(6) In a triangle, the sides have a ratio of 3:7:10. If the perimeter is 210 feet, what is the length of the longest side in feet? (A) * 10.5 (B) 31.5 (C) (D) 105​

Answer: midpoint is 4,5

Step-by-step explanation:

The probability that a student is in 4th grade given that they did not choose popular as the most important trait is 0.5 or 50%.

The probability is a concept used in statistics that measures the likelihood of an event occurring.

Let's call the event of a student being in 4th grade as A and the event of a student not choosing popular as the most important trait as B. We can find the probability of A and B happening together by dividing the number of students who are in 4th grade and did not choose popular by the total number of students. This can be represented as

P(A and B) = P(A | B) = (75 / 250) = 0.3.

Next, we can find the probability of B happening by dividing the number of students who did not choose popular by the total number of students. This can be represented as

P(B) = (150 / 250) = 0.6.

Finally, we can use Bayes' theorem to find the probability of A given B. Bayes' theorem states that

=> P(A | B) = P(A and B) / P(B).

Therefore,

=> P(A | B) = (75 / 250) / (150 / 250) = 0.3 / 0.6 = 0.5.

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The y-intercept will be at (0, 22,995) and the x -intercept at (9, 0).

The y-axis is calibrated in dollars and the x-axis in years.

The graph is a straight line which starts  on the positive y axis and ends on the positive x-axis and has a negative slope .

Y - intercept:

The point of intersection is the point on the Y-axis through which the slope of the straight line passes. This is the y-coordinate of the point where the line or curve intersects the y-axis. This is shown when writing the equation for the y = mx + c straight line. where m is the slope and c is the intersection with the y-axis.

X- Intercept:

The x-intercept is the point at which the graph of the equation intersects the x-axis, and the y-value must be 0 for the point to intersect the x-axis. Consequently, the x segment can always be represented as (x, 0). The x value indicates where the graph intersects the x-axis.

According to the question:

When X = 0, y = 22995

And, X = 9  and Y = 0.

So the intercepts are (0,22995) and (9,0) which are shown on the right.

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The ribbon needs to be 25.12 inches.

The distance along a circle's perimeter is referred to as its circumference.

Given:

She is putting ribbon around a cake tray that has a diameter of 8 inches.

The diameter = 8 inches.

The circumference = 8 x 3.14

                                = 25.12 inches.

The ribbon needs to be 25.12 inches.

Hence, ribbon should be 25.12 inches.

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Answer:

[tex]158[/tex][tex]cm^2[/tex]

Step-by-step explanation:

Since the formula is [tex]2(wl+hl+hw)[/tex], we can simply plug in the lengths.

Once calculated, the answer is [tex]158cm^2[/tex].

Hope it helped!

Answer:

  158 cm²

Step-by-step explanation:

You want the surface area of a rectangular prism whose net is shown.

The surface area of the prism is the area of the net. That area is the sum of the areas of the rectangles that make it up. The rectangles come in pairs that have the same area.

Down the middle we have two pairs of rectangles. One pair is 8 cm wide and 3 cm high; the other is 8 cm wide and 5 cm high. Together the area of those four rectangles is ...

  2(8 cm)(3 cm +5 cm) = 2(64 cm²) = 128 cm²

The "wings" of the net are rectangles that are 3 cm by 5 cm, so their total area is ...

  2(3 cm)(5 cm) = 30 cm²

The area of the net is then ...

  surface area = 128 cm² +30 cm²

  surface area = 158 cm²

__

Additional comment

If you like, you can use the area formula. It will tell you the same thing for this 3 × 5 × 8 cm prism.

  SA = 2(LW +H(L +W)) = 2(3·5) +8(3 +5)) = 2(15 +8·8) = 2(79) = 158 . . . cm²

As a result, the ratio of eighth students to seventh graders is 4:1.

A ratio is a comparison of two or more values, often expressed as a fraction or a colon-separated set of numbers. Ratios can be used to compare quantities of similar items, such as the ratio of the number of apples to the number of bananas in a basket. Ratios can also be used to describe the relationship between different aspects of a system, such as the ratio of length to width of a rectangle, or the ratio of time spent working to time spent sleeping. Ratios are a useful tool for making comparisons and understanding relationships between different values.

Here,

Out of the 15 students in the yearbook club, 3 are in 7th grade, and the rest are in 8th grade, which means there are 15 - 3 = 12 students in 8th grade.

