Toucans and blue-and-yellow macaws are both tropical birds. The length of the toucan in the picture to the right is about two thirds of the
length of the blue-and-yellow macaw. The toucan is about 26 in long. What is the length of the blue-and-yellow macaw?

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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(a) There are 2^7 or 128 subsets of A.

(b) The number of subsets of A containing 4 elements is 35.

(c) The number of subsets of A containing only even numbers is 16.

(d) The number of subsets of A containing an even number of elements is 64.

(a) The number of subsets of a set with n elements is 2^n. Therefore, the number of subsets of A, which has 7 elements, is 2^7 = 128.

(b) To find the number of subsets of A containing 4 elements, we need to choose 4 elements out of the 7, which can be done in (7 choose 4) = 35 ways.

(c) A subset of A containing only even numbers can be formed by choosing any combination of the three even numbers in A: 2, 4, and 6. There are 2^3 = 8 ways to do this, but we must exclude the empty set, so there are 8 - 1 = 7 subsets of A containing only even numbers.

However, we must also exclude the subset {2, 4, 6}, which has already been counted, so the total number of subsets of A containing only even numbers is 7 - 1 = 6.

(d) The number of subsets of A containing an even number of elements is equal to the number of subsets containing 0, 2, 4, or 6 elements. We can count the number of subsets of A containing 0, 2, 4, or 6 elements using the binomial coefficients: (7 choose 0) + (7 choose 2) + (7 choose 4) + (7 choose 6) = 1 + 21 + 35 + 7 = 64.

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Answer:

$450

Step-by-step explanation:

Mr. william's paid $1250 in cash for a new television set. But if he was to use the store's deposit plan, he will have to make some installmental payment after paying an initial deposit.

Initial deposit = $350

Installmental payments of $150 for 9months.

His total payment will be = Initial payment + the total amount of the installmental payment.

$350 + (9 x $150) = $350 + 1350 = $1700

$1700 - $1250 = $450 savings

By paying in cash he will be saving an amount of $450.

Answer:

Step-by-step explanation:

he is poooooooooooooorrrrrrrrrrrrrrrrrr

The given equation is

To solve for x, the logarithm to indices relationship will be applied

That is

Hence

This is simplified to get

Therefore, the value of x = 4

(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.

To perform a t-test for the population mean difference, follow these steps:

(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.

Mean difference = (Sum of differences) / Number of pairs

Using the given data gives:

Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5

Subtracting gives:

Mean difference = (3 - 1 - 1 + 3 + 7) / 5

Solving gives:

Mean difference = 11 / 5

Dividing gives:

Mean difference = 2.2

(b) Calculate the standard deviation of the differences:

To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.

Squared differences:\((3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2\)

Solving gives:

Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)

Solving gives:

The sum of squared differences = 48.36

The standard deviation of the differences \(= \sqrt{48.36 / 4}\)

Solving gives:

The standard deviation of the differences \(= \sqrt{2.09}\)

Rounded to three decimal places

The standard deviation of the differences ≈ 3.47

c) Calculate the test statistic:

The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))

Let's assume the null hypothesis is that there is no difference between the two fertilizers

(i.e., mean difference = 0).

\(t = (2.2 - 0) / (3.47 / \sqrt5)\)

Substituting \(\sqrt 5 = 2.236\)

t = 2.2 / (3.47 / 2.236)

Rounded to two decimal places

t ≈ 1.378

So, the test statistic is approximately 1.378.

The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma

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The probability of a five-card poker hand from a standard 52 card deck that is a two pair (two pairs of different ranks and a fifth card) is 4.75%.

To solve this question, you need to use the concept of probability. The probability is the likelihood of an event happening. It can be expressed as a ratio, fraction, or percentage.

Let's use the formula for probability:

P(E) = number of successful outcomes / total number of outcomes

The total number of possible five-card hands from a standard 52-card deck is 2,598,960. The number of successful outcomes, in this case, is the number of two-pair hands we can form. A two-pair hand contains two cards of one rank, two cards of another rank, and a fifth card of a third rank.

Let's break down the calculation of the number of two-pair hands. First, we need to choose two different ranks for the pairs, which we can do in C(13, 2) ways. (13 is the number of ranks, and we need to choose 2 of them.) For each of these choices, there are C(4, 2) ways to choose two cards of one rank and C(4, 2) ways to choose two cards of the other rank. Finally, we have 44 choices for the fifth card (any rank except the two ranks we've already chosen and any suit except for the four suits we've already chosen).

