Find the volume of a rectangular prism with the following dimensions: V = lwh Length:
4m Width
: 0.3 m Height
: 1.5 m​

The value of sin a + cos a is √7/2.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows

Here we have

sin a × cos a = 3/8  

Multiply with 2 on both sides

=> 2(sin a × cos a) = 2(3/8)

=> 2 sin a cos a = 3/4  

Add sin²a + cos²a on both sides

=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a    

As we know (a + b)² = a²+ b² + 2ab  

=> (sin a + cos a)² = 3/4 + 1

=> (sin a + cos a)² = 7/4

=> sin a + cos a = √7/2

Therefore,

The value of sin a + cos a is √7/2.

Learn more about Trigonometric identities at

https://brainly.com/question/24377281

#SPJ1

The shipping charge of an item on the purchase $56 is $2.52.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The percentage of a number is the value of the number out of 100.

For example, in a class, there are 26 boys and 24 girls. So, the percentage of boys in the class is 26/(26+24) × 100 = 26/50 × 100 = 52%, which means out of 100, 52 are boys.

A company charges  shipping fee = 4.5% of the purchase price for all items,

Cost of an item =$56

So, shipping fee = 4.5% of 56

= 4.5/100 × 56

= 0.045 × 56

= $2.52

Learn more about percentage here :-

https://brainly.com/question/29306119

#SPJ4

The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

we graphed the function y = 3x - 4

now, the required coordinates are, which satisfies the graph function.

as, we get,

(-1, -7), satisfies the graph function

(0, -4) , satisfies the graph function

(1, -1), satisfies the graph function

Hence, The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4

To learn more on function click:

brainly.com/question/21145944

#SPJ1

The fraction that is the ratio of the shaded area of the circle to the area between the two squares is (π−2)/2.

A fraction is a mathematical expression that represents a part or a proportion of a whole.

Let us assume that the radius of the circle is 'r' units. Therefore, the diameter of the circle is 2r units. The diagonal of the inner square is equal to the diameter of the circle, which is 2r units. Hence, the side of the inner square is r√2 units.

Now, let's consider the area of the circle. The formula for the area of a circle is

=>  A=πr².

Therefore, the area of the circle is πr².

The area between the two squares is the difference between the area of the outer square and the area of the inner square. The area of the outer square is

=> (2r)²=4r²,

and the area of the inner square is

=> (r√2)²=2r².

Hence, the area between the two squares is

=> 4r²−2r²=2r².

The shaded area of the circle is the area inside the circle but outside the inner square. We can find this area by subtracting the area of the inner square from the area of the circle. Therefore, the shaded area of the circle is

=> πr²−2r²=(π−2)r².

Now, let's find the ratio of the shaded area of the circle to the area between the two squares. We can express this ratio as a fraction. Thus,

ratio = (π - 2)r² / 2r

We can simplify this fraction by canceling out the common factor r^2 in both the numerator and denominator. Thus,

ratio = (π - 2) / 2

This fraction is closest to the ratio of the shaded area of the circle to the area between the two squares.

To know more about fraction here.

https://brainly.com/question/10354322

#SPJ4

When eight more than the quotient of a number 'b' and 25 is greater than 6 then the inequality representing the value of b is b > -50.

The expression used to represents :

Quotient of a number b and 25 is equal to b / 25

Next step is :

8 more than the b / 25 is equal to ( b / 25 ) + 8

Then ,

( b / 25 ) + 8  is greater than 6 is given by

⇒ ( b / 25 ) + 8 > 6

Simplify the above inequality for 'b' we get,

⇒ ( b / 25 )  > 6 - 8

⇒ ( b / 25 )  > -2

Multiply both the side by 25 we get,

⇒ b > - 2 × 25

⇒ b > -50

Therefore, the inequality representing the value of 'b' for the condition of quotient and a number is equal to b > -50.

The above question is incomplete , the complete question is:

8 more than the quotient of a number b and 25 is greater than 6 , then the value of b is ?

Learn more about quotient here

brainly.com/question/16134410

#SPJ4

So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.

What is Algebraic expression?

An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables can represent unknown values, while the constants represent known values.

