 4 x 4 = 256 bacteria.

Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring.

Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilised in probability distribution, in which you will learn about the possible results of a random experiment. To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

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Complete question:

There are four bacteria in an egg salad that is left out at room temperature. After two hours, how many bacteria will be in the egg salad?

- 32

- 2048

- 8

- 256

The margin of error for the confidence interval is approximately 0.014, indicating that the estimate of the proportion of dissatisfied customers could be off by approximately plus or minus 0.014. This means that we can be 95% confident that the true proportion of dissatisfied customers falls within the range of the estimated proportion ± 0.014.

(a) To find the sample size needed to achieve a margin of error of about 0.015 with a 95% confidence level, we can use the formula for sample size calculation for proportions:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = critical value (corresponding to the desired confidence level)

p = estimated proportion of the population

E = margin of error

In this case, the estimated proportion of dissatisfied customers is 0.17, and the desired margin of error is 0.015. Since we want a 95% confidence level, the critical value can be obtained from a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.

Plugging these values into the formula, we have:

n = (1.96^2 * 0.17 * (1-0.17)) / 0.015^2

n ≈ 1901.63

Therefore, the sample size needed is approximately 1902.

(b) If 25% of the sample say they are not satisfied, we can calculate the margin of error using the following formula:

MoE = Z * sqrt((p * (1-p)) / n)

Where:

MoE = margin of error

Z = critical value (corresponding to the desired confidence level)

p = proportion of the sample

n = sample size

Using the same critical value of 1.96 for a 95% confidence level and plugging in the values:

MoE = 1.96 * sqrt((0.25 * (1-0.25)) / 1902)

MoE ≈ 0.014

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Observing the cases provided with the formula of probability and implementing it with OR rule , The answer is 0.22.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

All potential results make up the sample space of a random experiment. A subset of the sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.

Probability that dice rolled shows a 5 once =  1/36

Probability that dice rolled shows a 5 twice =  2/36

Probability that the sum is 8 = 5/36

Total probability = 1/36 + 2/36 + 5/36 = 0.22

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Answer:

Below in bold.

Step-by-step explanation:

Starting height is when t = 0

It is 5 units.

To find the maximum height we convert the equation to vertex form:

h = -t^2 + 4t + 5

h = -(t^2 - 4t - 5)

=  - [(t - 2)^2 - 9]

= -(t - 2)^2 + 9

From this we see that the ball reaches max height after 2.

Maximum height = -2^2 +  4(2) + 5

= 9 units.

Ball reaches the ground after 2*2 = 4 .

Answer: A

Step-by-step explanation:

2x²-2x-9=0

this is a quadratic equation so we will use the quadratic formula .

 Δ= b²-4*a*c

let's calculate Δ to khow how many solutions this equations have .

 Δ= (-2)²-4*2*(-9)

    = 76

 we notice that 76>0

so this equation has two solutions :  (-b-√76)/4 and (-b+√76)/4

the trick here is to notice that :

\(\sqrt{76}\) = \(\sqrt{19*4}\)

      = \(\sqrt{19} *\sqrt{4}\)

      = 2\(\sqrt{19}\)

Now we will simplify Δ by factoring by 2

so the answer is a .

Answer= s > 10/2

s > -10/-2

s > 10/2

The house was in the shape of an octagon, with eight separate bedrooms on each side.

The house described in the statement has an octagonal shape. An octagon is a polygon with eight sides, characterized by its eight equal angles. In this case, each side of the house corresponds to one of these angles, resulting in eight separate bedrooms on each side of the octagonal structure.

The choice of an octagon as the shape of the house can have various implications. Octagonal buildings are often admired for their unique architectural design and aesthetic appeal. The shape provides symmetry and balance, allowing for an interesting and visually pleasing structure. Additionally, an octagonal layout can offer practical advantages in terms of space utilization and room distribution. In the case of the house described, each side of the octagon accommodates a separate bedroom, providing privacy and ample living space for its occupants. The symmetrical arrangement of the bedrooms around the central area of the house could create a harmonious and well-organized living environment. Overall, the octagonal shape of the house with eight separate bedrooms on each side offers both architectural and functional benefits.

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