Are of the square is 49 sq. ft
Find the value of x.

Answer:

B) 4%

Step-by-step explanation:

The total is

.8 + 4 + .2 = 5

[tex]\frac{r}{t}[/tex] = [tex]\frac{.2}{5}[/tex] = 0.04 = 4%  To change a decimal to a percent multiply by 100%

The 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

It is given to us that -

Numbers of items produced per hour by machine a and by machine b are normally distributed

There is a standard deviation of 8.4 items for machine a and a standard deviation of 11.3 items for machine b

The mean hourly amount produced by machine a for a random sample of 40 hours was 130 units

The mean hourly amount produced by machine b for a random sample of 36 hours was 120 units

We have to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines.

Let us say that -

x = Number of units of machine a

y = Number of units of machine b

According to the given information, we have

Number of units of machine a = x⁻ = 130

Standard deviation of machine a = σx = 8.4

Number of hours of machine a = [tex]n_{x}[/tex] = 40

Similarly,

Number of units of machine b = y⁻ = 120

Standard deviation of machine b = σy = 11.3

Number of hours of machine a = [tex]n_{y}[/tex] = 36

We know that mean of the differences can be find out as -

d⁻ = x⁻ - y⁻

=> d⁻ = 130 - 120

=> d⁻ = 10

In order to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines, we have to make use of the formula mentioned below -

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]  ---- (1)

From the z-score table, for a 95% confidence interval, we have -

α = 0.05

α/2 = 0.025

=> F(z) = 1 - α/2 = 1 - 0.025 = 0.975

For a z-distribution function of 0.975, we have -

[tex]z_{a/2}[/tex] = 1.96

Substituting all the values in equation (1), we have

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]

=> [tex]10-1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-1.96\sqrt{1.764+3.54 }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-(1.96 * 2.303)[/tex] < μd < [tex]10+(1.96 * 2.303)[/tex]

=> 10 - 4.516 < μd < 10 + 4.516

=> 5.483 < μd < 14.516

=> μd = 10 ± 4.516

Thus, the 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

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The p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year is 0.0060 and the value of test statistic is - 2.51

54% of business owners gave a holiday gift to their employees. a survey of business owners conducted this year indicates that 32 of them plan to provide a holiday gift to their employees.

The survey results are based on a sample of 80 business owners

We need to find the value of test statistic.

Expected number = np  = 32

80 x p = 32

p = 0.4

This is a left tailed test

test statistic is (p^ - p)/√(pq/n)

= (0.40 - 0.54)/√(.54 - (1 - 0.54) / 80)

= 0.14/√((0.54 - 0.46)/80)

= -2.51

p value = P(z < - 2.51)

= 0.00060366

= 0. 0060

Therefore, the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year is 0.0060 and the value of test statistic is - 2.51

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Answer:

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

Calculate it from end to start.

Before guard 3 he had:

Before guard 2 he had:

Before guard 1 he had:

This is the number of plants stolen.

q = 40 is the value of q in quadratic equation.

What is quadratic equation explain?

The equation x ax2+bx+c=0 is a quadratic equation, which is a second-order polynomial equation in a single variable. with a ≠ 0 .

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial equation. The answer could be simple or complicated.

the roots of a quadratic expression

             ax² + bx + c = 0

Since x' and x'' are the roots of this equation, then we can write the Vieta's formula

                 x' + x'' = -b/a

               x' * x'' = c/a

let's replace the 2nd equation of the Vieta's formula by that and make it a Linear System.

                  x' + x'' =  14/1

                 x' * x'' = 6

after solve the equations

               x' = 10

Solving the  equations

       10 + x''=14

           x'' = 4

Since we have a=1

   x^2-14x + q = 0

      Then we can make q as the parameter c.

    q = x' * x'' = 4 * 10 ⇒ 40      

x2−14x+ 40 = 0

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The complete question is -

The difference between the roots of the quadratic equation x2−14x+q=0 is 6. Find q.

As the tree grows 1& 3/4 feet per year, it will take 9 years to reach a height of 37 feet.

Division is a basic procedure in which an integer is divided. It's best to imagine of it as a number of things being distributed among a particular number of persons, such as in the previous example. In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 implies dividing 15 into three equal groups of five. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The dividend is the number that is being divided in this case. The divisor is the number, which divides the number (dividend) into equal parts.

Here,

37 - 21 and 1/4 = 36 and 4/4 - 21 and 1/4 = 15 and 3/4 = 63/4

63/4 divided by 1 and 3/4 = 63/4  divided by 7/4 = 63/4 * 4/7 = 9 years

It will take 9 years to reach at the height of 37 feet as the tree grow 1& 3/4 feet per year.