Based on the data provided by Celine's Cupcakes, out of the total of 15 cupcakes sold, 6 were lemon cupcakes. This means that the proportion of lemon cupcakes sold is:

6/15 = 0.4

To estimate how many of the next 20 cupcakes sold would be lemon cupcakes, we can assume that the proportion of lemon cupcakes sold will remain the same. Therefore, we can expect that:

0.4 x 20 = 8

Therefore, So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.

To learn more about Algebraic expression from given link.

https://brainly.com/question/28884894

#SPJ1

Answer: [tex]36/\pi[/tex] or approximately 11.4592

Step-by-step explanation:

The distance around a circle equals its circumference.

The circumference equation is: C = 2[tex]\pi[/tex] * r where r = radius.

Now, we know that the distance around the circle is 36 so C = 36

Using the equation, we have 36= 2[tex]\pi[/tex]*r

Now, we solve for r by dividing by 2[tex]\pi[/tex] to both sides.

r = [tex]36/2\pi[/tex] which equals [tex]18/\pi[/tex] which is approximately 5.7296

Now, since radius is half of the diameter, we need to multiply this by 2.

This finally gives us the answer of diameter = [tex]36/\pi[/tex] which is approximately 11.4592

Answer:

1 pound of strawberries

Step-by-step explanation:

4 x $1.20 = $4.80

$6 - $4.80 = $1.20

one pound is $1.20

Answer:

i think it x = 0 and x = 5

Step-by-step explanation:

[tex]y = {x}^{2} - 4x + 2[/tex]

[tex]y = x + 2[/tex]

[tex]x + 2 = {x}^{2} - 4x + 2[/tex]

[tex]0 = {x}^{2} - 4x + 2 - x - 2[/tex]

[tex]0 = {x}^{2} - 5x[/tex]

[tex]0 = x(x - 5)[/tex]

[tex]x = 0[/tex]

(or)

[tex]x - 5 = 0[/tex]

[tex]x = 5[/tex]

a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

Learn more about median here

https://brainly.com/question/28060453

#SPJ4

Answer:

Step-by-step explanation:

To find the volume of the container, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height. Plugging in the given values, we get:

V = π * 8.1^2 * 17.9 = 1146.4 cm^3

Since the sample contains 0.04 g of the trace element per cubic centimeter of water, the amount of trace element in the entire container can be found by multiplying the volume of the container by the concentration of the trace element:

0.04 g/cm^3 * 1146.4 cm^3 = 45.86 g

So Samir has collected approximately 45.9 g of the trace element, rounded to the nearest tenth.

Answer:147.6g

Step-by-step explanation

Answer:

Point (-3, 3) is not a solution to the system of equations

2y+x=3

y=x+0

Step-by-step explanation:

2y + x = 3

y = x + 0

2(3) + (-3) = 3

6 - 3 = 3

3 = 3

The point works in the first equation.

3 = -3 + 0

3 = -3

The point does not work in the second equation.

The equation of the polynomial is P(x) = 0.16875(x + 8)(x - 10)

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following readings:

A root of multiplicity 1 at x = -8

A root of multiplicity 1 at x = 10

y-intercept = -13.5

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 8)(x - 10)

The y-intercept is -13.5

So, we have

a * (0 + 8)(0 - 10) = -13.5

This gives

a = 0.16875

Hence, the expression is P(x) = 0.16875(x + 8)(x - 10)

Read more about polynomial at

brainly.com/question/7693326

#SPJ1

The result to the factorization of the polynomial is 3x (x + 10) (x - 10).

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.

= 3x³ - 300x

= 3x(x²) - 300x

= 3x(x²) - 3x(100)

= 3x(x² - 100)

= 3x(x² - 10²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );

where

= 3x (x+10) (x−10)

Learn more about factorizing polynomials here:

https://brainly.com/question/24351176

#SPJ1

Answer:

The function f: A -> B is defined by:

f(x) = { 11, if x = -1 or x = 2,

-1, if x = 0,

-2, if x = 1,

0, if x = 3 or x = 4 }

The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.

To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.

To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.

Therefore, the function f is one-to-one and onto both.

Answer:

slope = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, 2) ← 2 points on the line

m = [tex]\frac{2-0}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]

She travel  31.25 miles we calculate it by multiply by speed and time

Speed indicates how quickly something or someone is moving. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example because the distance is measured in metres (m) and the time is measured in seconds (s).The formula can be rearranged in three ways:

speed = distance ÷ time

distance = speed × time

time = distance ÷ speed

To calculate one of the variables (speed, distance or time) we need the other two.

