Directions: Based on the information given in the following problem, compute the gross pay.

Hours worked: 51

Overtime hours worked: 11

Regular rate of pay: $7.35 per hour

Round your answers to two decimal places.

gross pay: $

The slope of the line represented by the given data is; 1

The slope of a line is defined as the rate of change of y divided by the rate of change of x.

Thus, the formula to find the slope between two coordinates is;

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

Taking the last two coordinates gives us;

m = (16 - 13)/(7 - 3)

m = 3/3

m = 1

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Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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false :) thats ur answer

Answer:

To compare Bob and Alan's points per game, we can use the following summary statistics:

Mean: This is the average of the data set. It can be calculated by adding up all the values and dividing by the number of values.

Median: This is the middle value of the data set when it is arranged in order.

Range: This is the difference between the largest and smallest value in the data set.

Interquartile range (IQR): This is the range of the middle 50% of the data set, calculated as the difference between the 75th and 25th percentiles.

Mean absolute deviation (MAD): This is the average of the absolute differences between each value and the mean.

To compare the center of each player's data, the best measure of central tendency would be the mean. This is because it takes into account all the values in the data set and gives an overall average. The median can also be used, but it only considers the middle value and may not accurately represent the center if there are outliers in the data set.

To compare the spread of each player's data, the best measure of spread would be the range or IQR. This is because they give an idea of the range of values in the data set and how spread out the data is. The MAD can also be used, but it is a more complex calculation and may not provide as clear of an understanding of the spread of the data.

Based on the representations, summary statistics, and interpretations, it is not possible to determine if either friend is a basketball star without more context. A basketball star could have a high average points per game, a narrow range, and a small spread, but this would depend on the level of competition and the type of game being played. A player who consistently scores a high number of points and performs well under pressure could be considered a basketball star, but this cannot be determined solely based on the data presented.

given information are :- test mean () = 25.5 populace sd () = 5.3 example size (n) = 360 a).z critical value for 95% confidence level,

both followed tests be:- the 95% confidence interval for the mean load of every one of the one-year-old child young men in the US.

To get a 95% confidence interval, we should incorporate the focal 90% of the probability of the normal distribution. On the off chance that we incorporate the focal 90%, we leave out a sum of α = 10% in the two tails, or 5% in each tail, of the normal distribution.

To catch the focal 95%, we should go out 1.645 "standard deviations" on one or the other side of the determined example mean. The value 1.645 is the z-score from a standard normal probability distribution that puts an area of 0.90 in the middle, an area of 0.05 in the extreme left tail, and an area of 0.05 in the extreme right tail.

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The complete question is:

According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.

a. Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the United States

b. Should this confidence interval be used to estimate the mean weight of all one-year old babies in the United States? Explain.

c. Based on the confidence interval constructed in part (a), is it likely that the mean weight of all one-year-old boys is less than 28 pounds?

The linear function giving U.S. land-line phone households(in millions in year) is f(t) = 35 - 2t

The number of U.S. households with land-line phones stood at 35 million at the beginning of 2014 and was projected to decline at the rate of 2 million households per year for the next 8 years.

let t = 0 corresponds to the beginning of 2004.

so the linear function formed by this information.

f(t) = 35 - 2t

where t is number of years since 2014 and f(t) will be the number of land-line phone households (in millions in years) in that particular year.

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The value of x and y for the parallelogram PQRS is 2 and 5 respectively.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

The qualities of a parallelogram are shared by the shapes of a square and a rectangle.

PT=​y, TR=2x+​1, QT=45y, TS=7x+11

The diagonals of a parallelogram bisect each other:

So, PT = TR and QT = TS

Thus, the system of equation is:

y = 2x+1  

5y = 7x+11

Multiply the first equation by 5:

5y = 10x+5  

Set the two equations as equal:

10x + 5 = 7x + 11

Subtract 7x from each side.

10x + 5 -7x = 7x + 11 -7x

3x + 5 = 11

Subtract 5 from both sides:

3x + 5 - 5 = 11 - 5

3x = 6

x = 2

Now solve for y:

y = 2x+1

y =2(2)+1

y =5

Hence, the value of x and y for the parallelogram PQRS is 2 and 5 respectively.

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The plane is 361.99 miles from its starting point on a bearing of 147.72 degrees from due north.

To calculate the distance travelled by plane, we can use the formula:

distance = speed x time

First, let's calculate the distance travelled from point A to B:

distance = 110 mph x 1.6 hours = 176 miles

Next, let's calculate the distance travelled from point B to C:

distance = 110 mph x 2.9 hours = 319 miles

To calculate the total distance from the starting point, we need to find the hypotenuse of the triangle formed by points A, B, and C. To do this, we need to utilise the Pythagorean theorem:

c² = a² + b²

Where c is the distance between the two points and a and b are the distances travelled in each direction. In this case, a is the distance from A to B (176 miles), and b is the distance from B to C (319 miles).

c² = 176² + 319²

c = √(176² + 319²)

c = √(31,521 + 100,761)

c = √(132,282)

c = 361.99 miles (rounded to three decimal places)

So, the plane is 361.99 miles from its starting point.