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Complete question:

A tree grow 1& 3/4 feet per year. How long will it take the tree to grow from a height of 21 & 1/4 feet to a height of 37 feet?

The value of ∠WXY = 20.

What is Exterior angle theorem?

The exterior angle theorem describes the connection between the two remote angles in a triangle and the external angle created by an extended side outside the triangle.

Given: Measure of angle YWX = (3x + 17) °

Measure of angle WXY = (3x + 2) °

Measure of angle XYZ = (10x − 5) °

Therefore, m∠XYZ = m∠YWX + m∠WXY (exterior angle theorem)

⇒ (10x − 5) ° = (3x + 17) ° + (3x + 2) °

Solve for x,

⇒ 10x - 5 = 3x + 17 + 3x + 2

⇒ 10x - 6x = 17 + 7

⇒ 4x = 24

⇒ x = 6

∴ ∠WXY = (3x + 2) = 18 + 2 = 20

Hence, value of ∠WXY = 20.

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Answer:

question 1: T
question 2: F
question 3: C

Step-by-step explanation:

Answer:

1. True

2. False

3. D. {2,4,9,16}

Step-by-step explanation:

⭐What is a function?

Therefore, #1 is a function because for every x-value, there is 1 y-value.

Therefore, #2 is NOT a function because 6 has 2 y-values, and 12 has 2 y-values.

⭐What is the range of a function?

Therefore, {2,4,9,16} is the range of #3 because it lists all of the y-values in ascending order.

Answer:

the range of the function y = -3/4x + 3/2 when the domain is {-6,-2,6} is {15/4, 3, -3/4}. The range is the set of all possible values of y for x in the given domain, which includes the values 15/4, 3, and -3/4.

Step-by-step explanation:

The range of a function is the set of all possible values of the output (y) for a given set of inputs (x). To determine the range of the function y = -3/4x + 3/2 when the domain is {-6,-2,6}, you can plug in each value from the domain into the function and solve for y.

When x = -6, y = (-3/4)(-6) + 3/2 = 9/4 + 3/2 = 15/4.

When x = -2, y = (-3/4)(-2) + 3/2 = 3/2 + 3/2 = 3.

When x = 6, y = (-3/4)(6) + 3/2 = -9/4 + 3/2 = -3/4.

The given statement "the coefficients of dummy variables in multiple regression models must always be positive." is True.

Regression model:

In statistics, regression model means a statistical technique that relates a dependent variable to one or more independent variables.

Given,

Here we have the statement the coefficients of dummy variables in multiple regression models must always be positive.

Now, we have to find whether the given statement is true or not.

In order to find the statement creditability, we must know the definition of the terms coefficient and dummy variables.

Dummy variable refers the variable that takes values of 0 and 1, where the values indicate the presence or absence of something

Where as the coefficient means a number or symbol by which another number or symbol is multiplied.

Based on this definition we have found that the given statement is true.

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The correct option A: graph A, shows the logarithmic function;

f(x) = log₃x + 1

f(x) = log₃x + 1

f(1) = log₃1 + 1

f(1) = 0 + 1

f(1) = 1

(1, 1)

f(3) = log₃3 + 1

f(3) = 1 + 1

f(3) = 2

(3, 2)

Thus, the graph must contain the points   (1, 1), (3, 2).

Therefore, graph A define the given logarithmic function;

f(x) = log₃x + 1.

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Answer: 25 cars

Step-by-step explanation:

Take 10 divided by 8 = 1.25 car per men

Then take 1.25 times 20 = 25 cars

The difference between 5 hundreds 6 tens and 4 ones is the value of zeros after 1.

Each digit in a number has a unique place and value. A number might contain multiple digits. The first digit will be at the ones place, the second digit at the tens place, and the third digit at the hundreds place, starting from the right.

There are 10 tens in hundred.

5 hundreds= 5*100

6 tens =6*10

4 ones= 4*1

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The difference between 5 hundreds 6 tens and 4 ones is the value of zeros after 1.

Explain hundred, tens and ones.

Hundred, tens, and ones are a way of representing numbers in base 10. This means there are ten digits (0-9) used to represent all numbers. When counting in hundreds, tens, and ones, the number 100 is the largest number represented with one digit, followed by the numbers from 101 to 199. Tens are represented with two digits, such as 20, 30, 40, 50, and so on. Ones are single digits, such as 1, 2, 3, 4, and so on. This system of counting is used to represent all numbers, no matter how large or small.

