All categories

3 years ago

Ten less than 5 times the value of a number is equal to 10 times the quantity of

Mathematics

1 answer:

grandymaker [24]3 years ago

5 0

Answer:

Step-by-step explanation:

given that the number is a

The expression for Ten less than 5 times the value of a number is given by

5a - 10

10 times the quantity of 12 more than one-fourth of the number.

a/4 is one-fourth of number

12 more than one-fourth of the number

a/4 + 12

expression for 10 times the quantity of 12 more than one-fourth of the number. is given by

10(a/4 + 12) = 10a/4 + 12*10 = 2.5a + 120

Given that the above two expression are equal

equating them we have

5a - 10 = 2.5a + 120

adding 10 both sides

=>5a - 10+ 10 = 2.5a + 120 + 10

=> 5a = 2.5a + 130

subtracting 2.5a from both sides

=> 5a - 2.5a = 2.5a + 130 - 2.5a

=> 2.5a = 130

dividing both side by 2.5

=> a = 130/2.5 = 52

Thus, value of a is 52

You might be interested in

Write an equivalent ratio for 7:8 with 40 as one of the terms.

kvv77 [185]

Answer:

Step-by-step explanation:

Five equivalent ratios:

7:8 = 14:16

= 21:24

= 70:80

= 49:56

= 35:40

8 0

2 years ago

Which of the following statements is true of the correlation analysis? The null hypothesis for the Pearson correlation coefficie

ASHA 777 [7]

Answer:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degreed of freedom. df=n-2=10-2=8

For this case the null hypothesis represent that we don't have association betwen the dependent variable Y and the independent variable X and that means r=0. So then the best option for this case is:

The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

Solution to the problem

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degreed of freedom. df=n-2=10-2=8

For this case the null hypothesis represent that we don't have association betwen the dependent variable Y and the independent variable X and that means r=0. So then the best option for this case is:

The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero

4 0

3 years ago

A periscope is 5 feet above the surface of the ocean. Through it can be seen a ship that rises to 50 feet above the water. To th

Lyrx [107]

Sketch this, assuming the Earth is a sphere with radius R, so a plane slice through the periscope, ship and center of the Earth is a circle of radius R. Draw the lines out from the center (O) of the circle to point A at the top of the periscope and point B at the top of the ship. so that line AB is tangent to the circle at point C. That makes triangles OAC and OBC right triangles, each having the right angle at C. 

From the problem, the lengths OA = R+5, OC = R, and OB=R+50. Label the lengths AC = p and BC= q, then use Pythagoras: 

R² + p² = (R + 5)² 
R² + q² = (R + 50)² 

Solve those: 
p² = (R + 5)² - R² = 10R - 25 
p = √(10R + 25) 

q² = (R + 50)² - R² = 100R + 2500 
q = √(100R + 2500) 

Find a good value for the radius R (in ft. units!) and calculate. The distance from periscope top to ship top is (p + q) feet. Convert that to miles for your answer.

8 0

3 years ago

State A is in the shape of a rectangle with a perimeter of 1268 mi. The width is 90 mi less than the length. Find the length and

Agata [3.3K]

The length and width of the rectangle is 362 m and 272 m respectively.

Step-by-step explanation:

Let the length be "x m".

then the width = x - 90 m

Perimeter = 2 x (length + width) ------------------------------(1)

Substituting Length and width value in the above equation (1), we get,

2 x (x+x-90) = 1268

or, 2x - 90 = 1268/2

or, 2x - 90 = 634

or, 2x = 634 + 90

or, 2x = 724

or, x = 724/2

= 362

Thus the length = 362 m

width = 362 - 90 m = 272 m

6 0

3 years ago

Read 2 more answers

Grab the image of the rectangle DEFG reflection across the line x= 3

zubka84 [21]

Answers:

D ' at (9, -9)
E ' at (5, -9)
F ' at (5, -2)
G ' at (9, -2)

Refer to the diagram below

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

Explanation:

For points D,E,F,G we will follow these steps

Shift everything 3 units to the left so that the vertical line x = 3 will move on top of the y axis (which is the vertical line x = 0).
Reflect across the y axis using the rule $(x,y) \to (-x,y)$ . Here we have the x coordinate flip in sign from positive to negative, or vice versa. The y coordinate stays the same.
Shift everything 3 units to the right so we effectively undo the first step. This places the points in the proper final position.

Let's go through an example:

Point D is located at (-3, -9). Apply the three steps mentioned above.

Shift point D three units to the left to arrive at (-6, -9)
Reflect over the y axis to go from (-6, -9) to (6, -9)
Lastly, shift 3 units to the right to move to (9, -9) which is the location of D'

In short, D(-3,-9) reflects over the line x = 3 to land on D ' (9, -9)

The other points E, F, G will follow the same steps to get the answers you see at the top.

The diagram below visually summarizes everything.

-------------

Side notes:

The distance from D to the line of reflection is the same as the distance from D' to the line of reflection. Put another way, the line of reflection bisects segment DD'. Points E,F,G follow the same property.
Going from D to E to F to G has us go counterclockwise. Going from D' to E' to F' to G' has us go clockwise. Any reflection transformation will flip the orientation.

3 0

3 years ago