The first quartile of a data set is 2.5.
Which statement about the data values is true?
One fourth of the values are less than or equal to 2.5, and three fourths of the values are above 2.5.
Half of the values are less than or equal to 2.5, and half of the values are more than 2.5.
Three fourths of the values are less than or equal to 2.5, and one fourth of the values are above 2.5.
One fourth of the values are less than or equal to 2.5, and half of the values are above 2.5.

Answer: Option 'A' is correct.

Step-by-step explanation:

since we have given a line AB and CD such that AB║CD,

And a transversal say 'l' cut the two parallel lines

And we know that when a transversal cuts two parallel lines we get linear pair and corresponding angles

But relation between angle 'a' and angle 'd' is vertically opposite angles.

So, Option 'A' is correct.

Given that b is the number of calories that can be burned using the stationary bike, and the burning rate is 5 cal / min, therefore:

b = 5 t

where t is the time spent on the stationary bike

Answer:

B=5t

Step-by-step explanation:

Final answer:

The number that satisfies the original equation is -4.

Explanation:

A student's question involves finding a number that satisfies the equation: 'Twelve less than negative nine times a number is equal to 8 minus 4 times the number'.

To solve this, we set up the equation -9x - 12 = 8 - 4x.

Solving for 'x' involves simple algebraic steps.

First, add 9x to both sides to get the variable terms on one side:

Next, subtract 8 from both sides to isolate the variable term:

Finally, divide both sides by 5 to find 'x':

The number that satisfies the original equation is -4.

multiply the cost by 1.10 ( 10% plus cost price)

35.96 *1.10 = 39.556 rounded to $39.56

Answer:

C. JKM is not a right triangle because KM ≠ 15.3.

Step-by-step explanation:

We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.  

In order to triangle JKM be a right triangle [tex]KM^{2}=JK^{2}+JM^{2}[/tex].

We will find length of side KM using our right triangles JLM and JLK as [tex]KM=KL+LM[/tex].  

Using Pythagorean theorem in triangle JLM we will get,

[tex]LM=\sqrt{JM^{2}-JL^{2}}[/tex]

[tex]LM=\sqrt{8^{2}-5^{2}}[/tex]

[tex]LM=\sqrt{64-25}[/tex]

[tex]LM=\sqrt{39}=6.244997998\approx 6.24[/tex]

Now let us find length of side KL.

[tex]KL=\sqrt{JK^{2}-JL^{2}}[/tex]  

[tex]KL=\sqrt{13^{2}-5^{2}}[/tex]

[tex]KL=\sqrt{169-25}[/tex]

[tex]KL=\sqrt{144}=12[/tex]

Now let us find length of KM by adding lengths of KL and LM.

[tex]KM=12+6.24=18.24[/tex]

Now let us find whether JKM is right triangle or not using Pythagorean theorem.

[tex]KM^{2}=JK^{2}+JM^{2}[/tex]  

[tex]18.24^{2}=13^{2}+8^{2}[/tex]

[tex]18.24^{2}=169+64[/tex]

[tex]18.24^{2}=233[/tex]

Upon taking square root of both sides of equation we will get,

[tex]18.24\neq 15.264337522473748[/tex]

[tex]18.2\neq 15.3[/tex]  

We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.    

Answer:

I just took the test it is C

Answer:

The arrow should start at zero

Step-by-step explanation:

Because if it star any where else  it  would be incomplete

6(d+1) -2d=54

 distribute the 6

6d+6 -2d=54

 subtract 2d from 6d

4d+6 =54

subtract 6 from each side

4d=48

divide both sides by 4 to get d

d=48/4

d=12

Claire is currently 10 years old.

Let's assume that Claire's age is x.

According to the given information, Claire's cousin is now 3 times as old as Claire. This can be represented as Cousin's age = 3x.

In 10 years, Cousin's age will be twice as old as Claire's age. So, we can write the equation:

(3x + 10) = 2(x + 10)

Simplifying the equation:

3x + 10 = 2x + 20

Subtracting 2x from both sides:

x + 10 = 20

Subtracting 10 from both sides:

x = 10

Therefore, Claire is currently 10 years old.

Answer:

In standard equation format, the condition can be written as [tex]V=5x+12[/tex].

Step-by-step explanation:

The capacity of the bathtub is 32 gallons.

The water already in the tub is 12 gallon.

It takes 5 minutes for the tub to be filled.

Let x be the flow rate of water through tap, in gallon per minutes.

Now, the water filled in the tank in 5 minutes will be [tex]5x[/tex] gallons.

So, in equation, the given condition can be written as,

[tex]V=5x+12\\32=5x+12[/tex]

here V represents the volume of the bathtub.