How many tens are in hundred?
There are 10 tens in hundred.
5 hundreds= 5*100
6 tens =6*10
4 ones= 4*1

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The  probability that between 78% and 86% were non-teacher workers from private schools is 0.7689

Eighty-four percent of non-teacher workers were employed in private schools.

p = 0.84

q = 1 - p = 1 - 0.84 = 0.16

if a random sample of 200 non-teacher workers from private schools was selected

We need to find the  probability that between 78% and 86% were non-teacher workers from private schools.

n = 200

μρ = 0.84

αp = √(p(1 - p)/n) = √(0.84(0.16)/200) = 0.026

P(0.78 < P < 0.86) = P((0.78 - 0.84)/0.026 < (p - μp)/σp < (0.86 - 0.84)/0.026)

= P(-2.31 < z < 0.77)

= P(z < 0.77) - P(z < -2.31)

using z table

0.7794 - 0.0103

= 0.7689

Therefore, the  probability that between 78% and 86% were non-teacher workers from private schools is 0.7689.

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The given situation can be represented in inequality as t ≤ 45 °F.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, we are instructed to use t to denote the refrigerator's temperature (in°F).

Additionally, we are informed that the lab refrigerator's maximum temperature is 45 °F.

It must be either lower than or equal to 45 °F for the temperature inside the refrigerator to be no higher than that.

As a result, t must be lower than or equal to 45 °F.

Therefore, it can be expressed as inequality as follows:

t ≤ 45 °F

Therefore, the given situation can be represented in inequality as t ≤ 45 °F.

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Complete question:
The temperature inside the lab refrigerator is at most 35 Fahrenheit used to represent the temperature in Fahrenheit of the refrigerator in inequality.

The value of x is 23.22°. By using the Cosine rule

The Cosine Rule of trigonometry states that the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle included between them. The Law of cosines and Cosine Formula are other names for the cosine rule.

The expression for representing cosine rule is expressed as:

c² = a² + b² - 2ab cos C

Given,

a = 26

b = 50

c = 29

Substituting the value to the equation:

c² = a² + b² - 2ab cos C

29² = 26² + 50² - 2(26)(50) cos C

841 = 676 + 2500 - 2600cosC

2335 =2600cos C

cos C = [tex]\frac{2335}{2660}[/tex]

C = 23.22°

The value of x is 23.22°

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Answer: 23.2 rounded to nearest tenth

Step-by-step explanation:

a. The polynomials are given as follows:

1. 2x^4 + 18x³ - 4.

2. -8x³ + 4x + 2.

3. 2x² - x - 10

4. 3x³ + 10x² + 9x + 2.

b. The resulting degrees are given as follows:

1. 4.

2. 3.

3. 2.

4. 3.

c. The end behavior of each polynomial is given as follows:

1. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.

2. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> -∞.

3. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.

4. As x -> -∞, f(x) -> -∞, as x -> ∞, f(x) -> ∞.

The polynomials are obtained doing the operations and then combining the like terms.

Hence:

(6x³ + 3x² - 4) + (2x^4 - 3x² + 12x³)

2x^4 + (6 + 12)x³ + (3 - 3)x² - 4.

2x^4 + 18x³ - 4.

(10 + 4x - 3x³) - (5x³ + 8)

10 + 4x - 3x³ - 5x³ - 8

-8x³ + 4x + 2.

(x + 2)(2x - 5)

2x² - 5x + 4x - 10

2x² - x - 10

(x + 2)(3x² + 4x + 1)

3x³ + 4x² + x + 6x² + 8x + 2

3x³ + 10x² + 9x + 2.

The degree of a polynomial is given by the highest exponent in it's equation.

The end behavior of a polynomial is calculated as the result of elevating negative infinity and then positive infinity to the highest exponent of the polynomial, considering the leading coefficient.

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The common ratio of the geometric sequence will be negative 2.

Given that:

Geometric sequence: 17, -34, -68, .....

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The common ratio of the geometric sequence is calculated as,

r = (-34) / (17)

r = - 2

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On solving thr provided question, by help of arithmetic progression, we got to know that a10 = 207

There are two approaches to define arithmetic progressions (AP):

The difference between any two successive terms in an arithmetic sequence must always be equal, and it is sometimes referred to as a series in which all terms except the first are created by adding a predetermined number to the preceding term.

9,15,25..............

15-9 = 6

25-15 = 10

a4 - 25 = 14 => a4 = 39

a5-39 = 18 => a5 = 57

a6-57 = 22 => a6 79

...

...

...

...

...

a10 - 169 = 38 => a10 = 207

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91 as a product of its prime factors will be 7 and 13.

The highest common factor of 91 and 130 is 13.

The process of factorization simony has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.

The factor of 91 include 1, 7, 13 and 91

The factor of 130 include 1, 2, 5, 10, 13 65, and 130.

The highest factor is 13.

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Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:

The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).

The graph of the inverse function is a reflection in the line y = x.

