What is the interquartile range of the following data set? 45,12,48,96,61,84,29,1,72,5,14

Answer:

Greg spent $6.00

Step-by-step explanation:

Agnes spent $10 for 5 feet of wood molding to frame a picture.

Greg bought one yard of the same molding.

1 yard = 3 feet

We will calculate the answer with unitary method.

∵  5 feet of wood molding costs = $10.00

∴ 1 feet of wood molding costs = [tex]\frac{10}{5}[/tex]

∴ 3 feet of wood molding costs = [tex]\frac{10}{5}[/tex] × 3 = $6.00

Greg spent $6.00 in the molding of 1 yard wood.

Answer:

$6

Step-by-step explanation:

I took the test .

Answer:

the correct option is C.

Step-by-step explanation:

The x-intercept of both functions g(x) and f(x) occur at point (1, 0).

Now, we need to find where g(x) > f(x) and f(x) > g(x)

We know that the greater the base of a logaritmic function is, the faster it will grow/decay.

For that reason, we can say that g(x) > f(x)  on (1, +inf).

Now, when x<1 then y<0. So on the interval (0, 1) the function g(x) will decay much faster than the function f(x), so we can say that f(x) > g(x) on (0, 1). So the correct option is C.

Check the graph, to verify all this.

Options 1, 2, and 3 are valid based on the given information and calculations.

1. When added, the sum of the y-intercepts must be 8:

  - If the y-intercepts are denoted as b₁ and b₂ for f(x) and g(x) respectively, then . [tex]b_1 \times b_2 = 8[/tex].

2. When multiplied, the product of the y-intercepts must be 8:

  - This translates to [tex]b_1 \times b_2 = 8[/tex].

3. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change:

  - This implies that the slopes of the lines have opposite signs.

Checking the given U-turn points (-2, 8) and (8, 2). The slope (rate of change) between these points can be calculated as:

[tex]\[ m = \frac{change\:in\:y}{change\:in\:x} \][/tex]

[tex]\[ m = \frac{2 - 8}{8 - (-2)} = \frac{-6}{10} = -\frac{3}{5} \][/tex]

4. f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of -3:

  - This statement is inconsistent with the calculated slope.

5. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of -1:

  - This statement is also inconsistent with the calculated slope.

Therefore, options 1, 2, and 3 are valid based on the given information and calculations.

Answer:

1 When multiplied the product of the y intercepts must be 8

2 Either f(x) or g (x) has a positive rate of change and the other has a negative rate of change

3 f (x) could have a rate of change equal to 2 and g (x) could have a rate change of -1

Answer:

[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]

Step-by-step explanation:

The equation of an ellipse that has its center at the origin is given by the formula:

[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]

The given ellipse is 50 units high.

This means that length of the major axis is 50.

[tex]2a=50[/tex]

[tex]2\implies a=25[/tex]

The ellipse is 40 units wide.

[tex]2b=40[/tex]

[tex]\implies b=20[/tex]

We substitute these values into the formula to get:

[tex]\frac{x^2}{20^2}+\frac{y^2}{25^2}=1[/tex]

[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]

$1313.70 is the answer after a 51% markup

Final answer:

The selling price of a dining room set with a 51% markup on the selling price, and an actual cost of $870, is calculated to be $1775.51.

Explanation:

To determine the selling price of a dining room set with a 51% markup on the selling price based on the actual cost of $870, we first need to recognize the markup is on the selling price and not on the cost. Let the selling price be represented by the variable S. The markup can be represented by S multiplied by 51% (or 0.51), so we have:

Actual Cost + Markup = Selling Price

$870 + (0.51 × S) = S

To solve for S, we need to isolate it on one side of the equation:

$870 = S - (0.51 × S)

$870 = S(1 - 0.51)

$870 = S(0.49)

Now we divide both sides by 0.49 to solve for S:

S = $870 / 0.49

S = $1775.51

Therefore, the selling price of the dining room set at Macy's is $1775.51.