Therefore, the number of two-pair hands is C(13, 2) * C(4, 2) * C(4, 2) * 44 = 123,552.

Now, we can use the formula to calculate the probability:

P(E) = 123,552 / 2,598,960 ≈ 0.0475 ≈ 4.75%.

Therefore, the probability of a five-card poker hand from a standard 52 card deck that is a two pair (two pairs of different ranks and a fifth card) is 4.75%.

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The Equation for Table I is y= 1/3x + 5.

The solution of the Equation is (3, 6).

Equation for Table II

y= -1/3 x +7

Table I:

Slope = (6-5)/ (3-0)

slope = 1/3

and, using slope intercept form

y - 5 = 1/3 (x - 0)

y-5 = 1/3x

y = 1/3x + 5

Now, solving the equation for both table we get

x= 3 and y= 6

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Answer:

4

Step-by-step explanation:

The graph of part of an exponential function is given, the range of this exponential function is y > 0.

An exponential function is a mathematical function that describes the growth or decay of a quantity at a constant rate over time. It is a function of the form:

f(x) = \(a^x\)

where a is a positive constant, known as the base of the exponential function, and x is the independent variable, which can be any real number.

The domain of an exponential function is always the set of all real numbers. Therefore, the domain of this function is:

Domain: x ∈ ℝ

The range of this exponential function as per the given graph is all positive real numbers greater than zero. We can write this using interval notation as:

Range: y > 0

Therefore, the range of this exponential function is y > 0.

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The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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The mean of the finishers in the New York City 10-km run is 60 minutes and standard deviation is 9 minutes.

To determine the percentage of finishers who have times between 55 and 75 minutes, we need to find the Z-scores for both of these values as follows:

Z1 = (55 - 60) / 9 = -0.56Z2 = (75 - 60) / 9 = 1.67

Now, we need to find the area under the standard normal distribution curve between these two Z-scores as follows:

P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56) Using a standard normal distribution table,

we can find the probabilities as:

P(Z < 1.67) = 0.9525P(Z < -0.56) = 0.2881

Therefore , P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56)= 0.9525 - 0.2881= 0.6644Therefore, the percentage of finishers who have times between 55 and 75 minutes is 66.44%.

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9514 1404 393

Answer:

  45 yd²

Step-by-step explanation:

The area of a rectangle is the product of its length and width. If your given measures are the length and with of a rectangle, the area is found by multiplying them.

  A = LW

  A = (9 yd)(5 yd) = 9·5 yd·yd = 45 yd²

The area of a 9 yd by 5 yd rectangle is 45 square yards.

The required values of k for which given matrix is diagonalizable is 0.

A matrix is symmetric if and provided that it is equivalent to its translate. All sections over the primary inclining of a symmetric grid are reflected into equivalent passages beneath the slanting. ■ A lattice is slant symmetric if and provided that it is something contrary to its render.

We have,

A = \(\left[\begin{array}{cc}4&k&0&4\\\end{array}\right]\)

Keep in mind, each symmetric matrix with genuine coefficients is diagonalizable. Note that the coefficients of An are reals. In this way, on the off chance that we take with the end goal that An is symmetric.

For A is symmetric matrix,

k = \(a_{12}=a_{21}\) = 0

Thus, required value of k for given matrix is 0.

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Answer:

a) t = 4000/v

b) t = 4000/(v + 20)

c) see attached workings

Step-by-step explanation:

a)  A man jogs 4 km everyday at an average speed of v m/min

As the speed is measured in meters per minute, we need to convert the distance (4 km) into meters:

    1 km = 1000 m

⇒ 4 km = 4 x 1000 = 4000 m

   distance = speed x time

⇒ time = distance / speed

⇒ t = 4000/v  (where t = time in minutes)

b) If his average speed increased by 20 m/min, then his speed would now be  (v + 20) m/min

⇒ t = 4000/(v + 20)  (where t = time in minutes)

c) Given the man would take 3 min less if his average speed increased by 20 m/min, we can rewrite the second equation as:

t - 3 = 4000/(v + 20)

Now simply substitute the first equation t = 4000/v into the second:

(I have typed this used MS Word and attached, as the equation editor here in Brainly is not working at the moment).

Answer:

0

Step-by-step explanation:

1. To solve this question, we plug in the values of a and b into the expression.

Therefore, when we evaluate the expression when a = 7 and b = 42, we get 0.

