5) Roland has a basket of 24 fruits. If 3) out of 8 of these fruits are oranges, how many oranges are in Roland's basket? a) 5 b) 8 c) 9 d) 15​

The amount paralegal earned from the job is 1860 dollars.

The amount allocated for savings is 1116 dollars.

Paralegal bills the law firm for 15.5 hours of work at a rate of $120 per hour.

Therefore, the law firm have to pay paralegal 120 dollars for every hour worked.

Therefore,

the amount earned by paralegal = 15.5 × 120

the amount earned by paralegal = 1860 dollars

Paralegal splits her earnings between utilities and savings in a ratio of 2 ∶ 3.

Therefore, let's find the amount of money allocated for her savings.

amount allocated for savings = 3 / 5 × 1860

amount allocated for savings = 5580 / 5

Therefore,

amount allocated for savings = 1116 dollars

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The probability that that my dog tears up the trash and it rains tomorrow is 0.03.

From the information, the dog has a 30% chance of tearing up the trash on a given day and there's a 10% chance of rain tomorrow.

Therefore, the that my dog tears up the trash and it rains will be:

= Probability of tearing up × Probability of rain

= 30% × 10%

= 0.3 × 0.1

= 0.03

The probability is 0.03.

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15,0

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer: 6931

Step-by-step explanation:

79% of all students are taking math this semesters.  So there is an additional 21% of students not taking math.

5476/x = 79/100

cross multiply and divide to get the total number of students.

5476 x 100 = 547600

547600 divided by 79 = 6931  

check 5476 divided by 6931 = 79%  

Further proof of correct answer:

21% of 6931 = 1455

1455 + 5476 equals 6931, so the answer calculated is correct.    

The equation for the perpendicular bisector of the line segment whose endpoints are (-2, 4) and (-8,-6) is 3x + 5y + 20 = 0.

Given:

Endpoints of the line segment are (-2, 4) and (-8,-6).

Midpoint of the line segment = ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

                                                 = [tex]\frac{-2 +(-8) }{2}[/tex] , [tex]\frac{4 +(-6) }{2}[/tex]

                                                =( [tex]\frac{-10}{2}[/tex] , [tex]\frac{-2}{2}[/tex] ) = (-5, -1)

Slope of the line segment =  [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex]

                                            = [tex]\frac{(-6) - 4 }{(-8) - (-2) }[/tex]

                                            = [tex]\frac{-10}{-6}[/tex] = [tex]\frac{5}{3}[/tex]

The line perpendicular to the line segment will have a slope of the negative reciprocal of the line segment which is -3/5.

Therefore, the perpendicular bisector passes through (-5,-1) and has a slope of -3/5.

Equation of the line will be,

y - y₁ = m(x - x₁)

⇒ y - (-1) = -3/5(x -(-5))

⇒ 5( y + 1) = -3(x + 5)

⇒ 5y + 5 = -3x - 15

⇒ 3x + 5y + 20 = 0

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Answer:

it is often known as the unequal variance t test. It assumes that both groups of data are drawn from Gaussian populations, but does not assume that their standard deviations are the same.

Answer:

2(x-2)

Step-by-step explanation: distribute, add the numbers, common factor

Let the total marks are 100.

And Bradely got 66% marks.

So the marks of Bradely are:

And Zevel got one third of Bradely's marks so:

Answer:

y=13

Step-by-step explanation:

We will have that some of the principles that geometry works with, that are present in the image are:

Length, Area, Volume, Surfaces, Angles & Curves.

Answer:

13

Step-by-step explanation:

If a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter

The distance travelled by the car with 110 liters of fuel = 250km

To find the rate of fuel consumption we have to apply the unitary method

The distance travelled by the car with 1 liters of fuel = The distance travelled by the car with 110 liters of fuel /110

Substitute the values in the equation

The distance travelled by the car with 1 liters of fuel = 250/110

= 2.5 km

So a car consumes 1 liters of fuel to cover 2.5 km

The rate of fuel consumption = 2.5 km/liter

Hence, if a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter

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Answer

Area of the figure = 105.12 ft²

Explanation

The figure shown is a combination of a rectangle with length 10 ft. and width 8 ft., with a semicircle that has diameter 8 ft., which translates to a radius of 4 ft.

The area of the figure = (Area of the rectangle) + (Area of the semicircle)

Area of rectangle = L × W

L = Length = 10 ft.

W = Width = 8 ft.

