Mary is planning to buy a mobile phone that costs $500. She can choose any of five different payment plans with varying simple interest rates and periods:

plan 1: 6% for 10 months
plan 2: 8% for 12 months
plan 3: 10% for 14 months
plan 4: 12% for 18 months
plan 5: 14% for 12 months

Which plan offers the lowest monthly payments?

Answer:

D. 10 (6y-9-2x)

Step-by-step explanation:

10×6y 10× -9 10×-2x

60y -90 -20x

The sample space is (R, G, P, Y).(OB)

What is sample space?

A sample space is a collection  of possible outcomes of a random experiment. The sample space is represented by the symbol, “S”.  A sample space may contain a  finite number of outcomes which depends on the experiment.

You spin a spinner with 4 sections: 1 red (R), 1 green (G), 1 purple (P), and 1

yellow (Y).

So here is 4 sections

Red(R), Green (G), Purple (P), Yellow(Y)

So there are 4 sections in sample space

The sample space for one spin of the spinner is  (R, G, P, Y).

Hence, the sample space is (R, G, P, Y).

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Answer:

Step-by-step explanation:

Median: C) 13

First Quartile: A) 8.5

Third Quartile: B) 17.5

Explanation:

To find the median, we need to arrange the numbers in ascending order:

{3, 5, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(10 + 11)/2 = 10.5.

To find the first quartile, we need to find the median of the lower half of the data set.

The lower half is {3, 5, 5, 8, 9, 10, 11, 12}.

Since there are an even number of values, we take the average of the middle two numbers:

(8 + 9)/2 = 8.5.

To find the third quartile, we need to find the median of the upper half of the data set.

The upper half is {14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(17 + 18)/2 = 17.5.

2 is the value of C in the function by Rolle's theorem.

What is Rolle's Theorem ?

Rolle's theorem states that if f is a continuous function on the closed interval [a,b] differentiable on the open interval (a,b) and f(a)=f(b), then at least one number c is indicates that it exists. We get (a,b) such that f'(c) = 0. For Rolle's theorem to be true, all three of his conditions are important:

Condition 1:

f(x) is continuous on the closed interval [a,b]. Condition 2:

f(x) is differentiable on the open interval (a,b). Condition 3:

f(a) = f(b).  

F(x) = x² - 4x + 8  on the interval [0 , 4 ]

f(x) is continuous [0 , 4] & veriable on (0 , 4 )  (∵ f'(x) = 2x - 4 )

  f(0) = 8      f(4)  = 16 - 16 + 8   = 8

   ∴ f(0) = f(4)     hence  f(x) satisfies these conditions.

 ∴  F C ∈  (0 , 4)

     f'(c) = 2c - 4 = 0

            2c = 4

               c = 2

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The area οf family game rοοm is 152 square yards.

The tοtal space οccupied by a flat (2-D) surface οr the shape οf an οbject is defined as its area. The area οf a plane figure is the space enclοsed by its bοundary. The number οf unit squares that cοver the surface οf a clοsed fοrm is the figure's area.

Tο find the area let's divide the figure in 3 parts: twο rectangles and οne triangle.

1. Fοr area οf first rectangle:

Length = 12 yards and width = 8 yards

Area οf rectangle = L x B

Area οf rectangle = 12 x 8

Area οf first rectangle = 96 square yards

2. Area οf secοnd rectangle:

Length = 8 yards and width = 4 yards

Area οf secοnd rectangle = L x B

Area οf secοnd rectangle = 8 x 4

Area οf secοnd rectangle = 32 square yards

3. Area οf triangle:

Base = 6 yards and height = 8 yards

Area οf triangle = 1/2 x base x height

Area οf triangle = 1/2 x 6 x 8

Area οf triangle = 24 square yards

Area οf the family game rοοm = Area οf first rectangle + Area οf secοnd rectangle + Area οf triangle

Area οf the family game rοοm = 96 + 32 + 24

Area οf the family game rοοm = 152 square yards

Therefοre, the area οf family game rοοm is 152 square yards.

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Answer:

Already rounded?

Step-by-step explanation:

I mean 15.700 is a decimal. So thousandths place would be what you put. Sorry but you already have the answer.

