Express the gross salary g of a person who earns per hour as a function of the number x of hours worked.

Answer:

The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 1 oz. Using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard

Step-by-step explanation:

bran leist ple

Answer:

1954

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ²:

\(\boxed{X \sim \textsf{N}(\mu,\sigma^2)}\)

Given:

First find the probability that the weight of an orange is less than 5 oz.

\(\text{If \;$X \sim \textsf{N}(4,0.5^2)$,\;\;find\;\;P$(X < 5)$}.\)

Method 1

Using a calculator:

\(\implies \text{P}(X < 5)=0.977249868\)

Method 2

Converting to the z-distribution.

\(\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}\)

\(x=5 \implies Z=\dfrac{5-4}{0.5}=2\)

Using the z-tables for the probability:

\(\implies \text{P}(Z < 2)=0.9772\)

To find the expected number of oranges that will weigh less than 5 oz from a batch of 2000, multiply the total number of oranges by the probability calculated:

\(\begin{aligned}2000 \times \text{P}(X < 5)&=2000 \times 0.977249868\\&=1954.499736\\&=1954\end{aligned}\)

Therefore, 1954 oranges would be expected to weigh less than 5 oz.                                

Answer:

circumference of the circle =60.28

3x - 14 here, 2x + 10 here. Consequently, X has a value of 14. In algebra, the letter "x" is frequently used to denote a value that is still unknown. It is referred to as a "variable" or "unknown" at times.

In algebra, the letter "x" is frequently used to denote a value that is still unknown. The term "variable" or "unknown" is used to describe it. x in x+2=7 is a variable. Not only can a variable be "y," "w," or any other letter, name, or symbol, it can also be "x." Examine: Variable

Bring the variable to one side of the equation, and then move all the other values to the other side by performing arithmetic operations on both sides of the equation to find the value of x. To determine the answer, simplify the values.

An experiment's independent variable is a variable that stands in for a variable that is being altered. In equations, the independent variable is frequently denoted by the variable x. X is the variable here.

\($$3 x-14-(2 x)=0$$\\\)

We shift every term to the left:

\($3 x-14-(2 x)=0$\)

We combine all the numbers and all the variables.

\($$x-14=0$$\)

All terms containing x are shifted to the left, and all other terms are shifted to the right.

\($$x=14$$\)

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In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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Answer:

14

Hope it helped!

Answer:

19y/2 + 7y2

Step-by-step explanation:

Answer:

Step-by-step explanation:

( B ) . No; the input value x = - 5 pairs with two output values.

The mapping relation does not represent a function as the input value of x = -5 pairs with two output values.

A function is a relation between a dependent and a non - independent variable such that the value of dependent variable depends on the independent ones.

Given is a mapping diagram between two variables x and y.

From the mapping diagram, we can see that for one value of x, there are two values of y. If a relation is to be called a function, then multiple values of x can have same y value but for a unique value of x there should be a unique value of variable y. Hence, the given mapping does not represent a function.

Therefore, the mapping relation does not represent a function as the input value of x = -5 pairs with two output values.

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Answer:

h = 1200 - 34t

Step-by-step explanation:

25 minutes, descend 850 feet, so each minute, descend 850/25 = 34 feet

after t minutes, descend 34*t feet,

starting at 1200 feet, so the height is h = 1200 - 34t

Answer:

y < 25x , or y = kx { where k < 25 } , or choosing a time saving worker {as fee is in terms of hours}

Step-by-step explanation:

Services cost : y = 25x , where y is the total fee and x is the number of hours worked.

If customer is looking to choose the less expensive cleaning service ; he / she has following options -

Answer:

720 degrees

Step-by-step explanation:

sum of interior angles of any polygon is given by the equation

\(sum \: = (n - 2) \times 180\)

where n is the number of sides of the polygon. in the question the polygon has 6 sides. hence n = 6 and

\(sum \: = (6 - 2) \times 180 \\ = 4 \times 180 \\ = 720 \: degrees\)

Answer:

Y=3

3^3=27

Step-by-step explanation:

Answer:

If you simplify this it would become Y time Y times Y = 27. Y is a variable meaning it can be any number. In this case Y is 3 because, 3x3x3 = 27.

Step-by-step explanation:

Answer:

What is the sum equal to?

Step-by-step explanation:

Answer:

6x − 20y

Step-by-step explanation:

−2[−3(x − 2y) + 4y] =

= −2[−3x + 6y + 4y]

= −2[−3x + 10y]

= 6x − 20y

Answer:

Step-by-step explanation:

Here you go mate

PEDMAS:

Parenthesis

Exponent

Multiplication

Addition

Subtraction

Step 1

−2[−3(x − 2y) + 4y]  Equation

Step 2

-2[-3(x -2y) + 4y]  simplify

(-2)(-3(x-2y))+(-2)(4y)

Step 3

(-2)(-3(x-2y))+(-2)(4y)   Add,Subtract And Remove parenthesis

6x-12y-8y

answer

6x-20y

Answer:

Average speed of Aouita = 6.68 meter per second.

Step-by-step explanation:

To create a world record Aouita ran a distance = 3000 m

He took the time to cover this distance = 7 minutes 29.45 seconds

                                                                 = (7×60) + 29.45 seconds

                                                                 = 449.45 seconds

Since, formula for the average speed is given by,

Average speed = \(\frac{\text{Total distance covered}}{\text{Total time taken}}\)

Therefor, average speed of Aouita = \(\frac{3000}{449.45}\)

                                                          = 6.675

                                                          ≈ 6.68 meter per second

Average speed of Aouita was 6.68 meter per second.

Answer:

6.67 m/s

Step-by-step explanation:

7 * 60 = 420

420 + 29.45 = 449.45

V = 3000. / 449.45= 6.67 m/s

Answer: c=−ax^2−bx+y

Step-by-step explanation:

Answer: a= \(\frac{-bx-c+y}{x^{2} }\)

Step-by-step explanation: Step 1: Flip the equation.

ax²+bx+c=y

Step 2: Add -bx to both sides.

ax²+bx+c+−bx=y+−bx

ax²+c=−bx+y

Step 3: Add -c to both sides.

ax²+c+−c=−bx+y+−c

ax²=−bx−c+y

Step 4: Divide both sides by x^2.

\(\frac{ax^{2} }{x^{2} }\) = \(\frac{-bx-c+y}{x^{2} }\)

If I Helped, Please Mark Me As Brainliest, Have A Great Day :D

Answer:

2/5

Step-by-step explanation:

Find two integer coordinate sets  ( use the two points labelled)

slope = m = (y1-y2)/(x1-x2) =

                = ( 1 - -1 ) / (3- - 2) = 2/5

  (NOTE: it does not matter which point you choose to be  x1,y1  or x2,y2 )

The equation of line that passes through (2,3) and (-2,5) is y  = (-1/2)x + 4.

The point-slope form is expressed as;

( y - y₁ ) = m( x - x₁ )

Where m is slope, x₁ and y₁ are the coordinates of the point .

Given the data in the question;

Point 1 (2,3)

Point 2 (-2,5)

First, determine the slope.

Slope m = (y₂ - y₁)/(x₂ - x₁)

Slope m = ( 5 - 3 ) / ( -2  - 2)

Slope m = 2 / -4

Slope m = -1/2

Plug the slope m = -1/2 and point (2,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/2)( x - 2 )

y - 3 = (-1/2)x - (-1/2)2

y - 3 = (-1/2)x + 1

y = (-1/2)x + 1 + 3

y  = (-1/2)x + 4

Therefore, the equation of the line is y = (-1/2)x + 4.

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Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

(-10,0)

Step-by-step explanation:

y = 3/2 x + 15

To find the x intercept let y =0 and solve for x

0 = 3/2x +15

Subtract 15 from each side

-15 = 3/2x -15+15

-15 = 3/2x

Multiply each side by 2/3

2/3 *-15 = 2/3 * 3/2x

-10 =x

The x intercept is

(-10,0)

Answer: (-10,0)

Step-by-step explanation:

For given data the scatterplot is shown below and the linear correlation coefficient is r = 0.4693

In this question we have been given a data.

We need to use a scatterplot and the linear correlation coefficient r to determine whether there is a correlation between the two variables.

Given data is:

x| 0.8 1.6 2.7 3.3 4.2 5.8 6.5 7 8.9 9.3 10.8 11.3 12.4 13.7 14.9

y| 3.8 1.9 12.6 9.4 8.2 7.1 4.1 0.1 11.9 13.3 14.1 8.5 9.6 7.4 14.1

The scatter plot for given data is as shown below.

An equation of the line of best fit is: y = 0.4623x + 4.9176

And the coefficient of correlation is:

r = √0.2202

r = 0.4693

Therefore, the scatterplot of given data is shown below.