Answer:

[tex]\boxed{\text{14 in}^{2}}[/tex]

Step-by-step explanation:

The scale factor (C) is the ratio of corresponding parts of the two cylinders.  

The ratio of the areas is the square of the scale factor.  

[tex]\dfrac{A_{1}}{ A_{2}} = C^{2}\\ \\\dfrac{224}{ A_{2}} = \left (\dfrac{1}{\frac{1}{4}} \right )^{2}\\\\\dfrac{224}{ A_{2}}= 16\\A_{2} = \dfrac{224}{16\\\\}[/tex]

A₂ = 14 in²  

The surface area of the new cylinder will be [tex]\boxed{\textbf{14 in}^{2}}[/tex].  

I believe that the answer is A.

There are 26 letters in the alphabet, and 10 numbers to choose from: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

To find the answer, I used 26 • 10 • 10, which ends up being 2,600.

The reason I did this is because you can choose any 1 of the 26 letter, followed by any 1 of the 10 numbers, followed by any 1 of the 10 numbers again.

Answer:

Step-by-step explanation:

y=mx+b

8=-7m+b

2=0m+b

subtract

6=-7m

-6/7=m

2=0m+b

2=b

y=-6/7x+2

change to standard from

y+6/7x=2

B

12 is equal to 4y, or 4(3)

you can multiply 4 by x to get 9 since they’re inversely proportionate.

Answer:

A) 1.

Step-by-step explanation:

y is inversely proporcional to x so the equation has the form:

y = c/x

With c been any constant, to find the value of c we use y=4 and x=3:

4 = c/3

c=4*3

c=12

So the equation is

y=12/x

Using y=12 to find x:

12=12/x

(12/12)=x

x=1

Answer:

An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The interior or internal bisector of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles.

Step-by-step explanation:

Answer:

The set of all points in a plane that are equidistant from the two sides of a given angle.

Step-by-step explanation:

To find out how many minutes it takes for 1 person to paint 1 wall, we can set up a proportion using the rate of 6 people painting 6 walls in 23 minutes. Cross-multiplying and solving for the unknown, we find that it would take approximately 3.83 minutes for 1 person to paint 1 wall.

This question falls under the subject of Mathematics and is suitable for students in Middle School. To solve this problem, we can use the concept of rate. We know that 6 people can paint 6 walls in 23 minutes.

We can set up a proportion to find out how many minutes it would take for 1 person to paint 1 wall. Let x represent the unknown time:

6 people / 23 minutes = 1 person / x minutes

Cross-multiplying, we get 6x = 23. Dividing both sides by 6, we find that x = 23/6. Therefore, it would take approximately 3.83 minutes for 1 person to paint 1 wall.

Remember to always read the question carefully and identify the given information and the unknown variable in order to solve the problem accurately.

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The time that it would take for 8 people to paint the walls would be 18 minutes.

The number of walls painted is proportional to the number of people painting, and the time it takes to paint the walls is inversely proportional to the number of people painting.

Using the following formula, we can calculate the amount of time it will take 8 people to paint the 6 walls:

Time = (Number of walls) / (Number of people) * Time per wall

Time = (6 walls) / (8 people) * 23 minutes/wall

Time = 18 minutes

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The full question is:

It takes 23 minutes for 6 people to paint 6 walls​. How long would it take 8 people to paint those same 6 walls

Answer:

I would say the second car.

Step-by-step explanation:

372/15.2 = 24 miles per gallon

198/7.2 = 27.5 miles per gallon

So the answer is the second car is better on gas mileage!

Kyle) y= x Larry) 4y= x^2

The algebraic expression to represent the number of dogs Larry walked compared with Kyle is 2x +4 .

An algebraic expression can be defined as a mathematical statement which includes , variables , constant and mathematical operators.

It is given in the question that

Larry was able to walk 4 more than twice as many dogs as his friend Kyle  have.

Let number of dogs Kyle has = x

and Let Larry walks y miles.