According to the information, the combined total profit TechWiz made from selling both MP3 and DVD players would be: 35x + 18(128 - x)

Let x be the number of MP3 players sold. Then the number of DVD players sold would be 128 - x (since the total number of players sold is 128).

The profit made from selling x MP3 players would be $35 times x, which is 35x.

Similarly, the profit made from selling (128 - x) DVD players would be $18 times (128 - x), which is 18(128 - x).

Therefore, the combined total profit TechWiz made from selling both MP3 and DVD players would be:

35x + 18(128 - x)

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A. He earned GH¢12035.77 in interest over 7 years.

B. He received a total of GH¢26135.77 at the end of 7 years.

Compound interest is a type of interest where the interest earned is added to the principal amount and then the interest is calculated on the new total. In other words, it is interest earned on both the initial principal and the interest accumulated on that principal over time.

A man deposited GH¢14100.00 at 8% per annum compound interest. If at the end of 4

years he transfers the total amount to another bank offering 12% compound interest per

annum.

a. How much interest did he get at the end of 7 years?

b. Calculate the total amount he received at the end of seven years.

To solve this problem, we can use the compound interest formula:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where:

A = final amount

P = principal amount (initial deposit)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

Using this formula, we can solve the problem as follows:

a. First, we need to find the amount of money he will have after 4 years of compound interest at 8% per annum:

P = GH¢14100.00

r = 8% = 0.08

n = 1 (compounded annually)

t = 4 years

A =  P[tex](1 + r/n)^{(nt)}[/tex]

A = GH¢14100.00(1 + 0.08/1)^(1*4)

A = GH¢18285.12

So after 4 years, he will have GH¢18285.12. Now we need to find out how much interest he will earn over the next 3 years, when he transfers the money to another bank offering 12% compound interest per annum:

P = GH¢18285.12

r = 12% = 0.12

n = 1 (compounded annually)

t = 3 years

A =  P[tex](1 + r/n)^{(nt)}[/tex]

A = GH¢18285.12(1 + 0.12/1)^(1*3)

A = GH¢26135.77

So after 7 years, he will have GH¢26135.77. To find out how much interest he earned, we can subtract the initial deposit:

Interest = A - P

Interest = GH¢26135.77 - GH¢14100.00

Interest = GH¢12035.77

Therefore, he earned GH¢12035.77 in interest over 7 years.

b. Calculate the total amount he received at the end of seven years.

To calculate the total amount he received at the end of 7 years, we simply add the initial deposit to the interest earned:

Total amount = P + Interest

Total amount = GH¢14100.00 + GH¢12035.77

Total amount = GH¢26135.77

Therefore, he received a total of GH¢26135.77 at the end of 7 years.

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294 number of burgers, the food truck will be able to sell on the basis of the data given and probability of a person selected at random out of 900 will buy a burger is option C, 294 burgers.

What is probability?

It is a field of mathematics that assesses the potential outcomes of a given sample space as well as the relative likelihoods and distributions of those possibilities. The term "probability" is frequently used to refer to the likelihood that a specific event (or group of events) will occur, either as a number between 0 and 100% or on a linear scale from 0 (impossibility) to 1. Statistics is the study of probability applied to possibilities.

Given that,

Number of burgers on 3 different day:

Day-1=35 burgers

Day-2=18 burgers

Day-3=45 burgers

Total burgers sold in all three days= 35+18+45

                                                         =98 burgers

Total samples collected on all three days=100+100+100

                                                                    =300 people

Probability that person chosen at random out of 300, purchases a burger= [tex]\frac{favourable outcomes}{total outcomes}[/tex]

          =[tex]\frac{98}{300}[/tex]

Probability that person chosen at random out of 900, purchases a burger= probability of people chosen out of 300 x 900

           =[tex]\frac{98}{300}[/tex] x 900

           =98 x 3

           =294 burgers.

The number of burgers that will be sold by food truck=294 burgers.

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Step-by-step explanation:

Angle DFE is  360 - 256 = 104 degrees

 the area of this is   104 /360 the of the entire circle area ( pi r^2)

  Total Area = pi (14)^2  = 196 pi

104 / 360    *   196 pi = 177.9 cm^2

Answer:

E = 2(3x) = 6x

Step-by-step explanation:

To find the number of edges of a prism, we can use the formula E = (2n), where E is the number of edges and n is the number of vertices.