The ratio of 8th graders to 7th graders can be calculated by dividing the number of 8th graders by the number of 7th graders:

12/3 = 4:1

So, the ratio of 8th graders to 7th graders is 4:1.

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Answer:

5.3

Step-by-step explanation:

sin24 = x/13

x = sin24(13) = 5.3

A quadrilateral with two sets of parallel sides and 4 congruent sides is called a parallelogram. A parallelogram is a quadrilateral with two sets of parallel sides and 4 congruent sides.

A parallelogram is a four-sided polygon with two pairs of opposite sides that are parallel to each other and equal in length. This means that the shape has two sets of parallel sides and all of its sides have the same length.

Parallelograms have several key properties, including opposite sides that are equal in length and parallel, and opposite angles that are equal in measure. Additionally, the diagonals of a parallelogram bisect each other, meaning they split each other in half.

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The markup is $6.47 and the selling price is $31.87

percentage, a relative value indicating hundredth parts of any quantity.

A markup is the amount added to the cost price of a product to determine the selling price.

Let the cost price of a box of copy paper is $25.4 and the markup is 25.4%

Now let us find the selling price by given formula.

Selling price = Cost price + (Cost price x Markup percentage)

Selling price = $25.4 + ($25.4 x 25.4%)

Selling price = $25.4 + ($25.4 x 0.254)

Selling price = $25.4 + $6.47

Selling price = $31.87

So, the markup is $6.47 and the selling price is $31.87.

Hence,  the markup is $6.47 and the selling price is $31.87

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The equation of line that passes through (3,2) and has a slope of 1/3 in point-slope form is y - 2 = (1/3)( x - 2 ).

The point-slope formula is expressed as;

y - y₁ = m( x - x₁ )

Where x and y are the coordinates and m is the slope.

Given the data in the question;

Point (3,2)

Plug the values into the point-slope formula.

y - y₁ = m( x - x₁ )

y - 2 = (1/3)( x - 2 )

Therefore, the equation in point slope form is y - 2 = (1/3)( x - 2 ).

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There are 11,838,890 ways to arrange 7 elves and 5 goblins in a row without any goblins standing next to each other.

This can be calculated using the formula for combinations, n!/(r!(n-r)!), where n is the total number of elves and goblins (12) and r is the number of goblins (5). The calculation is written as 12!/(5!(12-5)!) = 11,838,890.

To illustrate, one possible arrangement is EE EG EEG EEG EGEE EG. Here, E stands for elf and G stands for a goblin. The arrangement starts with two elves, followed by an elf and a goblin, followed by three elves, followed by an elf and a goblin, followed by two elves, and finally ending with an elf.

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Total number of students that like chicken nuggets is 4/7 x G + 40/100 x B.

The percentage of entire student body that like chicken nuggets are (4/7 x G + 40/100 x B) / T x 100.

Given that 4/7 of the girls like chicken nuggets, if there are G girls, then the number of girls who like chicken nuggets is 4/7 x G.

Given that 40% of the boys like chicken nuggets, if there are B boys, then the number of boys who like chicken nuggets is 40/100 x B.

The total number of students who like chicken nuggets is 4/7 x G + 40/100 x B.

To find the percentage of the entire student body that likes chicken nuggets, divide the number of students who like chicken nuggets by the total number of students, and multiply by 100.

Let's say there are T total students.

The percentage of the entire student body that likes chicken nuggets is (4/7 x G + 40/100 x B) / T x 100.

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137 is not a term in this sequence due to the fact that  7n +2= 137 gives n = 19.285 which is not a whole number.

We have to use the formula

tn = a + ( n - 1) d

where we have tn = 137

a is the first term = 9

n i unknown

d is the difference = 16 - 9 = 7

We have to put these values in the formula such that

137 = 9 + (n - 1) 7

then we have to expand this

137 = 9 + 7n - 7

take the like terms

137 = 9 - 7 + 7n

137 = 2 + 7n

137 - 2 = 7n

135 = 7n

divide through by 7

135 / 7 = 7n / 7

n = 19.28571...

This is not a whole number, hence 137 is not a term in the sequence that we have here

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The solution to the equation cos(x + 2π/3) = √2/2 over the interval

(0, 2π) is [7π/12, 3π/4]

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

The given function is cos(x + 2π/3) = √2/2 over the interval (0, 2π).