Area of the rectangle = 10 × 8 = 80 ft²

Area of semicircle = Half of the area of a circle = ½ × πR²

π = pi = 3.14 (According to the question)

R = Radius of the semicircle = 4 ft.

Area of semicircle = ½ × 3.14 × 4² = 25.12 ft²

Area of the figure = 80 + 25.12 = 105.12 ft²

Hope this Helps!!!

We can tell the difference among linear, quadratic, and exponential functions just by looking at equation as Exponent functions are rapidly increasing or decreasing, and the highest power of variable for a linear function is 1. The highest power of variable for a quadratic function is 2.

Linear functions are functions that are used to model phenomena that increase or decrease at a constant rate. These types of functions are polynomial functions with a highest exponent of one on the variable. The graphs of these functions are in the shape of a straight line.

Exponential functions are functions that have the variable in the exponent. They increase or decrease slowly then quickly or quickly then slowly.

Quadratic functions are the functions that have the highest power of variables equal to 2.

For example,

Linear Equation : The population of a family of rabbits starts with 2 rabbits and doubles every month.

Expoential Equation : Compound interest is example of exponential function.

Quadratic Equation : When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster and a Quadratic Equation tells you its position at all times!

Therefore, we can conclude that linear function have highest power of variable as 1 , exponent functions are quickly increasing or decreasing, Quadratic functions have the power of variables equal to 2.

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The perimeter of the isosceles triangle whose base is 6 cm and two equal sides are 7.5 cm is 21 centi-meters.

What is isosceles triangle?

An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception. The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.

To calculate the perimeter of isosceles triangle, we use equation:

Perimeter = Base + 2(Two equal side)

Perimeter = 6 + 2(7.5)

Perimeter = 21 cm

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The inequality that represents having enough money to buy the gaming system is x ≥ 35.

The mathematical expression that represents the sentence " you charge $10 per dog" is x = 10 where x is the number of dogs.

x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

The cost of the gaming system = $500

Amount already saved = $150

Charges per dog = $10

The inequality that represents having enough money to buy the gaming system:

150 + 10x ≥ 500

10x ≥ 500 - 150

10x ≥ 350

x ≥ 35   where x is the number of dogs.

The mathematical expression that represents the sentence " you charge $10 per dog ":

x = 10 where x is the number of dogs.

x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.

Thus,

The inequality that represents having enough money to buy the gaming system is x ≥ 35.

The mathematical expression that represents the sentence " you charge $10 per dog" is x = 10 where x is the number of dogs.

x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.

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Ben must bowl 130 in his third game so that the average will be of at least 160.

Given that, Ben bowled 157 and 193 in his first two games. So, we have to calculate the average of his third bowl to have an average of at least 160.

Let the average of third bowl be x.

The average is known as the arithmetic mean which is the sum of all numbers in a collection, divided by the count of the numbers present in the collection. In other words, the average is the ratio of the sum of all given observations to the total number of observations. Hence, the average formula is:

Average = Sum of the Observations/Number of Observations

160 = 157+193+x/3

⇒ 160×3 = 157+193+x

⇒ 480 = 350+x

⇒ 480-350 = x

⇒  130 = x

Therefore, Ben must bowl 130 in his third game so that the average will be of at least 160.

Hence, 130 is the required answer.

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Answer:

mixed: 2 and 1/4

improper: 9/4

Step-by-step explanation:

The  mixed number in picture is [tex]2\frac{1}{4}[/tex] and improper fraction represented in the picture 9/4.

Fractions are the components of a collection or whole. Two parts make up a fraction. The numerator is the number at the top of the line. It indicates the number of equal portions taken from the collection or whole. The number beneath the line is known as the denominator. It indicates the total number of identical parts that make up a collection or the total number of parts that make up the whole.

Given picture shows three circles each are divided in 4 equal parts,

circle 1 and 2 are completely filled it can be counted 1 for each,

1 + 1 = 2

but for third circle only one part is filled out of 4,

it is represented by 1/4

total value of 3 figures is 1 + 1 + 1/4 = 2 + 1/4 = 9/8

and of mixed fraction   [tex]2\frac{1}{4}[/tex] .

Hence the mixed fraction  [tex]2\frac{1}{4}[/tex]  and improper fraction 9/8.

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It is to be noted that the ONLY option that the customer can select from when purchasing the product is  "(M2, C2, A3)" Option C.

The above exercise is a test of logic, as it is with a simple calculation.

The study of formal logic within mathematics is known as mathematical logic. Mathematical logic research frequently focuses on the mathematical aspects of formal logic systems, such as their expressive or deductive capability.

