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Answer:

The length of the missing piece is 2 ft 3 inches

Step-by-step explanation:

Here in this question, we are interested in calculating the length of the remaining piece of the board given that we have the total length of the board and two other pieces.

Mathematically, the remaining piece length can be calculated by subtracting the lengths of the known pieces

That would be;

10 ft - 4 ft 7 inches - 3 ft 2 inches

In a foot there are 12 inches

Thus

10 ft = 10 * 12 = 120 inches

4 ft 7 inches = 4(12) + 7 = 55 inches

3 ft 2 inches = 3(12) + 2 = 36 + 2 = 38 inches

Thus the length of the remaining piece would now be;

120 -55 -38 = 27 inches

That is same as 24 + 3 inches

24 inches = 2 ft

So 27 inches = 2 ft 3 inches

The simplifies expression is -5x/6 - 8

The expression "quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity" represents:

-(2/3)x - 6 - ( -14 + (1/6)x)

The process of simplifying an expression involves reducing the expression to its simplest form, making it easier to understand and manipulate. To simplify an expression, we combine like terms by adding or subtracting the coefficients.

We need to simplify this expression into its simplest form.

Thus,

-(2/3)x - 6 - ( -14 + (1/6)x) equals,

= -2x/3 - 6 +14 - x/6

= -(4+1)x/6 - 8

= -5x/6 - 8

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The option that correctly ranks the three boys in order from lowest to highest average speed is:

The average speed calculated is obtained by dividing the total distance covered by the total time taken. That said, we will obtain the average speeds for each of the boys as follows:

Terri = 3.95 km/48 min

= 0.082 km/min

Aaron = 2.65 km/31 min

= 0.085 km/min

Jamal = 6.50 km/81 min

= 0.080 km/min

When the results are obtained from lovwest to highest we will have:

0.080, 0.082, 0.085 which represent the figures for Jamal, Terri, Aaron.

Complete Question:

Terri, Aaron, and Jamal all walked along straight paths. Terri walked 3.95 km north in 48 min. Aaron walked 2.65 km west in 31 min. Jamal walked 6.50 km south in 81 min. Which of the following correctly ranks the three boys in order from lowest to highest average speed?

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a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

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

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

Answer:

A.   y = -1/2 x + 3/2

Step-by-step explanation:

An x-intercept of 3 means point (3, 0).

The line passes through points (3, 0) and (-5, 4).

y = mx + b

m = (4 - 0)/(-5 - 3) = 4/(-8) = -1/2

y = -1/2 x + b

0 = -1/2 × 3 + b

b = 3/2

y = -1/2 x + 3/2

The depth of the water increasing when the water is 13 feet deep is approximately 1.68 feet per minutes.

We know that the conical water tank has a radius of 12 feet and is 26 feet high.

We also know that water is flowing into the tank at a rate of 30ft³/min. In other words, our derivative of the volume with respect to time t is:

                                   \(\frac{dV}{dt} = \frac{10 ft^3}{min}\)

We want to find how fast the depth of the water is increasing when the water is 13 feet deep. So, we want to find dh/ dt.

First, remember that the volume for a cone is given by the formula:

                V = 1/3 π r² h    

We want to find dh/dt. So, let's take the derivative of both sides with respect to the time t. However, first, let's put the equation in terms of h.

We can see that we have two similar triangles. So, we can write the following proportion:

         \(\frac{r}{h} = \frac{12}{36}\)

Multiply both sides by h:

    ⇒ \(r = \frac{12}{36} h\)

So, let's substitute this in r:

\(V = \frac{1}{3} \pi \frac{12}{36} h^{2} h\)

Square:

\(V = \frac{1}{3} \pi \frac{144}{3888} (h^{2} ) h\)

Simplify:

\(V = \frac{144}{3888} \pi h^{2}\)

Now, let's take the derivative of both sides with respect to t:

\(\frac{d}{dt} (V) = \frac{d}{dt} [\frac{144}{3888} ] \pi h^{3}\)

Simplify:

\(\frac{dV}{dt} =\frac{144}{3888} \pi (3h^{2} ) \frac{dh}{dt}\)

We want to find dh/dt when the water is 13 feet deep. So, let's substitute 13 for h. Also, let's substitute 10 for dV/dt. This yields:

