How many pounds of candy worth 70 cents a pound must be mixed with 30 pounds of candy worth 90 cents a pound to produce a mixture which can be sold for 85 cents per pound?

Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

\(x \geqslant 4\)

The expression above means x can be any number starting from 4 and above .

Answer:

1. 11 married females because out of the 19 married, only 8 had more than 15 years of service and 19 - 8 = 11.

2. 10 married males because of out the 18 married with more than 15 years of service, 8 were females and 18 - 8 = 10.

3. 9 single females because out of the 17 with more than 15 years of service, 8 were married and 17 - 8 = 9.

4. 8 married females because it literally says, "8 married female with more than 15 years of service".

gotta go hope this helps sry

Assuming that the football field is a perfect rectangle, we will see that its area is 5,500 square yards.

We assume that the football field has a rectangular shape. Remember that for a rectangle of length L and width W the area is given by the formula below.

A = L*W

In this case, we know that the dimensions of the football field are:

L = 100 yards

W = 55 yards.

Then we just need to replace these values in the area formula that is written above, we will get:

A=  (100 yd)*(55 yd)

A = 5,500 yd²

The area of that football field is 5,500 yd², so the correct option is the second one.

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Answer:

a. dilation.

Step-by-step explanation:

In this problem, the triangle has been neither reflected nor rotated. Although you could say the triangle has been translated, translation will preserve the lengths of the legs of the triangle.

Since all the angles are still congruent, we can say that the triangle has been dilated. It has been enlarged.

Hope this helps!

The dilation is a transformation that transfers the pre-image to the final image. The correct answer is A.

When a point is relocated from its original place to a new location, it is changed. Different transformations include translation, rotation, reflection, and dilation.

As per the given figure, ΔKLM is transformed into ΔK'L'M'.

Here, the triangle hasn't been reflected or rotated.

Although we cannot claim the triangle has been translated, translation maintains the lengths of the triangle's legs.

We conclude that the triangle has been dilated because all of the angles are still congruent. It has grown in size.

Therefore, dilation is a transformation that transfers the pre-image to the final image.

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Answer:

Skewed

Step-by-step explanation:

The box plot is skewed because the box is towards 1 side and not near the middle

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

We have,

To determine the angle created by the bottom of the ramp and the ground, we can use the trigonometric function of sine.

In the given triangle, the height is 6 ft and the base is 16 ft.

The angle we want to find is opposite the height (let's call it θ).

The sine of an angle is defined as the ratio of the opposite side to the hypotenuse.

sin(θ) = opposite/hypotenuse

sin(θ) = 6/16

sin(θ) = 0.375

To find the angle θ, we can take the inverse sine (also known as arcsine) of 0.375:

θ = arcsin(0.375)

θ ≈ 22.62°

To meet safety regulations, the angle should be no more than 18°. Therefore, the contractor needs to lower the ramp by:

22.62° - 18° ≈ 4.62°

Thus,

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

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The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².

Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.

The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.

So, 1/2 * ( 9+5) * 3

   = 1/2 * 14 * 3

   =  1/2 * 42

   =  21 cm²

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Answer:

in 3 minutes and 50 seconds

Step-by-step explanation:

soup = 95c

after 1 minute = 83c

after 2 minutes = 71c

after 3 minutes = 59

soup cools down 0.2c in 1 seconds

so 10 seconds = 2c

in 3 minutes and 50 seconds = 49c

The temperature 49°C of soup bowl will be after 5.54 minutes

\((T-T_{s} )=(T_{0} -T_{s} )e^{-kt}\)

\(T =\) 83°C and 49°C

\(T_{s} =\) 22°C

\(T_{0} =\) 95°C

(83-22)=(95-22)\(e^{-k}\)

∴ k = -ln (61/73)

Now,

(49-22) = \(e^{ln(61/73)t}\)

∴ t = \(\frac{ln (27/73)}{ln(61/73)}\)

∴ t = 5.54 minutes

So, after 5.54 minutes temperature will be 49°C

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After answering the presented question, we may conclude that  the solution of the expressions are as follows.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

the solution of the expressions are as follows -

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1. Variable: A symbol or letter that represents an unknown value or quantity in algebraic expressions and equations.

2. Equation: A mathematical statement that shows the equality between two expressions, typically represented by an equal sign (=).

3. Coefficient: The numerical factor that is multiplied by a variable in a term.

4. Expression: A mathematical phrase that may contain variables, constants, and operations, but does not have an equal sign.

5. Linear Equation: An equation in which the highest power of the variable is 1, written in the form ax + b = 0, where a and b are constants and x is the variable.

Variable: In algebra, a variable is a symbol (usually a letter) that represents an unknown value or quantity. It allows us to express mathematical relationships and solve equations.

Equation: An equation is a mathematical statement that shows the equality between two expressions.

It consists of an equal sign (=) and can include variables, constants, and operations.

Solving equations involves finding the values of the variables that make the equation true.

Coefficient: A coefficient is the numerical factor that is multiplied by a variable in a term.

It represents the scale or magnitude of the variable.

For example, in the term 3x, the coefficient is 3.

Expression:

An expression is a mathematical phrase that can contain variables, constants, and operations, but does not have an equal sign.

Expressions can be evaluated or simplified, but they cannot be solved since they lack the equality found in equations.

Linear Equation:

A linear equation is an equation where the highest power of the variable is 1.

It can be written in the form ax + b = 0,

where a and b are constants and x is the variable.