(x + 2π/3) = cos⁻1(√2/2).

x + 2π/3 = π/4  or 21π/12   (As cos is +ve on I and IV)

Now,

x + 2π/3 = π/4.

x = π/4 - 2π/3.

x = (3π - 8π)/12.

x = - 5π/12.

x = π - 5π/12.

x = (12π - 5π)/12.

x = 7π/12.

And,

x + 2π/3 = 21π/12.

x = 21π/12 - 2π/2.

x = (21π - 12π)/12.

x = 9π/12.

x = 3π/4.

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The elements in (D∩B)' is A,B,D.

A set is defined as collection of well-defined object. It is denoted by capital letters and their elements are denoted by small letters.

Given that ,

In venn diagram, B is the swamp portion and D is the rainforest portion.

C represents the intersection of B and D. i.e., C= (D∩B)

A is the universal set.

(D∩B)' = A - (D∩B)

          = A - C

Hence, (D∩B)' contains  A, B, D.

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A high standard deviation indicates greater variability in the data set. A low standard deviation indicates lower variability in the data set.

A standard deviation is a measure of how spread out the values in a data set are. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. A high standard deviation indicates that the values in the data set are far from the mean and spread out over a large range of values. This suggests that there is a large amount of variation and diversity in the data. On the other hand, a low standard deviation indicates that the values in the data set are close to the mean and spread out over a smaller range of values. This suggests that there is less variability and diversity in the data. A standard deviation of zero indicates that all values in the data set are the same. This suggests that there is no variation or diversity in the data. No one set of data is more accurate than another; accuracy depends on the context and purpose of the data. For example, if the goal is to identify trends or outliers, a data set with a high standard deviation may be more useful than one with a low standard deviation.

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The root of the equation are x² + x − 5 = 0 are 2.85 and --3.85

quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

We can use the formula x =-b±√b²-4ac/2a to find the root of a quadratic equation

a = 1, b = 1 and c = -5

x= -(1) ± √ 5²-4× -5×1)/2

x = -1±√25+20)/2

x = -1±√45)/2

x = -1+6.7/2 or -1-6.7/2

x = 5.7/2or -7.7/2

x = 2.85 or -3.85

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The graph of the linear equation is attached

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

A bowling alley charges $6 for shoe rental and $2 for each game.

This means that

Intial value = 6

Rate = 2

The function is then represented as

f(x) = Initial + Rate * x

So, we have

f(x) = 6 + 2x

See attachment fr the graph

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The value of the angle 4 is 96 degrees as shown in the diagram.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.

From the given diagram, the measure of angle 1 and 3 are equal as well as 2 and 4.

Given the following angles

m<3 = 84 degrees

Since the measure of <3 and <4 lies on the same straight line, hence:

m<3 + m<4 = 180

84 + m<4 = 180

m<4 = 180 - 84

m<4 = 96 degrees

Hence the measure of angle 4 from the figure is 96 degrees

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A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

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Answer:

Amy is 14 years old and Sam is 10 years old.

Step-by-step explanation:

Let's represent Amy's current age as "A".

Since Sam is four years younger than Amy, his current age can be represented as (A - 4).

Five years ago, Amy's age was A - 5 and Sam's age was (A - 4) - 5 = A - 9.

At that time, Sam was half of Amy's age, so we can write the following equation:

(A - 9) = (A - 5) / 2

Expanding and simplifying the equation, we get:

A - 9 = 2A / 2 - 5 / 2

A - 9 = A - 5 / 2

7 = A / 2

A = 14

So, Amy is 14 years old and Sam is (14 - 4) = 10 years old.

An expression which best represents the value of pi include the following: D. C/7.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Making π the subject of formula, we have the following:

π = C/D

Substituting the given parameters into the circumference of a circle formula, we have;

π = C/7.

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Complete Question:

A circular pond has a circumference of about C feet. The diameter of the pond is 7 feet. Which expression best represents the value of pi?

A. C/14

B. 7/C

C. 14/C

D. C/7

Liliana's next step is to find the area of each of the two trapezoids.

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

Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid

This is done using

Area = 1/2 * (sum of parallel sides) * height

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Complete question

Area of Trapezoids and Other Figures quick check

Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?

The numbers have been matched accordingly as below.

Rational numbers are numbers which can be written in the form of a/b, b ≠ 0, and a and b are integers.

Irrational numbers cannot be written in this form.

√30 is not a perfect square. So it is real, irrational root.

-26 is a negative real integer. So it is a real rational integer.

√64 is actually a perfect square root, 8, which is a whole number. So it is a real, rational root, whole number.

1/4 is of the form a/b. So it is also real, rational.