\(10 = \frac{144}{3888} \pi (3(13^{2} ) \frac{dh}{dt}\)

\(10 = \frac{144}{3888} \pi (507) \frac{dh}{dt}\)

\(10 = \frac{73008}{3888} \pi \frac{dh}{dt}\)

\(38880 = 73008 \pi \frac{dh}{dt}\)

\(\frac{dh}{dt} = \frac{38880}{73008} \pi\)

\(\frac{dh}{dt} = \frac{38880}{73008} X\frac{22}{7}\)

≈ 1.6737109 feet / min

The water is rising at a rate of approximately 1.68 feet per minute.

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Answer:

3 dollars for each can of tuna

Step-by-step explanation:

9-3=6

6-3=3

3-3=0

In this problem, we are given a line L in R³ spanned by the vector [2][1][9]1. We are asked to find a basis for the orthogonal complement L⊥ of L.

To find the orthogonal complement L⊥, we need to determine the vectors that are orthogonal to every vector in L. The vectors in L⊥ are perpendicular to L and span a subspace that is perpendicular to L.

To find a basis for L⊥, we can use the fact that the dot product of any vector in L⊥ with any vector in L is zero. Let's call the vectors in L⊥ [x][y][z]1.

Taking the dot product of [x][y][z]1 with [2][1][9]1, we get:

2x + y + 9z = 0.

This equation represents a plane in R³. We can choose any two linearly independent vectors in this plane to form a basis for L⊥.

One possible basis for L⊥ is {[1][-2][0]1, [9][-18][2]1}. These two vectors are linearly independent and satisfy the equation 2x + y + 9z = 0. Therefore, they span L⊥, the orthogonal complement of L.

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Answer:

C

Step-by-step explanation:

The slope intercept form of a line is y=mx+b, where m is the slope of the line and b is the y intercept. Therefore, for A, the y intercept is 15, and for C it is -3. For B, the y intercept can be seen to be at -2, and for D it crosses the y axis at 2. Since -3 is the smallest of all of these, the correct answer is C. Hope this helps!

Based on the coordinates given, the location that is being described is Cook Inlet, in the Gulf of Alaska.

The coordinates of 61°N, 150°W means that the place is located in the Northern and Eastern hemisphere.

When a map is used, it points to an area in the Gulf of Alaska that is very close to the Cook Inlet which is close to Anchorage.

Question is:

Determine what country or place is located on the given approximate coordinates.

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To obtain the sample group using cluster sampling, where each cluster is an individual year and you want to randomly select 3 of these clusters for your sample, you would first need to identify all the individual years that you want to include in your sample frame.

Next, you would randomly select 3 of these years as your clusters. To do this, you could use a random number generator or write each year on a piece of paper, put them in a hat, and draw out 3 years. Once you have your 3 clusters, you would then select all the individuals within those clusters to be included in your sample.
For example, let's say you want to use cluster sampling to select a sample of high school students in the United States. You decide to use individual states as your clusters, and you want to randomly select 3 states for your sample. You first identify all 50 states in the US and write them down on a list.

Next, you use a random number generator to select 3 states from the list. Let's say the random numbers generated were 7, 23, and 49, which correspond to the states of Connecticut, Mississippi, and Wyoming, respectively. You would then select all the high school students within those 3 states to be included in your sample.

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Answer:

\( \displaystyle \boxed{k = 3}\)

Step-by-step explanation:

to determine the Value of k we need to find the equation of f(x) and g(x)

finding the equation of f(x):

f(x) is a linear function which form is given by:

\( \displaystyle f(x) =mx + b\)

where:

from the graph we acquire that

\(b = 4\)

to figure out m we can consider the following formula:

\( \displaystyle m = \frac{ \Delta y}{ \Delta x} \)

from the graph we obtain that both ∆x and ∆y is 1 thus substitute:

\( \displaystyle m = \frac{ 1}{ 1} \)

simplify:

\( \displaystyle m = 1\)

altogether we acquire:

\( \displaystyle f(x) =x + 4\)

finding the equation of g(x):

likewise f(x)

from the graph we obtain that

thus substitute:

\( \displaystyle m = \frac{ 3}{ 1} \)

simplify:

\( \displaystyle m = 3\)

from the graph we acquire

altogether substitute therefore

\( \displaystyle g(x) =3x + 4\)

finding the value of k:

given that,

\( \displaystyle \rm f(x) \: \text{and} \: g(x) =f(kx) = 3x + 4\)

so our equation is

\( \displaystyle kx + 4 = 3x + 4\)

cancel 4 from both sides:

\( \displaystyle kx = 3x \)

divide both sides by x:

\( \displaystyle \boxed{k = 3}\)

and we're done!

