This input-output table shows some values that satisfy the equation y = 4x + 21. Input (2) Output (y 2 29 37 5 [blank] 7 49 What number correctly fills in the blank in the table? Enter your answer as a number, like this: 42 ​

Area of the rectangle is 36x⁴y⁶ feet square

Given that;

Width of a rectangle = 4x³y feet

Length of the rectangle = 9xy⁵ feet

Find:

Area of the rectangle

Computation:

Area of the rectangle = (l)(b)

Area of the rectangle = (4x³y)(9xy⁵)

Area of the rectangle = 36x⁴y⁶ feet square

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Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

D: y= 10sin(\(\frac{\pi }{15}t\)) + 30

Step-by-step explanation:

30 feet above the ground is the k value.

10 feet long is how long the blades reach up and down which is also known as the amplitude.

The rest is given in all answers.

The volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.

It is defined as three-dimensional geometry that has six square faces and eight vertices.

We have a sphere with a 2-inch radius is packed in a cube so that all sided touch.

The volume of the sphere = (4πr³)/3 = (4π(2)³)/3 = 33.51 cubic inches

The side length of the cube = 4 inches

Because diameter of the sphere is 4 inches and all sided touch to the cube face.

Volume of the cube = 4³ = 64

The volume of the empty space = 64- 33.51 = 30.49 cubic inches

Thus, the volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.

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The percentage of yield after cleaning and trimming the celery is 75%.

Given, a bunch of celery is bought which weighs 16 ounces.

After cleaning and trimming the celery, you are left with 12 ounces.

let the x be the percentage yield.

Based on the conditions, formulate:

16 × x = 12

⇒ 16x = 12

⇒ x = 12/16

minimize the terms.

⇒ x = 3/4

to convert it into percentage, multiply by 100

⇒ x = 3/4 × 100

⇒ x = 75%

Hence the percentage of yield is 75%.

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Answer:

Consistent and independent

Step-by-step explanation:

The only touch at one point and they are not the same line and are not parallel

The process of enclosing the tens to form hundreds and writing the resulting number is called regrouping or carrying.

This involves taking the value of one or more digits in a number and carrying it over to the next place value. In this case, we are taking the tens digit and carrying it over to the hundreds place value, effectively regrouping the digits to form a new number. This process is commonly used in addition and subtraction when the sum or difference of two digits is greater than 9. By regrouping the digits, we can properly represent the total value of the numbers being added or subtracted.

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--The complete question is, What is the process of enclosing the tens to form hundreds and writing the resulting number called?--

Answer:

\( \sqrt[3]{8 + 6} = \sqrt[3]{14} \\ = 2.41\)

I hope I helped you^_^

The 0.0099 proportion of electric tooth brush prices are between 104.6 dollars and 108.2 dollers. It can be obtained by Z score table and Z score formula.

What is the formula of Z score?

The Z score is given by the following expression:

\(Z=\frac{x-\mu}{\sigma}\)

Here, Z is the Z score, x is the observed value, \(\mu\) is the mean, and \(\sigma\) is the standered deviation.

We need to watch the negative Z score if we want the proportion of students less than the observed value and we need to watch the positive Z score if we want the proportion of students more than the observed value.

Substitute 104.6 for x, 87 for \(\mu\), and 10 for \(\sigma\) in the above equation.

\(Z_1=\frac{104.6-87}{8}\\=2.2\)

Since we need to find the proportion of electric toothbrush price lower than 104.6 doller hence, watch the value of  z score 2.2 in the z table. Watch the value in frunt of 2.2 and below 0.00. It is 0.9861.

Substitute 108.20 for x, 87 for \(\mu\), and 10 for \(\sigma\) in the above equation.

\(Z_2=\frac{108.20-87}{8}\\=2.65\)

Since we need to find the proportion of electric toothbrush price lower than 108.20 doller hence, watch the value of  z score 2.65 in the z table. Watch the value in frunt of 2.6 and below 0.05. It is 0.9960.

Now, to find the proportion of elecric toothbrush prices between 104.60 and 108.20 doller, subtract \(Z_1\)  from \(Z_2\).

P(104.60<x<108.20) = \(Z_2-Z_1=0.9960-0.9861\\=0.0099\)

Hence, the proportion of electric toothbrush price between 104.60 doller and 108.20 doller is 0.0099.

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Mean = 13

Variance = 36.2

A right trapezoid is a quadrilateral that has exactly one pair of perpendicular lines, one pair of parallel sides, and no sides with equal lengths.

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are trapezium, square, rectangle and so on.

A right trapezoid is a quadrilateral that has exactly one pair of perpendicular lines, one pair of parallel sides, and no sides with equal lengths.

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The kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.