For a prism, we know that it has two identical polygonal faces (the bases), each with x sides. Each of these faces will have x vertices since each vertex is where two sides meet. The other vertices of the prism will be where the lateral faces meet the bases, which is equal to x for each base. Therefore, the total number of vertices in the prism is 2x + x = 3x.

Using the formula E = (2n), we can find the number of edges of the prism:

E = 2(3x) = 6x

Therefore, the expression for the number of edges of the prism is 6x, which is not listed as an option. The closest option is B, 3x, but that represents the number of edges of a triangular prism, not a prism with x sides.

Answer: B

Step-by-step explanation: I took the test.

The answer of given equation is = 1 { [tex]( a)^0[/tex] that means the value is 1}

An exponent and a power both refer to the same concept, which is a way to represent repeated multiplication of a number or a variable by itself. The exponent or power is usually represented as a superscript to the right of the base number or variable.There are 10 basic rule

For example, in the expression 2³, the base number is 2, and the exponent or power is 3. This means that 2 is being multiplied by itself three times. So, 2³ is equal to 2 x 2 x 2, which equals 8.

Similarly, in the expression[tex]x^4[/tex], the base is x, and the exponent or power is 4. This means that x is being multiplied by itself four times. So,[tex]x^4[/tex] is equal to x x x x, which can be written as x multiplied by itself four times.

Any number or variable raised to the power of 0 is equal to 1. Therefore,

[tex](x^36y^18z^12)^0[/tex] = 1  ( According to this rule, when the power of any integer is zero, then its value is equal to 1, such as;

[tex]a^0[/tex]= 1

where ‘a’ is any non-zero term.

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Answer:

Step-by-step explanation:

   To find the daily expense for food and lodging for the family, we can use the formula:

   z = (x - μ) / σ

   where z is the z-score, x is the daily expense for food and lodging, μ is the mean daily expense, and σ is the standard deviation. Rearranging this formula to solve for x, we get:

   x = z * σ + μ

Substituting z = 1.5, σ = $60, and μ = $247, we get:

x = 1.5 * $60 + $247 = $337

Therefore, the daily expense for food and lodging for the family was $337.

   To find the percentage of families who spent less than $367 per day, we can standardize the value using the same formula as above:

   z = (x - μ) / σ

   Substituting x = $367, μ = $247, and σ = $60, we get:

   z = ($367 - $247) / $60 = 2

Using a standard normal distribution table or calculator, we can find the percentage of families with a z-score less than 2, which is approximately 97.72%. Therefore, approximately 97.72% of families spent less than $367 per day.

   To find the percentage of families who spent more than $247 per day, we can use the same formula and standardize the value:

   z = (x - μ) / σ

   Substituting x = $247, μ = $247, and σ = $60, we get:

   z = ($247 - $247) / $60 = 0

Using a standard normal distribution table or calculator, we can find the percentage of families with a z-score greater than 0, which is 50%. Therefore, 50% of families spent more than $247 per day.

   To find the percentage of families who spent more than $350 per day, we can standardize the value:

   z = (x - μ) / σ

   Substituting x = $350, μ = $247, and σ = $60, we get:

   z = ($350 - $247) / $60 = 1.72

Using a standard normal distribution table or calculator, we can find the percentage of families with a z-score greater than 1.72, which is approximately 4.35%. Therefore, approximately 4.35% of families spent more than $350 per day.

   To find the percentage of families who spent less than $67 per day, we can standardize the value:

   z = (x - μ) / σ

   Substituting x = $67, μ = $247, and σ = $60, we get:

   z = ($67 - $247) / $60 = -3.00

Using a standard normal distribution table or calculator, we can find the percentage of families with a z-score less than -3.00, which is approximately 0.13%. Therefore, approximately 0.13% of families spent less than $67 per day.

   To find the percentage of families who spent between $200 and $300 per day, we need to standardize both values and find the area between them. Using the same formula as above:

   z1 = ($200 - $247) / $60 = -0.78

   z2 = ($300 - $247) / $60 = 0.78

Using a standard normal distribution table or calculator, we can find the percentage of families with a z-score between -0.78 and 0.78, which is approximately 53.91%. Therefore, approximately 53.91% of families spent between

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be Spοrts & Sοrts must sell abοut 607,385 vοlleyballs.