Disclaimer:

at the following link we posted the complete question

the complete question:

Answer:

k = 3

Step-by-step explanation:

Graph is in attachment .

Finding equation of first line [ f(x) ] :-

We can see that the line passea through point ( 0,4) . Therefore ,

Also it passes through (-4,0 )

Now let's find out slope .So that we can use the slope intercept form to find the equⁿ of the line.

Equation of f(x) :-

Similarly when we will find the equⁿ of g(x) :-

By question :-

Step-by-step explanation:

x^2 + 6x + 4x + 24 + x^2 - 7x -x + 7=

=2x^2 + 2x + 31

Answer:

5) 96.506 revolutions ≅ 97 revolution

6) circumference (c) = 83.1355

Step-by-step explanation:

5) A bicycle wheel has a radius of 33 cm. How many revolutions of the wheel are needed to cover a distance of 200 m?

If you read it twice through, you realize that the answer needs to be in meters, not centimeters. Therefore, convert the

33 cm to meters. 100 cm = 1 meter

33 cm= 0.33 meter

1 revolution= one complete time around the wheel The distance around the wheel or circle= Circumference

Use the circumference formula: C=2πr

2(3.14)(0.33) ≅ approximately equal to 2.0724M= 1 Revolution

At this point you can divide 200 by 2.0724 to find out how many revolutions it would take for 200 meters, or you can set

up a proportion as follows: 2.0724 meters/ 1 revolution ≅ 200 Meters/ X revolutions .

Cross multiply, and you get 88 ≅2.198X 200/2.0724 ≅ 96.506 revolutions. Answer

6) Radius (r) = 13.23142

Diameter = 26.46284

circumference (c) = 83.1355

Area = 550m²

Answer:

Step-by-step explanation:

 8     6     9      5    10     4     11

 1st = 3rd - 1

  3rd = 5th - 1 and so on

2nd = 4th + 1

4th = 6th + 1

6th = 8th + 1

 8th = 6th - 1

         =  4 - 1

         = 3

Answer:

1/4, -1/8, 1/16

Step-by-step explanation:

Answer:

Give brainliest to the other person they deserve it

Step-by-step explanation:

Answer:

4 regular coffees

Step-by-step explanation:

if the cafe served 10 coffees in total and it says that 40%

of them were regular, then that means you have to find 40% of 10 which is 4.

Answer:

r = 8 cm

Step-by-step explanation:

V = π·r²·h

1004.8 = 3.14(5)·r²

r² = 1004.8/15.7

r² = 64

r = √64 = 8

Answer:

The vertex form of y = x² + 24x - 15 is y = (x + 12)² - 159

Step-by-step explanation:

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

Let us use the facts above to solve the question

∵ y = x² + 24x - 15

∵ a is the coefficient of x² and b is the coefficient of x

∴ a = 1 and b = 24

∵ h is the x-coordinate of the vertex point

∵ h = \(\frac{-b}{2a}\)

→ Substitute the values of a and b to find h

∴ h = \(\frac{-24}{2(1)}=\frac{-24}{2}\)

∴ h = -12

→ To find k substitute y by k and x by h

∵ y = k and x = h

∴ k = (-12)² + 24(-12) - 15 = 144 - 288 - 15

∴ k = -159

∴ The coordinates of the vertex point are (-12, -159)

→ Substitute the values of a, h, and k in the vertex form above

∵ y = 1(x - -12)² + (-159)

→ Remember (-)(-) = (+) and (+)(-) = (-)

∴ y = (x + 12)² - 159

∴ The vertex form of y = x² + 24x - 15 is y = (x + 12)² - 159

Answer:

sure.

Step-by-step explanation:

The sale price of the 2nd Washing machine is more expensive and profitable than the first Washing machine, So Kareem should choose the 2nd Washing machine to get profit.