According to the  given data

y = 2x + 4

Therefore , the algebraic expression to represent the number of dogs Larry walked compared with Kyle is 2x +4 .

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Answer:

y=x+6

Step-by-step explanation:

If you need to find a standard linear equation from two points, you have to first find the slope, then find the y intercept.

To find the slope, you should do the change in y over the change in x.

that would be:

(4-9)/(-2-3)

(-5)/(-5)

the slope is 1

plug that in along with values of x and y taken from known point (3,9) to the standard equation of a linear relationship:

y=mx+b

m=1

y=9

x=3

b=?

9=(1)(3)+b

9=3+b

b=6

The equation of the line would be y=x+6

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Answer:

dfgedrgdrg32453245

Step-by-step explanation:4334534

rdgsdrg334523

45234453242

4

23

423

423

42

423

42

423

53465

Answer:

104

Step-by-step explanation:

Answer:

104

Step-by-step explanatio

Ueuhshsjaksjdsnygwhwhwhwhwg bdbehd jeuwjsnz ,judj

Answer:

X= O.8 or 10 over 12.5

Step-by-step explanation: Hope this helps darling

Their speeds are 45 mi/hr and 49 mi/hr

Answer:

The speed of the faster car is 68 miles/hr and speed of slower car is 40 miles/hr.

Step-by-step explanation:

Let the speed of the slower car be x

Now we are given that The speed of the faster car was 12 mph less than twice the speed of the other one.

So, Speed of faster car = 2x-12

Now we are given that In 6 hours the faster car got to San Diego, and by that time the slower one still was 168 miles away from the destination.

So, faster car completes the journey in 6 hours

Distance = [tex]Speed \times Time[/tex]

So, Distance traveled by faster car = [tex](2x-12)\times 6[/tex]

Distance traveled by slower car in 6 hours = [tex]Speed \times Time=6x[/tex]

Since we are given that when faster car completes the journey at that time slower car was 168 miles away from the destination .

A.T.Q

[tex](2x-12)\times 6-6x=168[/tex]

[tex]12x-72-6x=168[/tex]

[tex]6x-72=168[/tex]

[tex]6x=240[/tex]

[tex]x=\frac{240}{6}[/tex]

[tex]x=40[/tex]

So, speed of slower car is 40 miles/hr.

Speed of faster car = 2x-12 =2(40)-12=80-12=68 miles/hr.

Hence the speed of the faster car is 68 miles/hr and speed of slower car is 40 miles/hr.

Step-by-step explanation:

"Is" means equals.  "Less than" means subtracted from.

28 = k - 12

Add 12 to both sides to solve for k:

k = 40

The equation representing the statement '28 is 12 less than K' is 28 = K - 12. By adding 12 to both sides of the equation and simplifying, we find that K = 40.

To represent the statement '28 is 12 less than K' with an equation, you write: 28 = K - 12. To solve for K, you would add 12 to both sides of the equation.

Step 1: Add 12 to each side of the equation to isolate K.

28 + 12 = K - 12 + 12

Step 2: Simplify each side.

40 = K

Therefore, the value of K is 40.

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Answer: -3(5t+2

Step-by-step explanation:

Answer:

−3(5t+2)

Step-by-step explanation:

lets factor out "3" from -15t-6

so factoring out "3" would give you -3(5t+2)

you can check ur work by distributing "3" hope this helps!

Answer:

The first term is 28.

Step-by-step explanation:

Given: 8th term of Geometric sequence , [tex]a_8=-3584[/tex]

and 3rd term of Geometric Sequence, [tex]a_3=112[/tex]

We have to find First term of given geometric Sequence.

Let a be the first term of geometric sequence.

We know that,

[tex]a_n=ar^{n-1}[/tex]

So,

[tex]\frac{a_8}{a_3}=\frac{ar^{8-1}}{ar^{3-1}}=\frac{-3584}{112}[/tex]

[tex]\frac{r^{7}}{r^{2}}=-32[/tex]

[tex]r^5=-32[/tex]

[tex]r=-2[/tex]

So, 3rd term = 112

a × (-2)² = 112

a = 112 / 4

a = 28

Therefore, The first term is 28.