The well-knοwn straightfοrward apprοach, actual variables, and any relevant infοrmatiοn frοm the initial and specialist questiοns can all be used tο finish the assignment. Custοmers may be given anοther chance tο try the gοοds in respοnse. If nοt, significant expressiοn in οur understanding οf prοgrams will be lοst.

Here,

We must figure οut hοw many vοlleyballs must be sοld tο cοver the fixed and variable cοsts in οrder tο estimate the break-even pοint.

The quantity οf vοlleyballs needed tο break even is X.

Fixed cοst plus variable cοst equals tοtal cοst.

Selling price x Number οf units sοld equals tοtal revenue.

The tοtal revenue and entire expense are equal at the break-even pοint.

Thus, we can cοnstruct the equatiοn:

Fixed cοst plus variable cοst multiplied by the selling price equals the quantity sοld.

=> $25.12 X = $3,709,246.60 + $19.01 X

=> $25.12 X - $19.01 X = $3,709,246.60

=> $6.11 X = $3,709,246.60

=> X = $3,709,246.60 / $6.11

=>  X ≈ 607,385

In οrder tο break even, Spοrts & Sοrts must sell abοut 607,385 vοlleyballs.

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Kaya will pay $728 for skiing 2 regular-season weekdays, 8 regular-season weekend days, and 3 holiday-season days with the Flex Pass option.

Amount is a quantity or number that can be measured, counted, or compared. It is usually used to refer to a numerical value, such as a sum of money, an amount of time, a quantity of goods, or a measure of a person's height or weight. It is also used to refer to the total or aggregate of something, such as the amount of rainfall in a given year.

The total amount Kaya will pay for skiing 2 regular-season weekdays, 8 regular-season weekend days, and 3 holiday-season days with the Flex Pass option is $728. This is calculated as follows:

2 regular-season weekdays × $80/day = $160
8 regular-season weekend days × $90/day = $720
3 holiday-season days × $95/day = $285
Total = $160 + $720 + $285 = $1,165
Flex Pass discount = $1,165 × 0.37 = $432
Total amount Kaya will pay = $1,165 − $432 = $728.

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Answer:

9b ≤ 15

Step-by-step explanation:

The inequality that represents the given sentence is:

9b ≤ 15

Here, "9b" represents the product of b and 9, and "≤" represents "less than or equal to".

The shortest side is the middle side minus 14. The length of the shortest side is x=-12.

Length is the measurement of something. It is measured n meters and kilometers.

Since the triangle is a right triangle you can use the Pythagorean theorem to find the lengths of each side

a² + b² = c²

The longest side of every right triangle is the hypotenuse so right away we know that 26 m.

One side is a = x and the other is b = 14 + a. This is because it says "One of the shorter sides is 7 m longer than the other" which can be translated into the equation 7 + x which leaves the remaining side as simply x.

Put these equations into the Pythagorean Theorem.

c = 26

a = x

b = 7 + x

a² + b² = c²

x² + (14 + x)² = 26²

Distribute then solve for x to find the shortest side.

x² + x² + 26x + 196  = 676

2x² + 26x - 480 = 0

x² + 13x - 240 = 0

x + -12

x=-12 x=5

Thus, the shortest length is x = 12.

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The equation sin²a / (1 + cos a) simplifies to 1 - cos a.

Trigonometry is one of the most significant branches of mathematics, with numerous applications in a wide range of fields. The study of the relationship between the sides and angles of a right-angle triangle is the focus of the "Trigonometry" branch.

To simplify sin²a / (1 + cos a), we can first use the identity:

sin²a + cos²a = 1

Rearranging this identity, we get:

sin²a = 1 - cos²a

Substituting this expression into the numerator of the fraction, we get:

sin²a / (1 + cos a) = (1 - cos²a) / (1 + cos a)

Now, we can use the identity:

a² - b² = (a + b) (a - b)

to factor the numerator:

(1 - cos²a) = (1 + cos a) (1 - cos a)

Substituting this expression back into the fraction, we get:

sin²a / (1 + cos a) = [(1 + cos a) (1 - cos a)] / (1 + cos a)

Simplifying the fraction, we get:

sin²a / (1 + cos a) = 1 - cos a

Therefore, sin²a / (1 + cos a) simplifies to 1 - cos a.