A polynomial equation is a sum of constants and variables. A polynomial is an expression consisting of indeterminate's (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

For the given situation,

The equation \(f(x) = x^3 - x^2 - x + 1\)

The roots of the polynomial equation can be found as follows,

Step 1:

Substitute the value of x in which the equation f(x) equals zero.

⇒ Put \(x = 1\), the equation becomes

⇒ \(f(1) = 1^3 - 1^2 - 1 + 1\)

⇒ \(f(1) = 0\)

Thus \((x - 1)\) is the one root of the equation.

Step 2:

The other roots can be found by framing the quadratic equation on dividing the equation \(f(x) = x^3 - x^2 - x + 1\) by \((x - 1)\)

On dividing \(f(x) = x^3 - x^2 - x + 1\) by \((x - 1)\) we get the quotient,

⇒ \((x^{2} -1)\)

Step 3:

Now factorize the quadratic equation, \((x^{2} -1)\)

It can be expand using the identity,

⇒ \((x^{2} -1^{2} ) = (x+1)(x-1)\)            [∵ (a^2 - b^2) = (a+b)(a-b) ]

Thus the factors of the equation are \((x-1)(x+1)(x-1)\). So the roots are \(1,-1,1\).

Hence we can conclude that the kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.

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The upper value for the range within which the middle 90% of all sample averages of resignations per week of casual staff should lie is approximately 34.55 resignations per week.

To determine the range within which the middle 90% of all sample averages of resignations per week of casual staff should lie, we can use the Central Limit Theorem and the properties of the normal distribution.

The Central Limit Theorem states that the distribution of sample averages approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. In this case, the sample size is 52, which is considered large enough for the Central Limit Theorem to apply.

Given that the population mean is 33.0 resignations per week and the variance is 46.2 resignations per week squared, we can calculate the standard deviation (σ) by taking the square root of the variance: σ = √46.2 ≈ 6.79.

Since we are looking for the middle 90% of the sample averages, we need to find the z-scores corresponding to the lower and upper ends of the middle 90% (5% on each tail). Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to a 5% tail is approximately 1.645.

To find the upper value for the range, we can use the formula:

Upper Value = sample mean + (z-score * standard deviation / √sample size)

Upper Value = 33.0 + (1.645 * 6.79 / √52) ≈ 33.0 + (1.645 * 0.944) ≈ 33.0 + 1.554 ≈ 34.55 (rounded to 2 decimal places).

Therefore, the upper value for the range within which the middle 90% of all sample averages of resignations per week of casual staff should lie is approximately 34.55 resignations per week.

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Answer:

yes, yes, yes, no, yes

Step-by-step explanation:

Answer:

i got 16.25=2

Step-by-step explanation:

Answer:

X = - 12.8

Step-by-step explanation:

To use traces to sketch the surface x = 5y^2 − 5z^2, we can fix one of the variables and plot the resulting curve in the remaining two variables.

For example, when we fix x to a constant value, say x = 0, we get 0 = 5y^2 − 5z^2, which simplifies to y^2 - z^2 = 0. This equation represents two intersecting planes: y = z and y = -z.

Similarly, when we fix y or z to a constant value, we get other traces that can help us sketch the surface. For instance, fixing y = 0 gives us x = -5z^2, which is a downward opening parabola in the z-x plane. Fixing z = 0 gives us x = 5y^2, which is an upward opening parabola in the y-x plane.

By plotting these traces and connecting them appropriately, we can sketch the surface of the equation x = 5y^2 − 5z^2 in three-dimensional space.

To sketch the surface x = 5y² - 5z² using traces, follow these steps:

1. Find the traces for the x-y, x-z, and y-z planes.

x-y plane (z = 0):
x = 5y² - 5(0)²
x = 5y²

x-z plane (y = 0):
x = 5(0)² - 5z²
x = -5z²

y-z plane (x = 0):
0 = 5y² - 5z²

2. Sketch the traces for each plane.

x-y plane: This is a parabola opening in the x direction with the vertex at the origin (0, 0, 0).

x-z plane: This is a parabola opening in the negative x direction with the vertex at the origin (0, 0, 0).

y-z plane: This is a hyperbola, as we can rewrite the equation as y² - z² = 0 or y²/z² = 1. It opens along the y and z axes and passes through the origin (0, 0, 0).

3. Combine the traces to sketch the surface.

The surface is a hyperbolic paraboloid, as it is a combination of the parabolic traces from the x-y and x-z planes and the hyperbolic trace from the y-z plane. The vertex of the hyperbolic paraboloid is at the origin (0, 0, 0), with the parabolic branches opening in the x direction and the hyperbolic branches opening along the y and z axes.

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Answer is given below :

Step-by-step explanation:

Answer:

the correct answer is D. 145.8

The probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We can use the central limit theorem to approximate the distribution of the sample mean. According to the central limit theorem, if the sample size is sufficiently large, the distribution of the sample mean will be approximately normal with a mean of 30,641 and a standard deviation of sqrt(variance/sample size).