0.363363336.... is a real irrational decimal.

0.424242..... is a real rational decimal, since it is repeating in nature.

[tex]\sqrt{-7}[/tex] or [tex]7i[/tex] is an imaginary number.

Hence the numbers has been matched according to the properties.

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The exponential function is [tex]y = 1505.88(0.85)^x[/tex].

The monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To model the monthly number of defective parts, we can use an exponential equation of the form:

[tex]y=a(b)^x[/tex]

Where y is the number of defective parts, x is the number of months after Jane was hired, a is the initial number of defective parts, and b is the common ratio between consecutive months.

To find the values of a and b, use the two data points given -

In the first month, there were 1,280 defective parts, which means that y = 1280 when x = 1.

In the second month, there were 1,088 defective parts, which means that y = 1088 when x = 2.

Substituting these values into the exponential equation -

1280 = a(b)

1088 = a(b)²

Dividing the second equation by the first equation -

1088/1280 = (a(b)²)/(a(b))

0.85 = b

Substituting b = 0.85 into the first equation -

1280 = a(0.85)

1280 = 0.85a

a = 1505.88 (rounded to two decimal places)

So the exponential equation that models the monthly number of defective parts is -

[tex]y = 1505.88(0.85)^x[/tex]

To find when the monthly number of defective parts will be less than 500, we can set y = 500 and solve for x -

[tex]500 = 1505.88(0.85)^x[/tex]

Dividing both sides by 1505.88 -

[tex]0.332 = (0.85)^x[/tex]

Taking the logarithm of both sides (with any base) -

log(0.332) = x log(0.85)

Dividing both sides by log(0.85) -

x = log(0.332) / log(0.85)

x ≈ 6.87

Therefore,  the monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

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Answer:

The value of [tex]r[/tex] is 24 cm.

Option C. 24 cm

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the missing side.

Here is the formula for the Pythagorean theorem.

[tex]a^2+b^2=c^2[/tex]

[tex]a[/tex] and [tex]b[/tex] are the legs of the triangle

[tex]c[/tex] is the hypotenuse

In this example we are given the value of 1 leg and the hypotenuse.

Knowing 2 of the 3 sides, we can evaluate the missing leg.

Let [tex]a=r[/tex]

We are given

[tex]b=10\\c=26[/tex]

Inserting our values into the Pythagorean theorem gives us

[tex]r^2+10^2=26^2[/tex]

Lets solve for [tex]r[/tex].

[tex]r^2+10^2=26^2[/tex]

Evaluate [tex]10^2[/tex].

[tex]r^2+100=26^2[/tex]

Evaluate [tex]26^2[/tex].

[tex]r^2+100=676[/tex]

Subtract [tex]100[/tex] from both sides of the equation.

[tex]r^2=576[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]r=\sqrt{576}[/tex]

[tex]r=24[/tex]

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Answer:

I would recommend taking practice quizzes online for the level of math you are taking to find what areas you understand well and what areas you are struggling in. From there, you can review that specific area of math and refine your knowledge. Taking practice quizzes repeatedly until you are confident both in the mathematics and the test taking itself(if you struggle with test taking in general) will help a lot.

Answer:

Step-by-step explanation:

Study Time: I suggest you study over a period of time and try to understand the topic. For example, try to include breaks to help yourself relax. DO NOT cram lots of math into your head on an overnight studying marathon. Many people try that, and unless you have a photographic memory, it does not help at all.

Topics: Try to study one topic at a time so the information does not get mixed up in your head. Try to remember things with variables.

Resources: Ask your teacher what topics the test will cover and how many questions will be on the test. You can find lots of worksheets online and review explanations to similar questions on websites.

Morning before the test: Sleep early and wake up early. Try to relax and eat a healthy breakfast.

I wish you luck on your test!

The number of possibilities are 20,160. Therefore, the option A is the correct answer.

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.

Factorials is used in mathematics or statistics to denote the possibilities of an event in an outcome.

The number of specialty pizzas that is being offered by pizza parlor = 8

The number of specialty that Almeida's family wants to order = 2

To calculate the number of possibilities;

= 8!/2!

= 8×7×6×5×4×3×2×1/2×1

= 20,160.

Therefore, the option A is the correct answer.

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The exact area of the circle would be = 36πcm². That is option B.

The area of a circle can be calculated through the use of the formula = πr²

Where,

radius (r) = 6 cm

area = π × 6²

= 36π cm² ( in the terms of π)

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