Solving linear equations involves finding the value(s) of x that satisfy the equation.

These are just a few key definitions that form the foundation of understanding introductory algebra.

Mastering these concepts will provide a solid basis for further exploration and learning in algebraic principles and problem-solving.

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The probability that a randomly selected point within the square falls in the red-shaded square is 0.36

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

The areas of the above shapes are

Red square = 3² = 9

White square = 5² = 25

The probability is then calculated as

P = Red square/White square

So, we have

P = 9/25

Evaluate

P = 0.36

Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.36

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Answer:

Step-by-step explanation:

You want points A(-4, 0), B(0, -1) and C(-3, -3) reflected across the y-axis and translated left 5 and up 2.

The reflection across the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

The translation adds the translation vector to the reflected coordinates.

  (x, y) ⇒ (x -5, y +2) . . . . . . translation (by itself)

Then the result of both transformations is ...

  (x, y) ⇒ (-x -5, y +2)

For a number of points, this arithmetic is conveniently accomplished by a calculator. The result is ...

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

-60

Step-by-step explanation:

Find -60 and drag sum onto that value

In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

\(4\frac{2}{4}\) that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

\(4\frac{2}{4} = \frac{16+4}{2}\)

=\(\frac{18}{4}\)

Then \(4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}\)

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that \(\frac{18}{4}\) is less than \(\frac{37}{4}\) Hence, Darren is wrong.

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Answer:

We can use the formula for compound interest to solve this problem. The formula is:

A = P * (1 + r/n)^(n*t)

where:

A = the amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:

A = 5000 * (1 + 0.03/12)^(12*10)

A = 5000 * (1.0025)^120

A ≈ $6,621.36

So the investment will be worth approximately $6,621.36 after 10 years.

Answer:

the answer is a

Step-by-step explanation:

This is my work: -10 does not equal 3, so therefore there is no solution

Answer:

The minimum number of parallel faces that a prism should have is three pairs

Answer:

The minimum number of parallel faces that a prism should have is three faces

Answer:

x is greater than or equal to 16.

Step-by-step explanation:

Hi! It says atleast 80 points, so your sign should be flipped over to show that x+64 needs to be ATLEAST 80. Then they asked you to solve for x. To solve for x, you subtract 64 from each side to get x is greater than or equal to 80-64, otherwise known as 16.

The inequality is \(x +64 \ge 80\)

It solves to \(x \ge 16\)

She needs at least 16 more points.

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

Further Explanation:

"At least 80" means "80 or more"

In other words, the lowest grade she can get is 80

x = number of points she needs

x+64 = number of points she has, after adding on the earlier 64 points

The x+64 must be 80 or larger. So the inequality to set up is \(x+64 \ge 80\)

You had the right idea, but need to flip the inequality sign.

To solve this inequality, you subtract 64 from both sides and you should end up with \(x \ge 16\)

This says she needs at least more 16 points to go with the 64 points she already has.

Answer:

\(Fraction = \frac{1}{5}\)

Step-by-step explanation:

Given

\(Trays = 20\)

\(Each\ Tray = 5\ colors\)

\(Each\ set = 1\ Purple\)

Required

Fraction of purple in 20 trays

If there are 20 trays, then the total colors is:

\(Colors= 20 * 5\)

\(Colors= 100\)

This also means that, there are 20 purple colors in the set (i.e. 20 trays * 1 purple)

So, the fraction of purple color is:

\(Fraction = \frac{Purple}{Total}\)

\(Fraction = \frac{20}{100}\)

\(Fraction = \frac{1}{5}\)

Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150

Answer:

16.2

Step-by-step explanation:

12*1.35=16.2

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1 × 10 ^7 + 6 × 10 ^6 + 2 × 10 ^5 + 0 × 10 ^4 + 4 × 10 ^3 + 7 × 10 ^2

+ 9 × 10 ^1 + 0 × 10 ^0

The vοlume οf the prism is 14 cubic feet.

A three-dimensiοnal structure having six rectangular faces is called a prism. It is alsο knοwn as a rectangular cubοid οr a rectangular parallelepiped.

The prism is cοmpletely filled with 1750 cubes that have an edge length οf 1/5 ft. This means that the vοlume οf each cube is \((1/5)^3 = 1/125\) cubic feet.

Tο find the vοlume οf the prism, we can divide the tοtal vοlume οf the cubes by the number οf cubes:

Vοlume οf prism = (Vοlume οf οne cube) x (Number οf cubes)

Vοlume οf prism = (1/125) x 1750

Vοlume οf prism = 14 cubic feet

Therefοre, the vοlume οf the prism is 14 cubic feet.

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If May was three times as old as Ann 12 years ago, and the sum of their ages is now 48, then:

May is 30 years old

Ann is 18 years old

Let the present age of May be represented by y

Let the present age of Ann be represented by x

Sum of their present ages is 48

x   +  y   =  48..........(1)

12 years ago:

Mary's age = y - 12

Ann's age = x - 12

Mary was three times as old as Ann

y  -  12   =  3(x  -  12)

y  -  12   =  3x   -  36

y    =  3x  -  36   +  12

y   =  3x   -  24........(2)

Substitute equation (2) into equation (1)

x   +  (3x  - 24)   =  48

x  +  3x  -  24   =  48

4x    =  48  +  24

4x   =  72

x   =  72/4

x   =  18

Substitute x = 18 into equation (2)

y  =  3(18)  -  24

y  =  30

May is 30 years old

Ann is 18 years old

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