To find the bearing of the plane from its original location, we need to use the arctangent formula:

θ = arctan(b/a)

Where θ is the bearing, and a and b are the distances travelled in each direction. In this case, a is the distance from A to B (176 miles) and b is the distance from B to C (319 miles).

θ = arctan(319/176)

θ = 57.72 degrees (rounded to three decimal places)

This means the plane is 57.72 degrees from due north. To find the actual bearing from due north, we need to add 90 degrees since the plane is travelling in the northeasterly direction:

Bearing = 90 + 57.72 = 147.72 degrees (rounded to three decimal places)

In conclusion, the plane is 361.99 miles from its starting point on a bearing of 147.72 degrees from due north.

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Answer:

c below

Step-by-step explanation:

you: 25 +$3 /week * x weeks

sis: 40 + 2/week * x weeks

they have to equal to each other

so 25 + 3x = 40 +2x

move x around & simplify

so x = 15

total 25+3*15 = 25+45 = 70

The volume of the sphere of radius 7 feet is given as follows:

1372 ft³.

The volume of the cube of sides 12 ft is given as follows:

1728 ft³.

The volume of a sphere of radius r is given by the multiplication of 4 by pi = 3 by the cubed radius, and the multiplication is then divided by 3, hence:

V = 4 x 3 x 7³/3

V = 1372 ft³.

The volume of a cube of side length s is given by the side length cubed, hence:

V = 12³

V = 1728 ft³.

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Step-by-step explanation:

A,No, there isn't a more efficient way to solve this system.

B.Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.

C.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate y, then solve for x.

D.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate x, then solve for y.

Answer:

$66.43

Step-by-step explanation:

In order to see how much one sweater cost you need to divide 47.45 by 5 and you will get 9.49 then after that you will multiply 9.49 by 7 and get 66.43

[tex]\begin{array}{ccll} sweaters&\$\\ \cline{1-2} 5 & 47.45\\ 7& x \end{array} \implies \cfrac{5}{7}~~=~~\cfrac{47.45}{x} \\\\\\ 5x=7(47.45)\implies x=\cfrac{7(47.45)}{5}\implies x=66.43[/tex]

Answer:

1 year

Step-by-step explanation:

the equation to find simple interest

A = P (1 + rt)

so plug in yore numbers

400=300(1+0.4*t)

400=300+120t

120=120t

1=t

Answer:

[tex]0 < \text{x} \le 4[/tex]

If x is an integer, then x is any value in the set {1,2,3,4}

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

Work Shown:

x = length of each side

6x = perimeter of the regular hexagon

The perimeter must be greater than 0.

Also, the perimeter must be less than or equal to 24. This is because of the phrasing "perimeter is at most 24 inches".

In other words, the perimeter is between 0 and 24, excluding 0 and including 24.

[tex]0 < \text{ perimeter } \le 24\\\\0 < 6\text{x} \le 24\\\\0/6 < 6\text{x}/6 \le 24/6\\\\0 < \text{x} \le 4\\\\[/tex]

If x is an integer, then x can be any value in the set {1,2,3,4}

Examples:

The required value of the cos(θ) for the interval 0 < θ < π/2 is given as 0.857.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

The value of cos(θ) can be found using the Pythagorean identity:

cos²(θ) + sin²(θ) = 1

Substituting the given value of sin(θ) = 0.515, we have:

cos²(θ) + 0.515² = 1

cos²(θ) = 1 - 0.515²

cos(θ) = √(1 - 0.515²)
        = √(1 - 0.265)
        = √(0.735) ≈ 0.857

So, cos(θ) = 0.857.

Thus, the required value of the cos(θ) for the interval 0 < θ < π/2 is given as 0.857.

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Answer:

5(2x-3)-7x=x-10

or, 10x -15 -7x = x-10

or, 3x-15=x-10

or, 3x- x = 15-10

or, 2x = 5

or, x= 5/2

The value for x is 30 cm.

equivalent triangles

According to  the following equation is valid:

x/75 = 12/30

30x = 900 is obtained by dividing by 12 * 75.

Divide both sides of 30x/30 to get 900/30x = 30.

As a result, the value of x is 30 cm.

Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.

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I understand the question looking for is :

What is the value of x?

X= 4.8 cm

X= 30 cm

X= 93 cm

X= 187.5 cm

The value for x is 30 cm.

equivalent triangles

x/75 = 12/30

30x = 900 is obtained by dividing by 12 * 75.Divide both sides of 30x/30 to get 900/30x = 30.

As a result, the value of x is 30 cm.

What are some similar triangles?

Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.

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I understand the question looking for is :

What is the value of x?

X= 4.8 cm

X= 30 cm

X= 93 cm

X= 187.5 cm

Answer:

196.1 cm^2

Step-by-step explanation:

The area of a circle is given by Area = πr^2

R is (15.8 cm)/2 = 7.9 cm

Area = (3.14)*(7.0cm)^2

Area = 196.1 cm^2

Answer:

The formula to calculate the area of a circle is given by: A = π * r^2, where r is the radius of the circle.