As given in Question she cycled at speed 12 1/2 miles per hours

12 1/2  can be written as 12.5 miles per hours

and she cycled for 2 1/2 hours which can be written as 2.5 hours

and to find the distance how much she total travel we have to multiply the speed and time

distance = 12.5x2.5 = 31.25 miles

know more about speed and distance click here;

https://brainly.com/question/29020947

#SPJ4

Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.

For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., [tex]^{n} C_{r} = \frac{n!}{(n-r)!.r!}[/tex]

A combination is a way of selecting items from a collection where the order of selection does not matter.

We will have to apply the formula separately for vegetarian and meat items.

Combinations available

A. 1 vegetarian item and 2 meat items              

    [tex]^{5} C_{1} and ^{4} C_{2}[/tex]                                 (In combination "and" means to multiply)                                                                                        

   = [tex]\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}[/tex]

   = [tex]\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}[/tex]

   = 5.3.2

   = 5.6

   = 30

B. 2 vegetarian items and 1 meat item

    [tex]^{5} C_{2} and ^{4} C_{1}[/tex]

   = [tex]\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}[/tex]

   = [tex]\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}[/tex]

   = 5.2.4

   = 10.4

   = 40

C. 3 vegetarian items and no meat item

   = [tex]^{5} C_{3} and ^{4} C_{0}[/tex]

   = [tex]\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}[/tex]

   = [tex]\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1[/tex]

   = 5.2

   = 10

Now, we will add all the different combination

Total combinations = 30+40+10

                                = 80 different type of dinners

To know more about combination

https://brainly.com/question/13387529

#SPJ4

Object is kind of a vector with the same size as the coefficients in the linear regression model.

In the least squares optimization target, the sum of squared errors (SSE) is typically minimized with respect to the coefficients of the linear regression model. The gradient of the SSE with respect to the coefficients is a vector that provides the direction of steepest ascent, or the direction in which the SSE increases the most rapidly. Setting this gradient vector to zero and solving for the coefficients yields the least squares solution to the linear regression problem.

Therefore, in this context, " " is likely a vector of coefficients that are being optimized to minimize the SSE.

To learn more about regression model here:

https://brainly.com/question/14983410

#SPJ4

I would need to work at least 27 hours to make enough money to reach my goal.

What are arithmatic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

Let's start by finding the amount of money I receive from my allowance and how much more money I need to make to reach my goal:

Allowance per month = $60

Amount of money I need for social life = $260

Additional amount of money I need to make = $260 - $60 = $200

Now, let's divide the additional amount of money I need to make by the amount I make per hour to find how many hours I need to work:

$200 ÷ $7.50 per hour = 26.67 hours

Since we can't work a fraction of an hour, we need to round up to the nearest whole number.

Therefore, I would need to work at least 27 hours to make enough money to reach my goal.

To learn more about the arithmatic operations visit:

https://brainly.com/question/13181427

#SPJ1

The zeroes of 5x^4-26x^3-64x^2+9x-14 are -2, 7 ,  [tex]\frac{1+i\sqrt{19} }{10}[/tex]  and   [tex]\frac{1-i\sqrt{19} }{10}[/tex]  by Using the rational theorem.

f(x) = [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

Now, put x = -2

f(-2) = [tex]5(-2)^{4} - 26(-2)^{3} - 64(-2)^{2} +9(-2) -14[/tex]

f(-2) = 0

so, -2 is a zero of f(x)

or (x+2) is a factor of  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

putting x = 7

f(7) = [tex]5(7)^{4} - 26(7)^{3} - 64(7)^{2} +9(7) -14[/tex]

f(7) = 0

so, (x-7) is a factor of  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

Now (x+2)(x-7) would also be a factor so

Divide  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by (x+2)(x-7)

or divide  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by [tex]x^{2} -5x -14[/tex]

The quotient or other factor will be [tex]5x^{2} - x +1[/tex]

[tex]5x^{2} - x +1[/tex]

By factorizing  [tex]5x^{2} - x +1[/tex]