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The appropriate type of F-test for this scenario would be a repeated measures ANOVA.

An F-test is a statistical test used to compare the variances of two or more populations. Specifically, an F-test compares the ratio of the variances of the populations to determine whether they are significantly different from each other.

(a) The appropriate type of F-test for this scenario would be a repeated measures ANOVA, which is used when the same group of subjects is tested multiple times under different conditions.

(b) The appropriate type of F-test for this scenario would be an independent samples t-test or a two-way ANOVA with one factor being gender and the other being the speaker's gender.

(c) The appropriate type of F-test for this scenario would be a matched pairs t-test or a repeated measures ANOVA with the factor being the gender of the speaker. The requirement that each man has a woman of the same age implies that the two groups are matched on a demographic variable (age) that could potentially affect the outcome of the study.

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Answer:

A.

Step-by-step explanation:

I had this question before but instead of finding the equation, it gave me THE equation to solve.

We may infer after addressing the stated question that As a result, the vertices of triangle A'B'C' are as follows: A'(-2, -4) (-2, -4); B'(-7, -6) (-7, -6); C'(-1, -13) (-1, -13)

A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.

To reflect a point (x,y) over the line y=-x, we first swap its x and y coordinates, then negate both:

The inverse of point (x,y) is (-y, -x).

Hence, by reflecting each of A, B, and C over the line y=-x, we can obtain the vertices of triangle A'B'C':

Vertex A' is the mirrored image of A. (-2, -4)

Vertex B' is a mirror of Vertex B. (-7, -6)

Vertex C' is the mirrored image of C. (-1, -13)

As a result, the vertices of triangle A'B'C' are as follows:

A'(-2, -4) (-2, -4)

B'(-7, -6) (-7, -6)

C'(-1, -13) (-1, -13)

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Among the given options expressions that will be equivalent to given expression is that of first and second option.

A mathematical expression having one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division is known as an algebraic expression. Algebraic expressions are used to depict connections and describe mathematical situations in which the variables' values are unknown or change.

On simplifying given expression, we get

[tex]\frac{2}{3} (12-x)+6(\frac{1}{3} x-1)=8-\frac{2x}{3} +2x-6=2+\frac{4x}{3}[/tex]

Now, checking given options,

A. [tex]2+\frac{4x}{3}[/tex] is equivalent.

B. [tex]8-\frac{2x}{3} +2x-6[/tex] is equivalent.

C. [tex]\frac{x}{3} +2[/tex] in not equivalent.

D. [tex]6-\frac{2x}{3} +3x-6[/tex] is not equivalent.

Hence, only expressions in first and second option are Equivalent to given expression.

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The contractor will not be able to reach them with this ladder alone.

What is Trigonometric ratio?

Trigonometric ratios are mathematical tools used to relate the angles and sides of a right triangle. These ratios are defined as the ratios of the lengths of two sides of a right triangle to a given angle. There are six basic trigonometric ratios, which are sine, cosine, tangent, cosecant, secant, and cotangent.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

To solve this problem, we need to use trigonometry. Let's call the height the ladder reaches up the wall "h".

We know the length of the ladder is 19 feet and the angle it makes with the ground is 65°.

Using trigonometry, we can find the height the ladder reaches up the wall as follows:

sin(65°) = h/19

Multiplying both sides by 19, we get:

h = 19 × sin(65°)

h ≈ 16.37 feet

So the ladder reaches a height of about 16.37 feet up the wall. Since the repairs are 17 feet up the wall, the contractor will not be able to reach them with this ladder alone.

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There are 7 pencils measuring more than 5 1/2 inches but less than 7 2/4 inches.

An inch is a unit of length in the imperial and US customary systems of measurement. Equal to 1/12 of a foot, it is usually denoted by the symbol "in". It is also equal to 2.54 centimeters. The inch is commonly used in the construction industry, engineering, and other fields.

To answer this question, we must first convert all of the measurements into the same unit of length. We will convert 5 1/2 inches and 7 2/4 inches into decimals by dividing the fractions by their denominators. 5 1/2 inches is equal to 5.5 inches and 7 2/4 inches is equal to 7.25 inches.

Now, we can calculate how many pencils are measuring more than 5.5 inches but less than 7.25 inches. To do this, we will subtract the smaller number (5.5) from the larger number (7.25).