Given the diameter of 15.8 cm, we can calculate the radius by dividing the diameter by 2: r = 15.8 cm / 2 = 7.9 cm

Plugging the value of the radius into the formula: A = π * 7.9^2 = 3.14 * 62.41 = 196.0794 cm^2

Rounding the answer to the nearest hundredth, the area of the circle with a diameter of 15.8 cm is approximately 196.08 cm^2.

Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

In a math equation, the comparable symbol (=) is used to denote equality between two propositions. It is demonstrated that by using mathematical formulas, which have been expressions of reality, different numerical factors can be compared. The equal sign, for instance, splits the integer 12 or the equation y + 6 = 12 to 2 different halves. It is possible to determine how many characters each side of such a symbol has. It's common for symbols to have conflicting meanings.

Here,

Given :

=> g -3 = 9

To find the value of g :

=> g = 9 + 3

=> g = 12

Thus , value of g is 12.

Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

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Number of employees that are in favor of stocking healthier snacks in the break room are 192.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given;

4/5 ​start fraction of the survey respondents are in favor of stocking healthier snacks in the break room

The employees surveyed are representative of all 240 employees

Now, the number of employees in favor;

=4/5 * 240

=4*48

=192

Therefore, the answer according to the given ratio will be 192.

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The area of the square with side measuring 10 cm and 10 cm is 100 cm²

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The area of a figure is the amount of space that is occupied by the two dimensional shape. The area of a square is the product of its length . It is given by:

Area = length * length

Let us assume that each side of the square is 10 cm, hence:

Area = 10 cm * 10 cm = 100 cm²

The area of the square is 100 cm²

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If x > y and a > b, the option that must be true is D. x + a > y + b.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

If two inequalities have inequality symbols facing the same direction, we can add the inequalities

For example: 4 < 7 and 1 < 10

So, we can add them to get: 4 + 1 < 7 + 10

Since x > y and a > b have inequality symbols facing the same direction, we can add the inequalities to get: x + a > y + b

The correct option is D.

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If x > y and a > b, which of the following must be true?

A. x > a

B. y > b

C. x + b > y + a

D. x + a > y + b

E. a + b > x + y

The circumference of the circle in terms of π is 8π yards.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the diameter of the circle = 8yrd

the circumference of the circle in terms of π

=π  * 8

= π8 yrd.

Hence, The circumference of the circle in terms of π is 8π yards.

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The division problem that the area model represents is; 0 remainder 32

We are given that the accurate division;

3600/45 = 80

We are also given that the accurate division as;

315/45 = 7

Now, we want to find 32/45 which would lead to a remainder. Thus, we have;

45 cannot go into 32 at all and as such, we will have the result as 0 remainder 32

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Answer:

-5z - 10

Step-by-step explanation:

Subtract 9z from 4z.

Answer:

Step-by-step explanation:

You want a drawing of the vector between (1, 3) and (-8, -9), along with its component form as sum of unit vectors i and j, its magnitude and direction, and the corresponding unit vector.

See the attachment for the drawing.

The difference between the head and tail coordinates is ...

  (-8, -9) -(1, 3) = (-9, -12)

That is, the vector extends -9 units in the +x direction, and -12 units in the +y direction, so its component form is ...

  -9i -12j

The magnitude of a vector is the root of the sum of squares of its components:

  |v| = √((-9)² +(-12)²) = √(81+144) = √225

  |v| = 15

The direction can be found using the arctangent function:

  ∠v = arctan(-12/-9) = 180° +51.13° . . . . . accounting for quadrant

  ∠v =  = 233.13°

The unit vector in the same direction is found by replacing the magnitude in polar form by 1.

  u = 1∠233.13°

The component form is found by dividing the vector by its magnitude:

  u = v/|v| = (-9i -12j)/15

  u = -0.6i -0.8j

__

Additional comment

The attached calculator output shows the polar form angle as negative. That is another way the direction can be expressed. The positive angle value is found by adding 360° to that negative value.

The functions are classified as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

Hence the conditions needed for a function to be a linear function are given as follows:

The functions are given as follows:

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The volume of the solid given by rotating the region bounded by the curves y = x^2, x = 5, and y = 0 about the x-axis is 625π.

When the region bounded above by the graph of f, below by the x-axis, and on the sides by x = a and x = b is rotated about the x-axis, the volume V of the generated solid is given by V = ∫ab π [f(x)]^2 dx. We can also find solids by revolving curves about the y-axis.

Whereas the basic formula for the area of a rectangular shape is length * width, the basic formula for volume is length * width * height. How we refer to the different dimensions does not change the calculation. We may, for example, use depth instead of height.

In this case, the bounds of integration are from 0 to 5. The radius function is going to be:

r (x) = x^2

Now, substitute the value into the formula for the disk method:

V = π * ∫ba * [r(x)]^2 * dx

So, in this case it will be:

V = π * ∫5 0 * [x^2]^2 * dx

= π * ∫5 0 * x^4 * dx

= π * x^5 / 5 ∣ 5 0

= π * ((x^5 / 5) – (0 / 5))

= 625π

Hence, the volume of the solid is 625π.

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Answer:

REGULAR

Step-by-step explanation: