The neck of a gifaffe is 4 1/2 feet in length. Its neck is 30 perocent of it height whats the higet of the giffae

The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.

To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.

Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.

The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).

Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:

yz + λ = 0

xz + 3λ = 0

x*y + 4λ = 0

x + 3y + 4z - 9 = 0

Solving these equations simultaneously, we get:

x = 1.5, y = 1, z = 2.25, and λ = -0.5625

Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.

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Answer:

1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).

2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).

3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).

Answer:11

Step-by-step explanation:

The probability of rolling one of these five numbers is 5/37.

Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:

35 | 25 | 33 | 9 | 19.

The total number of sides of a die is 37. As a result, there are 37 numbers in the die.

Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.

Therefore, the probability of rolling any of these numbers is:

1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37

So, the probability of rolling one of these five numbers is 5/37.

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Answer: Incorrect

Step-by-step explanation:

Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.

The claim of the production manager is not true because more than 4000 insulating washers are defective per day.

The total amount of insulating washer for the electrical devices produced per day = 225,000.

The amount chosen at random for sampling = 200 washers.

The amount shown to be defective in the chosen sample = 4

If every 200 = 4 defective

225,000 = X

Make c the subject of formula;

X = 225000×4/200

X = 900000/200

X = 4,500.

This shows that the claim is wrong because more than 4000 insulating washers are defective per day.

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By answering the presented question, we may conclude that Therefore, the solution to the system of equations is: x = 36/31 and y = 57/31.

In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation "x2 + 2x - 3 = 0," for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.

From the given system of equations, we have:

[tex]8x + 7y = 17 ...(1)\\x - 3y = -5 ...(2)\\x = 3y - 5 ...(3)\\8(3y - 5) + 7y = 17\\24y - 40 + 7y = 17\\31y = 57\\y = 57/31\\x = 3(57/31) - 5\\x = 36/31[/tex]

Therefore, the solution to the system of equations is:

x = 36/31 and y = 57/31.

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The solution to the system of equations is: x = 36/31 and y = 57/31.

In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,[/tex]" for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.

From the given system of equations, we have:

[tex]$\begin{aligned} & 8 x+7 y=17 \ldots(1) \\ & x-3 y=-5 \ldots(2) \\ & x=3 y-5 \ldots(3) \\ & 8(3 y-5)+7 y=17 \\ & 24 y-40+7 y=17 \\ & 31 y=57 \\ & y=57 / 31 \\ & x=3(57 / 31)-5 \\ & x=36 / 31\end{aligned}$[/tex]

Therefore, the solution to the system of equations is:

x = 36/31 and y = 57/31.

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The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.

The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.

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Answer:

54

Step-by-step explanation:

Add six each time -> 24 + 6 = 30 + 6 = 36 etc

Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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Answer:

2 + r = 6

Step-by-step explanation:

2 + r = 6

r = 6 - 2 = 4

6 on the left balanced by 2 plus r on the right

The required volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.

A measurement of three-dimensional space is volume. It is frequently expressed mathematically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are linked.

First, let's find the volume of the cylinder:

[tex]$$V_{cylinder} = \pi r^2 h = \pi (5)^2 (8) = 200\pi$$[/tex]

Next, let's find the volume of the hemisphere:

[tex]$V_{hemisphere} = \frac{2}{3}\pi r^3 = \frac{2}{3}\pi (5)^3 = \frac{250\pi}{3}$$[/tex]

To find the volume of the entire shape, we simply add the volume of the cylinder and hemisphere:

[tex]$$V_{shape} = V_{cylinder} + V_{hemisphere} = 200\pi + \frac{250\pi}{3} = \frac{850\pi}{3}$$[/tex]

Therefore, the volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.

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If at practice, each player shoots 20 free throws, the standard deviation of x is 0.975.

To calculate the standard deviation of x, we need to first determine the variance. The variance is the average of the squared differences of each observation from the mean.

In this case, Faith is a 95% free throw shooter, so she is expected to make 19 out of 20 shots on average. The probability of making a free throw is 0.95, and the probability of missing a free throw is 0.05. Therefore, the mean of x is:

mean(x) = 20 * 0.95 = 19

To calculate the variance, we need to find the expected value of (x - mean(x))^2. Since Faith's free throw shooting is independent, we can use the binomial distribution to find the probability of making x shots out of 20.

The formula for the variance of a binomial distribution is np(1-p), where n is the number of trials and p is the probability of success. Therefore, the variance of x is:

var(x) = 20 * 0.95 * 0.05 = 0.95

Finally, the standard deviation is the square root of the variance:

sd(x) = √(var(x)) = √(0.95) = 0.975

This means that on average, Faith is expected to make 19 out of 20 free throws, but there is a standard deviation of 0.975, which indicates the degree of variability or spread around the mean. In other words, we can expect Faith to make between 18 and 20 free throws in most cases, but there is a small chance that she may make fewer or more than that.

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Answer: Mike is ( 3x + 4 ) years old

Step-by-step explanation:

K -> x y/o

L -> 3x y/o

M -> (3x + 4) y/o

The answer of the given question based on the finding the m∠QTS from a circle with the measure of minor arc the answer is the measure of angle ∠QTS is 60° degrees.

In geometry, arc is  portion of a curve or  circle. It is defined as the part of the curve that is contained between two points, called endpoints, on curve. The length of  arc is  fraction of the circumference of  circle, determined by the measure of  central angle that subtends it.