7.25 - 5.5 = 1.75

This means that there are 1.75 inches between the two measurements. Since each pencil takes up about 0.25 inches, we can divide 1.75 by 0.25 to determine how many pencils would fit in that space.

1.75 / 0.25 = 7

Therefore, there are 7 pencils measuring more than 5 1/2 inches but less than 7 2/4 inches.

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Complete questions as follows-

how many pencils measure more than 5 1/2 inches but less than 7 2/4 inches?

The volume of water that flowed through the pipe in 3 minutes is 29100 cm³

First, we need to find the area of the shaded area. This given by:

Area of shaded area = Area of sector - area of triangle AOC

Area of shaded area = (72/360 * π * 4.8²) - (1/2 * 4.8 * 4.8 * sin 72)

Area of shaded area = (72/360 * 22/7 * 4.8²) - (1/2 * 4.8 * 4.8 * sin 72)

Area of shaded area = 11.56 cm²

Volume of water  = area * rate * time

Volume of water in 3 minutes = 11.56  * 14 * 180    (3 minutes = 180 sec.)

Volume of water in 3 minutes = 29131.2 cm³

Volume of water in 3 minutes = 29100 cm³ (to 3 significant figures)

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The probability that the flight will be no more than 5 minutes late is 0.02 (to 2 decimals).

The probability that the flight will be more than 10 minutes late is 1 - 0.0083 = 0.9917 (to 2 decimals).

The expected flight time is 126 minutes.

The probability density function for flight time in minutes would be a horizontal line that starts at 0 and ends at a height of 5/12 (since the flight time is uniformly distributed between 2 hours and 2 hours, 12 minutes, which is a range of 12 minutes, and the total area under the curve must equal 1).

To find the probability that the flight will be no more than 5 minutes late, we need to find the area under the probability density function from 0 to 5 minutes late. This area is equal to:

(5/12) * (5/60) = 0.0208

So the probability that the flight will be no more than 5 minutes late is 0.02 (to 2 decimals).

To find the probability that the flight will be more than 10 minutes late, we need to find the area under the probability density function from 10 to 12 minutes late, and then subtract that from 1 (since we want the probability that the flight is more than 10 minutes late). This area is equal to:

(5/12) * (2/60) = 0.0083

So the probability that the flight will be more than 10 minutes late is 1 - 0.0083 = 0.9917 (to 2 decimals).

To find the expected flight time, we need to find the mean of the uniform distribution, which is equal to the average of the minimum and maximum values:

(mean) = (2 hours + 2 hours, 12 minutes) / 2 = 2 hours, 6 minutes = 126 minutes

Therefore, the expected flight time is 126 minutes.

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Answer

approximately 0.0067

Step-by-step explanation:

If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.

Part A: The total surface area of the bench is 134.8 square feet. Part B: It will cost $103.90 to cover the bench in ceramic tiles.

Surface area is a measurement of the overall space occupied by an object's surface. It is the total area of a three-dimensional object faces or surfaces. Square units like square inches, square feet, or square metres are commonly used to express surface area.

Calculating the surface area of a cube, for instance, requires multiplying the area of one face (length x width) by the number of faces (6 in the case of a cube).

For the given dimensions of the rectangular prism we have:

Part A: The surface area is:

Front and back faces: 6 ft x 5 ft = 30 sq ft x 2 = 60 sq ft

Top and bottom faces: 6 ft x 3.4 ft = 20.4 sq ft x 2 = 40.8 sq ft

Side faces: 5 ft x 3.4 ft = 17 sq ft x 2 = 34 sq ft

Total surface area = 60 + 40.8 + 34 = 134.8 sq ft

Therefore, the total surface area of the bench is 134.8 square feet.

Part B:

The cost of covering in tiles is:

Cost of tiles = Total surface area x Cost per square foot

Cost of tiles = 134.8 sq ft x $0.77/sq ft

Cost of tiles = $103.90

Therefore, it will cost $103.90 to cover the bench in ceramic tiles.

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Answer: 106°

Step-by-step explanation:

First add the two angles together: 51+23=74

Then subtract it from 180 because the sum of all angles in a triangle is 180°: 180-74=106

Therefore, the answer the 106°