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Answer:

x<2 or x>5

Step-by-step explanation:

3x+2<8 4x+4>24

4x>24-4

3x<8-2

4x>20

3x<6

x>5

x<2

Answer: x∈(-∞,2]U(5,∞)

Step-by-step explanation:

\(\displaystyle\\\left [ {{3x+2\leq 8} \atop {4x+4 > 24}} \right. \ \ \ \ \left [ {{3x\leq 6\ (1)} \atop {4x > 20}\ (2)} \right.\)

Divide both parts of the equation (1) by 3 and divide both parts of the equation (2) by 4:

\(\displaystyle\\\left [ {{x\leq 2} \atop {x > 5}} \right. \\\\Hence,\\\\x\in(-\infty,2]U(5,\infty)\)

Answer:

1

Step-by-step explanation:

2a-21 / b

2(4)-21/3

8-7=1

Answer:

1

Step-by-step explanation:

(FIRST THING FIRST REMEMBER PEMDAS)

First you rewrite the number sentence with the clues you got.

2 x 4 - 21 / 3

Then you do 2x4 to get 8, then you rewrite the # sentence again

8 - 21 / 3

Next you divide 21 / 3 to get 7 and rewrite the sentence again

8-7

FINALLY you subtract 8-7 to get 1

The area of the rectangular figure with two semicircles on the opposite side is  36.56 sq cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A rectangle with two semicircles on two opposite sides.

The length of the rectangle is 6cm and the width of the rectangle is 4cm.

The two given semicircles have a diameter of 4cm seems obvious.

∴ The area of the total figure is an area of the rectangle added to the area of 2 semicircles which makes up to a circle with a radius 2 cm.

∴ (4×6) + π(2)² sq cm.

= 24 + 4π sq cm.

= 24 + 12.56 sq cm.

= 36.56 sq cm.

The area which is not taken up in the rectangle and two circle questions are

(area of the rectangle - 2 times the area of a circle).

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The number of miles planned on Saturday is 19 milea

This means the sequence where the difference between one term and the next term is a constant.

In this case, the following information are illustrated:

Sunday: 1 miles

Monday: 4 miles

Tuesday: 7 miles

Wednesday : 10 miles

Thursday: 13 miles

Friday: 16 miles

As we can see there's a difference of three between them. This can be seen as:

= 4 miles - 1 mile

= 3 miles

Therefore, the number planned on Saturday will be:

= Friday + 3 miles

= 16 miles + 3 miles

= 19 miles

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Answer:

choice 1,2,4,5 from top to bottom

Step-by-step explanation:

1:the points given are in the line where both planes intersect

2:point H is not on any plane

3:in the diagram point F is on plane R so false

4:if you connect the points given they will intersect so not collinear

5:the points F and G are on the plane R

6:so F is on plane R but H is not on any do false

The value of the given limits \(\lim_{x \to \infty} 1/x^2\) is 0,\(\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}\) is 4  ,\(\lim_{x \to \pi} sinx\\\) is 0 and \(\lim_{x \to \55} e\) is e.

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

Because the value of that function at that point doesn't define.

a)

\(\lim_{x \to \infty} 1/x^2\) by substitute limit 1/∞² = 0

b)

\(\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}\) here (x² - 4)/(x - 2) = (x - 2)(x + 2)/(x - 2) = (x + 2)

Putting x = 2 will give the limit as 2 + 2 = 4.

c)

\(\lim_{x \to \pi} sinx\\\) herer put x to π so sinπ = 0.

c)

\(\lim_{x \to \55} e\) here no variable thus e will be the answer.

Hence "The value of \(\lim_{x \to \infty} 1/x^2\) is 0,\(\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}\) is 4  ,\(\lim_{x \to \pi} sinx\\\) is 0 and \(\lim_{x \to \55} e\) is e".

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Based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

To determine the distance between Houston, TX and Dallas, TX using the given scale, we can set up a proportion using the distances on the map and the actual distances.

Let's denote the distance between Houston and Dallas as "x" (in miles).

According to the scale provided, 2.3 centimeters on the map represents a distance of 348 miles. This can be expressed as:

2.3 cm / 348 miles = 1.6 cm / x miles

To find the value of "x," we can cross-multiply and solve the equation:

(2.3 cm) * (x miles) = (1.6 cm) * (348 miles)

2.3x = 556.8

Divide both sides by 2.3 to isolate "x":

x = 556.8 / 2.3

x ≈ 242.0869565

Therefore, based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

Please note that this is an approximation based on the given scale and the assumption that the scale is linear and consistent throughout the map. Actual distances may vary and should be verified using more accurate measurements or reliable sources.

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Answer:

6x^2 + 23x + 21

Step-by-step explanation:

3x+7 x 2x+3

= 3x(2x) + 3x(3) + 7(2x) + 7(3)

= 6x^2 + 9x + 14x + 21

= 6x^2 + 23x + 21