Therefore, in standard equation format, the condition can be written as [tex]V=5x+12[/tex].

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The standard equation for the volume of water in the bathtub at time t is V(t) = 12 + 4t, indicating the tub starts with 12 gallons and fills at a rate of 4 gallons per minute.

To write a standard equation for filling a bathtub, we need to find the rate at which the tub fills. Since the tub starts with 12 gallons and ends up holding 32 gallons, it needs an additional 20 gallons to be filled. If it takes 5 minutes to fill these 20 gallons, then the fill rate is 20 gallons per 5 minutes.

The equation for the volume V of water in the tub at any given time t (in minutes) is:

V(t) = 12 + r × t

where r is the rate of filling the tub. We already calculated r to be 4 gallons per minute (20 gallons/5 minutes). Therefore, the equation becomes:

V(t) = 12 + 4t

This equation represents the amount of water in the bathtub at any given time t, assuming it starts with 12 gallons and fills at a rate of 4 gallons a minute.

The original price of the dryer would be; 38.75 dollars.

Unit means 'single entity, the fundamental constructing block. Usually, it is 1 in mathematics and science. Thus, the unit price of something is the price of 1 thing.

Given that Susan grody paid $155 for a clothes dryer.

The price paid by her reflects a 75% discount off the original price.

Required the original price of the dryer.

Thus,

100 - 75 = 25%

Therefore,

155 x 25%

155 x 0.25 = 38.75

Hence, the original price of the dryer would be; 38.75 dollars.

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A protractor is preferred over a ruler when measuring angles, especially in geometric shapes or when dealing with rotational aspects. While a ruler is great for measuring lengths and distances, it can't accurately measure angles.

For example, let's say you want to measure the angle between two lines on a piece of paper. A ruler can only give you an approximation by comparing lengths, but a protractor will give you an exact measurement of the angle in degrees.

To use a protractor, align the center hole of the protractor with the vertex of the angle. Then, align one side of the angle with the zero-degree mark on the protractor. Finally, read the number where the second side of the angle intersects the protractor scale. This gives you the precise measurement of the angle.

In conclusion, when dealing with angles, a protractor is the preferred tool for accurate measurements, providing exact angles in degrees.

Answer:

m= 19

Step-by-step explanation:

In a linear function the rate of change of y-variable respect x-variable must be constant. In mathematical terms:

Δy/Δx = constant

Given two points of the function: (x1, y1) and (x2, y2), Δy = (y2 -y1) and Δx = (x2 -x1).  So,

Δy/Δx = (11 -27)/(12-10) = -8

(m -27)/(11-10) = -8

(m -27) = -8*(11-10)

m = -8 + 27

m = 19

Final answer:

To calculate the account balance at the end of the first year for an investment of $8,000 at 7% per year, the formula for simple interest is used. After applying the formula, the final account balance is determined to be $8,560.

Explanation:

The retiree invests $8,000 in a savings plan that pays 7% per year. To find out what the account balance will be at the end of the first year, we can use the formula for simple interest because it is only for one year. The formula is:

Final amount = Principal amount (1 + (Interest rate * Time))

Let's calculate:

Now, substituting the values into the formula:

Final amount = $8,000 (1 + (0.07 * 1))

Final amount = $8,000 (1 + 0.07)

Final amount = $8,000 (1.07)

Final amount = $8,560

So, the account balance at the end of the first year will be $8,560.

The dimensions of the one whose area is largest is 39 by 39

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2(L + W)

L is the length of the rectangle

W is the width

Given that the perimeter is 156, hence;

2(L + W) = 156

2L + 2W = 156

L + W = 78

W = 78 - L

The area of the rectangle is expressed as:

A = LW

A = L(78-L)

A = 78L - L^2

To get the dimensions of the one whose area is largest, dA/dL = 0

dA/dL = 78 - 2L

0 = 78 - 2L

2L = 78

L = 78/2

L = 39

Recall that 2(L+W) = 156

2(39 + W) = 156

39 + W = 78

W = 78 - 39

W = 39

Hence the dimensions of the one whose area is largest is 39 by 39

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The function rule of the line is, f(x)=2/3x-2

What is a straight line?

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (0,-2) and, (3,0)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y+2)/(x-0)=(0+2)/(3-0)

=>3y+6=2x

=>y=2/3x-2

Let, y= f(x)

So, the required function rule of the line is f(x)=2/3x-2

Hence, the required  function rule of the line is, f(x)=2/3x-2

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Answer:

The diagonals intersect each other

Step-by-step explanation:

One of the distinguishing features of triangles is the congruency of the diagonals. The diagonals are bisected into two. Each perpendicular bisector gives a segment of the diagonal that is equal to the other.