The other two zeroes are [tex]\frac{1+i\sqrt{19} }{10}[/tex] and  [tex]\frac{1-i\sqrt{19} }{10}[/tex]

To know more about polynomial

https://brainly.com/question/30503176

#SPJ4

The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the quadrilateral be represented as ABCD

Now , the coordinates of ABCD is given as

A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )

Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin

Substituting the values in the equation , we get

A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )

On simplifying the equation , we get

The coordinates of A' is = A' ( -2 , 4 )

The coordinates of B' is = B' ( 4 , 4 )

The coordinates of C' is = C' ( 6 , -2 )

The coordinates of D' is = D' ( 0 , -2 )

Hence , the dilated figure is solved

To learn more about dilation click :

https://brainly.com/question/13176891

#SPJ9

Part (a)

ASA = angle side angle

To use ASA, we need two angles and a side between those angles. We already have one pair of angles (DFE and GHI). The other pair of angles must be DEF and GIH to have the side sandwiched between the angles.

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

Part (b)

HL = hypotenuse leg

The sides EF and IH are congruent to one another because of the tickmarks. They are the legs of each right triangle. So that takes care of the "L" of "HL". We need to have the hypotenuses congruent to each other to be able to use HL. This theorem only applies to right triangles.

If the sum of two angles is 90 degrees, then the angles are called complementary angles.

Complementary angles are a type of angle relationship where two angles add up to exactly 90 degrees. In other words, when you add the measures of two complementary angles together, the sum is always equal to 90 degrees.

For example, if angle A measures 30 degrees, and angle B measures 60 degrees, then angle A and angle B are complementary angles, because 30 degrees + 60 degrees = 90 degrees.

Complementary angles are important in geometry and trigonometry, because they often appear in problems involving right triangles. In a right triangle, one of the angles measures 90 degrees, which means that the other two angles must be complementary.

For example, if one angle in a right triangle measures 30 degrees, then the other angle must measure 60 degrees, since 30 degrees + 60 degrees = 90 degrees.

Understanding complementary angles can be useful in a wide range of mathematical and real-world contexts. For example, in construction or engineering, understanding complementary angles can help ensure that structures are built at the correct angle to provide the necessary support and stability.

To learn more about trigonometry click on,

https://brainly.com/question/12849010

#SPJ4

The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The length of both tapes is the same. Then the equation is given as,

w + 1.3 = 2.7

Simplify the equation for w, then we have

w + 1.3 = 2.7

w = 1.4

The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.

More about the solution of the equation link is given below.

https://brainly.com/question/29797035

#SPJ1

The required coordinates of B are (0, 6) for the given parabola.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.

To determine the coordinates of B, we can use the information given in the problem.

A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).

The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.

Therefore, we can set x = 0 in both equations to find the y-coordinate of B.

For f(x), we have:

f(0) = a × 0² + b × 0 + c = c

For g(x), we have:

g(0) = 3 × 0 + 6 = 6

Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:

c = 6

So, the coordinates of B are (0, 6).

Learn more about the x-intercept here:

https://brainly.com/question/14180189

#SPJ9

Answer:

Step-by-step explanation:

4.8

i got u brainliest please it helps a lot

To get the total number of different ways, multiply 1,536 x 18 = 7,344.

7,344 different ways. Raven has 19 choices for drinks, 12 choices for appetizers, and 8 choices for desserts. The formula for calculating the number of different ways is 19 x 12 x 8 = 1,536. Since Raven needs to pick 3 drinks, 3 appetizers, and 2 desserts, the formula is 3 x 3 x 2 = 18. To get the total number of different ways, multiply 1,536 x 18 = 7,344.

The formula can be used to calculate the number of different ways to combine any number of choices. For example, if Raven had 24 choices for drinks, 15 choices for appetizers, and 7 choices for desserts, the formula would become 24 x 15 x 7 = 3,240. If Raven still had to pick 3 drinks, 3 appetizers, and 2 desserts, the total would be 3 x 3 x 2 = 18. Multiplying 3,240 x 18 = 57,720 different ways.

learn more about number here

https://brainly.com/question/10547079

#SPJ4

Answer: height = 1.91 m

Step-by-step explanation: Using the formula

V=πr2h

Solving for h

h=V

πr2=37.5

π·2.52≈1.90986m