Hey there!

b/6 - a

= 42/6 - 7

= 7 - 7

= 0

Therefore, your answer is: 0

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 in the presence of a platinum catalyst are related as enantiomers.

Hence, the correct option is E.

Enantiomers are stereoisomers that are non-superimposable mirror images of each other. In this case, the (E)- and (Z)-isomers have different spatial arrangements around the C=C double bond. When they react with D2 in the presence of a platinum catalyst, the deuterium atoms add to the double bond, resulting in two new chiral centers.

Since the two isomers have different spatial arrangements around the double bond, the addition of deuterium atoms will produce enantiomeric products. Therefore, the products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 are related as enantiomers.

Hence, the correct option is E.

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Answer:

Please check the explanation.

Step-by-step explanation:

Part a)

Given

It is clear that m∠ABD and m∠CBD lie on a straight line.

Thus, the sum of m∠ABD and m∠CBD will be 180°.

Hence,

m∠ABD and m∠CBD are supplementary angles.

Part b)

As m∠ABD and m∠CBD are supplementary angles, so the sum of m∠ABD and m∠CBD will be 180°.

Thus,

m∠ABD + m∠CBD = 180°

substitute m∠ABD = (7q-46)° and m∠CBD = (3q + 6)°

(7q-46)° + (3q + 6)° =  180°

Part c)

Given the equation

(7q-46)° + (3q + 6)° =  180°

Combining the like terms

7q + 3q - 46 + 6 = 180

10q - 40 = 180

10q = 180 + 40

10q = 220

divide both sides by 10

10q/10 = 220/10

q = 22

Therefore, the value of q = 22

Part d)

As

m∠ABD = (7q-46)°

substituting q = 22

m∠ABD = 7(22) - 46

             = 154 - 46

             = 108°

also

m∠CBD = (3q + 6)°

substituting q = 22

m∠CBD = 3(22) + 6

              = 66+6

              = 72°

Therefore,

Answer:

$1,585.70

Step-by-step explanation:

15% of $2,200 = $330

7.65% of $2,200 = $168.3

3% of $2,200 = $66

$330 + $168.3 + $66 = $564.3

$564.3 + $50 (healthcare cost) = $6.14.3

$2,200 $614.3 = $1585.70

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

perpendicular

Step-by-step explanation:

(perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

1. The area of one rhombus is 1.875 square inches.

2. The area of the entire logo is 9.375 square inches.

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

Shape = rhombus

Where we have the diagonals to be 2.5 inches and 1.5 inches

The area of one rhombus is calculated as

Area = product of dimensions/2

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

Area = 2.5 * 1.5/2

Area = 1.875

We know that there are 5 shapes

So, we have

Area = 1.875 * 5

Evaluate

Area = 9.375

Hence, the area of the entire logo is 9.375

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The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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Answer:

∠8 is 400°

Step-by-step explanation

50 x  8 = 400

that means that the measure of ∠8 is 400°

Answer:

130 degrees I got it correct trust me

Answer:

coordinate of B(2,-8)

Answer:

(4,-8)

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

The 2 indicated angles are alternate and congruent, that is

26x - 4 = 24x + 4 ( subtract 24x from both sides )

2x - 4 = 4 ( add 4 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

  A, B, E are irrational

Step-by-step explanation:

You want to know which expressions result in an irrational number from the given expressions involving rational and irrational numbers.

  M + N = √2 +√5 . . . . irrational

  MN = (√2)(√5) = 10 . . . . irrational

  S + T = 2 + 5 = 7 . . . . rational

  ST = 2·5 = 10 . . . . rational

  N + T = √5 + 5 . . . . irrational

  N² = (√5)(√5) = 5 . . . . rational

__

Additional comment

When in doubt, you can use your calculator to evaluate these expressions. If the decimal fraction uses all available digits, the number is likely irrational.

If the number cannot be expressed exactly without using symbols (√, ∛, π, e), then it is irrational. The attached calculator display shows this nicely.

Answer:

The area of this trapezoid is 8cm

Answer:

130

Step-by-step explanation:

first decompose the trapezoid into a square in the middle and 2 triangles on the left/right side, both triangles are congruent so you only find the area of one triangle, which is 9 because do 2x9 = 18/2 = 9, now let's move on to the middle square 14 x 18 = 112, then you add them all up remember there are 2 triangles,

112 + 9 + 9 = 130