So, we have:

mean = 30,641

variance = 14,561,860

sample size = 242

standard deviation = sqrt(variance/sample size) = sqrt(14,561,860/242) = 635.14

Now, we need to calculate the z-score corresponding to a sample mean of 31,358 miles:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

= (31,358 - 30,641) / (635.14 / sqrt(242))

= 2.43

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 2.43. The probability is approximately 0.9925.

Therefore, the probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

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Answer:

yass dude lets go

Answer:

Yo, thats one of my fav games...

ur sus

LOL

The half of the time that Arnold skied without falling is 712 as 2 x 356=712>223 .

Inequality is a mathematical statement that illustrates the connection between two expressions by using the inequality symbol. The phrases on both sides of an inequality sign are distinct. It indicates that the left expression should be larger or smaller than the right expression, or vice versa. When the link between two algebraic expressions is expressed using inequality symbols, literal inequalities arise.

The discrepancy represents the incident in which Kelvin skied for more than twice as long as anybody else in his family:

2f < 223

Here 223 is the time for Kelvin.

Check for Lori as follows:

2f < 223

2 x 55=110 < 223

Kelvin skied without falling more than twice as long as Lori.

Check for Vanessa as follows:

2f < 223

2 x 265=530>223

Check for Arnold as follows:

2f < 223

2 x 356=712>223

Kelvin skied without falling less than twice as long as Arnold.

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Complete question:

Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.

Lori 55

Vanessa 265

Devon 172

Celia 112

Arnold 356

Answer: Yes, the point (3,4) is a solution to the system.

===================================================

Proof of this:

Replace x with 3 and y with 4 in the first equation

x+y = 7

3+4 = 7

7 = 7

This confirms the first equation. Repeat for the second equation

x-2y = -5

3-2(4) = -5

3 - 8 = -5

-5 = -5

We get true equations for both when we plug in (x,y) = (3,4). This confirms it is a valid solution to the system of equations. It turns out it's the only solution to this system of equations. Visually, the two lines cross at the single location (3,4).

The correct statements regarding the domain and the range of the function in this problem are given as follows:

B. The domain is the set of all real numbers.

C. The range is the set of all real numbers.

The function in this problem is defined for all real values, and assumes all real values, hence options B and C are the correct options for this problem.

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Answer:

36 days

Step-by-step explanation:

The answer is the lcm of (9,12)=36 days

We have to find LCM of 9 and 12

2 | 9,12

2 | 9,6

3 | 9,3

3 | 3,1

LCM=2×2×3×3=4×9=36

Today is 36 th day

Answer:

1.9x+3.7

Step-by-step explanation:

Combine like terms

3.6x + (-1.7x)= 1.9x

5.9 - 2.2= 3.7

Hence, 1.9x + 3.7.

[RevyBreeze]

Answer:

1.9x+3.7

Step-by-step explanation:

start by combining like terms

(3.6x-1.7x)+(5.9-2.2)

1.9x+3.7

\(y=\dfrac{x-r}{x+r}\\\\y(x+r)=x-r\\xy+ry=x-r\\ry+r=x-xy\\r(y+1)=x-xy\\r=\dfrac{x-xy}{y+1}\)

Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Answer:  Selling price, x, = 8.3333 units

Step-by-step explanation:

We can find the vertex by one of two methods:

1)  Take the derivative of the equation and set it to zero.  The derivative gives us the slope at any point x.  The vertex has a slope of zero (it changes direction).

y=-6x^2 + 100x– 180

y' = -12x + 100

0 = -12x + 100

12x = 100

x = 8.333

2) Graph the function and locate the vertex.  Attached.

The vertex of the parabola is (8.33, 236.66).

A plane curve produced by a moving point such that its separation from a fixed point equals that of a fixed line is a parabola.

Given, the expression;

y = -6x² +100x - 180,

where x = selling price of each soccer ball and y = daily profit from soccer balls.

A parabola's vertex is the location where its symmetry line and parabola intersect.

To find the vertex of a parabola:

Step  1: Compare the equation of the parabola with the standard form

y = ax² + bx + c.

By comparing,

y = -6x² +100x - 180 with the above equation, a = -6, b = 100, and c =-180.

Step - 2: Find the x-coordinate of the vertex using the formula,

h = -b/2a

Then we get,

h = -(100) / (2 × -6)

h = 8.33

Step - 3: To find the y-coordinate (k) of the vertex,

substitute x = h in the expression, y = -6x² +100x - 180.

Then k = -6(8.33 x 8.33) + 100(8.33) -180

k = 236.66

Step - 4: Write the vertex (h, k) as an ordered pair.

The vertex = (h, k) = (8.33, 236.66).

Therefore, (8.33, 236.66) is the vertex of the parabola.

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