An arc is typically denoted by  two endpoints, with  small arc or arc symbol above the two letters. For example, an arc with endpoints A and B would be denoted as "⌒AB" or "AB".Arcs can be classified based on their measure or  position of their endpoints.

An arc with measure less than 180 degrees is called  minor arc, while an arc with measure greater than 180 degrees is called  major arc. An arc with measure equal to 180 degrees is called semicircle.

Since arc QS is a minor arc, we know that angle ∠QTS is half the measure of arc QS. Therefore, we have:

m∠QTS = (1/2) m arc QS

m∠QTS = (1/2) (120°) [Substituting the given value of m arc QS]

m∠QTS = 60°

Therefore, the measure of angle ∠QTS is 60° degrees.

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The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.

Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:

Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.

Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.

Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.

The numbers of the form 35n in the interval [1000, 9999] are

1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.

To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.

Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is

9000 - 399 - 204 + 285 = 4680.

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(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.

(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.

(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²

Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).

n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74

Since we need a whole number, we round up to the nearest whole number:
n = 51

(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):

n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65

Again, rounding up to the nearest whole number:
n = 68

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Option (A) x+1 is a positive odd integer.

Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.

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a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.

b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.

c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.

(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.

(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.

(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.

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Answer:

Step-by-step explanation:

To find the perimeter of an equilateral triangle is equalled to 3s.

35 x 3

105

The expressions that have values less than 0 are a) and b)

According to the question

Here's how you can use a number line to solve this problem:

For example in expression a) -5 + 3, start at zero and move 5 units to the left (because of the negative sign on 5), and then move 3 units to the right. The final position is at -2, which is to the left of zero. Therefore, expression a) has a value that is less than zero.

Similarly expression b) has a value that is less than zero.

Also expressions c) and d) can be solved in the same way. If the final position is to the right of zero, the expression does not have a value that is less than zero.

In conclusion, expressions a) and b) have a value that is less than zero, while expressions c) and d) do not.

What is a number line?

A number line is a visual representation of real numbers arranged in a straight line used to compare, add, and subtract numbers.

What is meant by expressions?

An expression is a combination of numbers, variables, and mathematical operations used to represent a quantity or a mathematical statement.

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The equation representing total fraction strip is  ³/₃ + ¹/₃ = ⁴/₃.

option B.

A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.

For this case, 1 is divided into, and 1 divide into 3.

To obtain the total fractions, we will add the individual fractions as shown below;

For this first fraction = ¹/₃ + ¹/₃ + ¹/₃

For the second fraction = ¹/₃

Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃

Total fraction = ³/₃ + ¹/₃ = ⁴/₃

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From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm

To construct triangle ABC, we can follow these steps:

To measure the length of BC in triangle ABC, we can use the law of sines.

The law of sines states that in any triangle ABC:

a / sin(A) = b / sin(B) = c / sin(C)

Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.

In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:

angle ACB = 180 - angle BAC - angle ABC

= 180 - 96 - 35 = 49 degrees

Now, we can apply the law of sines to find the length of BC:

BC / sin(35) = 6 / sin(96)

BC = 6 × sin(35) / sin(96)

Using a calculator, we can evaluate this expression to get:

BC ≈ 4.22 cm

Therefore, the length of BC in triangle ABC is approximately 4.22 cm.

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If 7/9 of the box is green counters, and there are 24 yellow counters in the box, then there are 84 green counters .

Let's assume that the total number of counters in the box is x.

We are given that 7/9 of the box is filled with green counters, which means that the remaining 2/9 of the box must be filled with yellow counters. We are also given that there are 24 yellow counters in the box.

We can set up an equation to represent the relationship between the number of yellow counters and the total number of counters:

2/9 x = 24

To solve for x, we can multiply both sides of the equation by the reciprocal of 2/9, which is 9/2:

(2/9) x * (9/2) = 24 * (9/2)

x = 108

This means that there are a total of 108 counters in the box. To find out how many of these are green counters, we can use the fact that 7/9 of the box is filled with green counters:

(7/9) * 108 = 84

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The measure of the angle that it is complementary which is represented by 90-x is always true. Option A

An acute angle is simply defined as an angle that measures from 90° and 0°. This means that it is smaller than a right angle.

It is formed in the space between two intersecting lines or planes, or from the intersection of two shapes.

A complementary angle can be defined as a pair of angles whose sum is equal or equivalent to 90 degrees.

From the information given, we have that;

x is the acute angle

The complementary angle is 90 - x

We can see that the angle x must be complementary to be subtracted from 90 degrees.

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The complete question:

If the measure of an acute angle is represented by x, then the measure of its complement is represented by 90 – X.

always true

sometimes true

never true

Using simple mathematical operations we know that 4.5 ft of fabric is needed.

A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.

Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

So, to find the fabric needed:

1 2/7 feet of fabric

Then, 3 1/2 hands will need:

= 9/7 * 7/2

= 9/2

= 4.5 ft of cloth

Therefore, using simple mathematical operations we know that 4.5 ft of fabric is needed.

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Correct question:

Emily needs enough fabric for 3 1/2 hat's since she has half a hat done already. if each hat requires 1 2/7 feet of fabric, how much fabric will she need to make the 3 1/2 hat's?

Answer:

C. (0, –5) and (2, –1)