Therefore, the endpoints of the inverse function are:

The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).The graph of the inverse function is a reflection in the line y = x.Therefore, the endpoints of the inverse function are:(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Step-by-step explanation:

The absolute value of the complex number - 3 + 2i is √13 plotted on the z plane(a + ib).

As the name suggests it is a combination of real numbers and imaginary numbers.

A complex number (a + ib) where a is the real part and b is the imaginary part.

'i' here is called iota and i = √-1, i² = - 1, i³ = - i and i⁴ = 1.

We know the absolute value or magnitude of a complex number

z = a + ib is | z | = [tex]\sqrt{a^2+b^2[/tex].

∴ The absolute value of z = -3 + 2i is,

| z | = [tex]\sqrt{(-3)^2 + (2)^2[/tex].

| z | = [tex]\sqrt{13}[/tex].

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Answer:

y = - 8x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 8 and c = 5 , then

y = - 8x + 5 ← equation of line

The independent variables, the ones that are intentionally manipulated, are temperature and surface time.

The dependent variable, the one that you measure the response in, is the reaction time.

The physical concept of temperature indicates in the numerical form how hot or cold something is. Temperature is measured with a thermometer.

Thermometers are calibrated in numerous temperature scales that historically have depended on various reference factors and thermometric materials for definition. The most common scales are the Celsius scale with the unit image °C (previously referred to as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (okay), the latter being used predominantly for clinical functions. The kelvin is one of the seven base units within the worldwide machine of gadgets (SI).

Absolute zero, i.e. 0 kelvin or −273.15 °C, is the bottom factor within the thermodynamic temperature scale. Experimentally, it can be approached simplest very intently, however, no longer genuinely reached, as diagnosed in the 0.33 law of thermodynamics. it'd be not possible to extract power as the warmth from a body at that temperature.

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The coordinates of the end point of the line AC is C(8.6) using the section formula.

For the given question,

The coordinates are-

The formula for the mid point using the section formula is-

x(m) = x2 + x1 / 2

5 = m + 2 / 2

10 = m + 2

m = 8

y(m) = y2 + y1 / 2

0 = n - 6/ 2

0 = n -6

n = 6

Thus, the coordinates of the end point of the line AC is C(8.6) using the section formula.

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The complete question is-

Segment AC is bounded by points A(2, -6) and C(m,n). If points (5,0) is the mid point of the segment AC, find the coordinates of the point C.

The snow level at 8 a.m., when x = 8, was 30cm.

The simplest equation for expressing and resolving an unknown number is a linear equation in one variable. It is usually a straight line and is easily pictorial portrayed. A simple way to convey a mathematical assertion is with a linear equation. Unknown numbers can be represented by any variable or symbol. There are several easy ways to solve a linear equation.

y = 2x + 14.

Here, y is the amount of snow in inches, and x is the number of hours after midnight

To find the snow level at 8 a.m. we take the value of x = 8.

⇒ y = 2*8 + 14

⇒ y = 16 + 14

⇒ y = 30cm

So, The snow level at 8 a.m., when x = 8, was 30cm.

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this question is incomplete. The complete question is

the snow level is modeled by the function y = 2x + 14. Here, y is the amount of snow in inches, and x is the number of hours after midnight (x = 0). 10. What was the snow level at 8 a.m., when x = 8?

Answer: x=500,000

Step-by-step explanation:

60,000=.12x

60,000/.12=x/.12

500,000=x

The slope and y-intercept of the linear function are -5 and 7 respectively.

Linear functions are those whose graph is a straight line. In other words, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line.

A linear function has one independent variable and one dependent variable.

A linear function has the following form. y = mx + b.

where

Therefore, let's find the slope of the function.

slope = m = Δy / Δx

using (0, 7) and (4, -13)

slope = m = -13 - 7 / 4 - 0

slope = - 20 / 4

slope = -5

Let's find the y-intercept using (0, 7).

y = -5x + b

7 = -5(0) + b

b = y-intercept = 7

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Considering the expression of a line, the y intercept has a value of 3.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷(x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)=(2,15) and (x₂, y₂)=(6,39), the slope m can be calculated as:

m= (39 - 15)÷(6 - 2)

m= 24÷ 4

m= 6

Considering point 1 and the slope m, you obtain:

15= 6×2 + b

15= 12 +b

15 - 12= b

3=b

Finally, the value of the y intercept is 3.

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The given equation is a linear equation.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

g(x) = 1/3x - 6

We need to identify whether the given equation is Linear, Quadratic, Exponential, or None and why.

g(x) is the term that shows the rate of change with respect to x.

1/3 is the coefficient of the variable x

and the 6 is the constant term in the equation.

so, comparing the given equation with standard form of linear equation,

y = mx + c.

we can say here,

y = g(x)

m = 1/3,

c = 6

Hence, the given equation is a linear equation.

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