Answer:

1 and a8 =16,384

Step-by-step explanation:

Answer:

[tex]\large\boxed{Domain:\ x\in\mathbb{R}\to\text{the set of all real numbers}}[/tex]

Step-by-step explanation:

The domain of roots:

[tex]\sqrt[n]{p(x)}[/tex]

If n is an odd number, then p(x) can be any real number.

If n is an even number, then p(x) must be a non-negative number.

We have

[tex]f(x)=\sqrt[3]{2x^2-3x-9}[/tex]

n = 3 → odd number.

Therefore the domain is the set of all real numbers.

Incorrect

1000g=1kg

Therefore we would need 100 beads with a mass of 10g to estimate a total mass of 1kg or 1000g

So the estimate of 10beads at 10g each is only about 100g or 0.1kg or 1/10kg

Answer:

Step-by-step explanation:

Let x represent Jane's age

Let y reprsent her brother's age

x=3y-5

x=11-y

subtract

0=4y-16

-4y=-16

y=4

plug back into equation

x=3y-5

x=3(4)-5

x=7

Answer:

3,172

Step-by-step explanation:

The "Money saved that week" is an arithmetic progression, where the next term is found by adding a constant value to the previous term. In this case, the variation is 2.

So that could be modeled with this equation: [tex]a_{n} = a_{1} + (n-1)V[/tex]

Where a1 is the first term of the series, in our case: 10, and the V is the variation each week, in our case: 2.

To be able to calculate the overall sum and answer the question, we first need to calculate the amount she will save on the last week (n=52).

[tex]a_{52} = 10 + (52-1) * 2 = 10 + 102 = 112[/tex]

Now that we know she'll save $112 on the 52nd week, let's calculate the total, using this formula:

[tex]S_{n} = \frac{(a_{1} + a_{n}) * n}{2}[/tex]

We know n (52), a1 (10) and an (112), so...

[tex]S_{52} = \frac{(10 + 112) * 52}{2} = \frac{122 * 52}{2} = 3,172[/tex]

At the end of the year, she will have saved $3,172

ANSWER

[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]

EXPLANATION

[tex] \sin(x) = \frac{Opposite}{hypotenuse} [/tex]

[tex]\sin(x) = \frac{3}{4} [/tex]

This means the opposite side is 3 units and the hypotenuse is 4 units.

We use Pythagoras Theorem to find

[tex] { |ZX| }^{2} + {3}^{2} = {4}^{2} [/tex]

[tex]{ |ZX| }^{2} +9=16[/tex]

[tex]{ |ZX| }^{2} =16 - 9[/tex]

[tex]{ |ZX| }^{2} = 7[/tex]

[tex]{ |ZX| } = \sqrt{7} [/tex]

[tex] \tan(x) = \frac{opposite}{adjacent} [/tex]

[tex] \tan(x) = \frac{3}{ \sqrt{7} } [/tex]

[tex] \tan(x) = \frac{3}{ \sqrt{7} } \times \frac{\sqrt{7}}{\sqrt{7}} [/tex]

[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]

Final answer:

Given sin(X) = 3/4 in a right-angled triangle XYZ, by using trigonometric identities and the Pythagorean theorem, we find that tan(Y) is 1/3.

Explanation:

In triangle XYZ with angle Z being a right angle (90 degrees or π/2 radians), if we are given that sin(X) = 3/4, we can use trigonometric identities to find tan(Y). Since sin(X) is the ratio of the opposite side to the hypotenuse in a right-angled triangle, we have a side opposite angle X which is 3 units long and a hypotenuse that is 4 units long. From this, we can deduce that the side adjacent to angle X, which is also the side opposite to angle Y, is 1 unit long (using the Pythagorean theorem, as the square of the hypotenuse is equal to the sum of the squares of the other two sides: 3² + 1² = 4²).