Hence, from the above, we can see that:

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Full Question:

Apple has created a new i-Pad. There are 4 choices for memory size (M), 8 choices for color (C) and 3 apps (A) to select when you purchase the product. From the options below what is the ONLY option the customer can select?

(M1, C2, A4)

(M1, C9, A3)

(M2, C2, A3)

(M4, C2, A8)

Answer:

6(3+7)

Step-by-step explanation:

The factors of 18 are 1, 2, 3, 6, 9, 18.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

The greatest common factor is six.

To put it in distributive form, divide both by 6:

6(3+7)

The equation of parallel line is y = 2x + 3

Given,

The line below is the function y=2x-1.

From the figure,

Identify the equation of a parallel line.

Now, According to the question:

We are given that line a represented by the equation

y = 2x -1

and, We know that

Slope- intercept form of line is given by

y = mx + c

Where m=Slope of line a

c = y- intercept

Comparing it  with the given equation then, we get

Slope of line a = 2

We know that

When two lines are parallel then their slopes are equal.

Hence, Option (b) slope is equal to the given function

It means, y = 2x - 1 and y = 2x +3

Value of slope m = 2 = 2

Hence, The equation of parallel line is y = 2x + 3

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Answer:

252558855555335555422358236

Answer:

[tex]y=\frac{-1}{4}x+2[/tex]

Step-by-step explanation:

The function can be written in point-slope form following this equation:

[tex]y=m(x-x_{0} )+y_{0}[/tex]

where y and x are variables, and [tex]x_{0}[/tex] and [tex]y_{0}[/tex] are x and y values of any chosen point on the curve (line)

m (slope) can be calculated by the equation [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] where you need to find 2 chosen points on the line where [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the x and y values of the first set, and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the x and y values of the second set.

solve for m and we get [tex]-\frac{1}{4}[/tex]

Plug it into the equation with any set of x and y values on the line into the point-slope form equation, then you get the answer

The measure of angle:-

angle 1 = 78 degree

angle 2 = 40 degree

angle 3 =  140 degree  

A triangle is a type of polygon which have only three vertices and no parallel sides.

 In this question we use property of triangle that :-

1:- Sum of interior angle is 180 degree

2:-Exterior angle of a triangle is equal to the sum of angle of opposite sides

A.T.Q:-

  lets vertices of triangle be A,B, and C    

  so,

       angle A + angle B +angle C = 180

       62 +78+ angle C = 180

      140 + angle C = 180

      angle C =40 degree

we know that , angle C and angle 3 makes 180 degree

                        angle C + angle3 =180     , 40+ angle 3= 180

angle 3 = 140 degree                                                                                     And ,  angle 2 = angle C

                :- angle 2=40                                                                               finally;

               angle 1 =  angle B

               angle 1 = 78 degree

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The equation of the line is y = -1x + 3.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines. No matter how far we extend a parallel line, it will never meet another parallel line.

The slope so rewrite the equation for the line as y = -x + 1.

The equation in “y = mx + b” form, the slope is always the number m in front of x.

The slope is -1.

First, by using “y = mx + b” form,

we know m is -1 so only need b.

To get b, plug in the (x, y) coordinates for the point (-1, 4)

(4) = -1×(-1) + b.

The y-coordinate 4 on the left side, and the x number -1 on the right.

b = 3.

Therefore, the equation of the line is y = -1x + 3.

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The inverse of the conditional statement w > ~v is ~v < w

An inverse statement is seen as a type of conditional sentence having an immediate change that is made from original statement.

It is known to carry the negation of both the hypothesis and conclusion from the given original statement.

It is known to carry the opposite of the original statement that is given.

An inverse statement is formed by negating the hypothesis and conclusion of a statement.

It is expressed as;

Original statement:  If a, then b

Inverse statement: If not b, not a

Given the expression;

w > ~v

The inverse is represented as;

~v < w

Hence, the inverse is ~v < w

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The solution set for all possible side lengths for side L is;

⇒ L < 7

What is Triangle?

A triangle is a three sided polygon , which has three vertices and three angles.

Given that;

The longest side of a triangle must be less than the sum of the other two sides.

Suppose a triangle is made up of lengths 2 inches, 5 inches and L. inches, where, L is the longest side.

Now, By the given condition;

''The longest side of a triangle must be less than the sum of the other two sides.''

We can formulate;

L < 2 + 5

L < 7

So, The solution set for all possible side lengths for side L is;

⇒ L < 7

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