The price a buyer pays for a good or service is known as the selling price. When the selling price is greater than the cost price, then we will get a Profit. Marked price, is the amount that a seller actually receives from a customer after negotiating a price or striking a deal.

Here we have

The selling price of washing machines is $520

The first one is marked down by 40%.

The second is marked down by 10% with an additional 30% off.

For the first Washing machine,

Let x be the sale price of the machine

Given that the price is 40% marked down

=> the selling price of Washing machine = x - 40% of x

= \(x - \frac{40x}{100}\)

= x - 0.4x = 0.8x

As we know the selling price of the washing machine = $ 520

=> 0.8x = 520

=> x = 520/0.8

=> x = 650

The sale price of the first washing machine = $ 650.

For the 2nd Washing machine,

Let y be the sale price of the machine

Given that the price is 10% marked down

=> the selling price of Washing machine = y - 10% of y

= \(y - \frac{10y}{100}\)

= x - 0.1x = 0.9x

And given 30% off

30% off on 0.9x = 30% of 0.9x

The selling price will be = 0.9x - 30% of 0.9x

=> 0.9x - 0.27x = 0.63x

As we know the selling price of a washing machine = $ 520

=> 0.63x = 520

=> x = 520/0.63

=> x = 825.39

The sale price of the 2nd washing machine = $ 825.39.

By the above calculations

The sale price of the 2nd Washing machine is more expensive and profitable than the first Washing machine, So Kareem should choose the 2nd Washing machine to get profit.

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Answer:

tip amount = $23.68

Step-by-step explanation:

t = tip percentage (as decimal, so 5% would be 0.05)

c = cost

tip amount = c * t

tip amount = (118.40) * (0.20) = $23.68

hope this helps :)

The difference between finite sample and large sample properties of estimators lies in how they perform when applied to a finite sample size or in the limit as the sample size approaches infinity, respectively.

Finite Sample Properties:

Finite sample properties refer to the behavior and characteristics of estimators when applied to a specific, finite sample size. These properties are concerned with the accuracy, precision, bias, efficiency, and consistency of estimators based on the specific sample.

In a finite sample, the properties of estimators can vary. The estimator may be unbiased, meaning that its expected value is equal to the true value of the parameter being estimated. However, it can also be biased, meaning that its expected value deviates from the true value. Additionally, the estimator's precision, or variability, can be high or low. In some cases, estimators with lower bias may have higher variability, and vice versa.

Large Sample Properties:

Large sample properties, on the other hand, focus on the behavior of estimators when the sample size becomes very large, approaching infinity. Large sample properties are based on statistical theories and asymptotic results.

In the large sample limit, certain desirable properties tend to emerge consistently. These properties include consistency, efficiency, and asymptotic normality.

Consistency refers to the property that as the sample size increases, the estimator converges to the true value of the parameter being estimated. In other words, the estimator becomes more accurate as the sample size increases.

Efficiency refers to the property that the estimator has the smallest variance among all unbiased estimators. In other words, it achieves the best precision for a given sample size.

Asymptotic normality refers to the property that the sampling distribution of the estimator approaches a normal distribution as the sample size increases. This property allows for the application of various statistical inference techniques, such as hypothesis testing and confidence interval estimation.

In summary, finite sample properties describe the behavior of estimators in a specific sample size, while large sample properties focus on the behavior of estimators as the sample size becomes large. Large sample properties provide valuable insights into the long-term behavior of estimators, allowing for more robust statistical inference.

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Answer:

1. 12

2. 0

3. 9

Step-by-step explanation:

The equation typically used for modeling population growth is the logistic growth equation.

To provide a comprehensive answer, I would need the specific equation you are referring to in relation to population dynamics. The equation typically used for modeling population growth is the logistic growth equation, which is commonly written as:

dP/dt = rP(1 - P/K),

where:

dP/dt represents the rate of change of the population over time,

r is the intrinsic growth rate of the population,

P is the population size at a given time,

K is the carrying capacity, which represents the maximum population size that can be sustained by the environment.

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Answer:

30 cents

Step-by-step explanation:

24=1.20

6=x

Algebra here to solve.

1.20=24

x=6

Divide by 4

1.20÷4=$0.3

$0.3=30 cents