Now, to find tan(Y), which is the ratio of the side opposite to Y to the side adjacent to Y, we just take the length of the side opposite to X (which is the same as the side adjacent to Y) and the length of the hypotenuse. Therefore, tan(Y) = opposite side / adjacent side, which in this case is 1/3.

____________________________________________________

Answer:

Your answer would be 1,385.44 ft²

____________________________________________________

Step-by-step explanation:

To find the area of a circle, we would use the equation [tex]\pi r^2[/tex]

In this case we have the diameter, and that's 42.

The radius of a circle is half of the diameter, therefore the radius would be 21.

Now we know the radius,we can plug that in to our equation.

Your equation should look like this:

[tex]\pi (21)^2[/tex]

Pi would be 3.14159

Now, you can solve.

[tex]3.14159(21)^2\\\\3.14159*441\\\\=1,385.44[/tex]

When you'r edone solving, you should get 1,385.44

1,385.44 ft² would be your FINAL answer.

____________________________________________________

Answer:

1384.74

Step-by-step explanation:

diameter = 42

radius = 42/2 = 21

area of a circle = πr2 (pie r square)

= 3.14 X 21 X 21

=1384.74 sq.ft

Answer:

Obtuse isosceles

Step-by-step explanation:

Two sides are the same length, so we know this is an isosceles triangle.

To determine if it's acute, right, or obtuse, we can compare it to a right triangle using Pythagorean Theorem:

c² = a² + b²

c² = 3² + 3²

c² = 18

c = √18

So if this were a right triangle, c would be √18, which is somewhere between 4 and 5.

Since the long side is greater than √18, we know this must be an obtuse triangle.

So this is an obtuse isosceles.

Answer:

The correct answer is option B.

x = 10 and y = 46

Step-by-step explanation:

From the figure we can see a trapezium.

To find the value of x

We can write,

2x - 13 = x - 3

2x - x = 13 - 3

x = 10

To find the value of y

from the figure we can write,

3y - 4 + y = 180

4y = 180 + 4

4y = 184

y = 184/4 = 46

Therefore the correct answer is option B

x = 10 and y = 46

Answer:

0.953081279

Step-by-step explanation:

we have been given the following data set;

x; 4, 5, 8, 9, 13

y; 2, 9, 10, 12, 23

We are required to determine the r value of the data set.The r-value is the correlation coefficient that is used to measure the degree of association between two variables. It gives us information on the strength and direction of the association.

We can easily compute r in Ms. Excel;

We first enter the data into any two adjacent columns of an excel workbook.

Then we proceed to type;

=CORREL

into any blank cell. This is an in-built function that computes the correlation coefficient. Ms. Excel returns a value of  0.953081279

as the r value

Answer:

The value of r is 0.953.

Step-by-step explanation:

The correlation coefficient i.e. r is calculated by the formula,

[tex]r=\dfrac{n\sum{xy}-(\sum x)(\sum y)}{\sqrt{(n\sum x^2-(\sum x)^2)(n\sum y^2-(\sum y)^2)}}[/tex]

where n=5 is the sample size.

We create a table of required values,

         x        y          x²          y²           xy

        4        2         16           4             8  

        5        9         25         81            45

        8        10        64         100         80

        9        12         81         144         108

        13       23       169        529        299

∑      39      56        355       858        540

Substitute the values in the formula,

[tex]r=\dfrac{5\times 540-(39)\cdot (56)}{\sqrt{(5\times 355-(39)^2)(5\times 858-(56)^2)}}[/tex]

[tex]r=\dfrac{2700-2184}{\sqrt{(254)(1154)}}[/tex]

[tex]r=\dfrac{516}{\sqrt{293116}}[/tex]

[tex]r=\dfrac{516}{541.4018}[/tex]

[tex]r=0.9530[/tex]

Therefore, the value of r is 0.953.