The ratio of boys to girls in a group is 3:1. If there are 28 more boys than girls, work out how many people there are in total.

The expression 2.5 + 2t gives the cost, in dollars, of t tulips at a flower store. Joanna has $14.00.

Elena-2011 [213]

Answer:

5 tulips.

Step-by-step explanation:

Given:

The expression for the cost of the tulips is $Cost=2.5+2t$

Where, $t$ is the number of tulips.

Now, Joanna has $\$ 14.00$ .

So, number of tulips that can be bought with the above amount can be obtained by substituting $\$ 14.00$ for cost. This gives,

$Cost=2.5+2t\\14=2.5+2t\\2t=14-2.5\\2t=11.5\\t=\frac{11.5}{2}=5.75 \approx 5$ .

As the number of tulips cannot be in decimals or fractions, so the maximum number of tulips that can be bought will be 5.

6 0

3 years ago

I don’t understand! Help me Please!

Valentin [98]

Answer:

1.) Slope = -1.5

2.) y-Intercept = 11.5

3.) y = -1.5x+ 11.5

Step-by-step explanation:

1.) Slope

Every time x decreases by two units, y increases by three units.

Slope = m = Δy/Δx = 3/(-2) = -1.5

2.) y-intercept

The y-intercept (b) is the value of y when x = 0.

When x = -1, y = 13.

If we increase x by 1 unit, x will equal 0.

The slope tells us that when x increases by 1 unit, y decreases by 1.5 units.

y = 13 - 1.5 = 11.5

The y-intercept is at y = 11.5.

3.) Equation

The equation for a straight line is

y = mx + b

m = -1.5 and b = 11.5, so

y= -1.5 x + 11.5

The figure below shows your points and the graph of y = -1.5x + 11.5, with a y-intercept at x = 0, y = 11.5.

8 0

3 years ago

Can someone help me please

allochka39001 [22]

Answer:

90,56,7867,45,89,45,24,67

5 0

3 years ago

Sample annual salaries (in thousands of dollars) for employees at a company are listed. (a) Find the sample mean and sample s

Helen [10]

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

The value is attached in the image file please find it.

In point a:

First, we calculate the find the mean,

Formula:

$\to Mean (\bar{x}) = \frac{( \sum x)}{n}$

$=\frac{540}{13}\\\\ = 41.54$

To calculate the standard deviation, subtract the mean value from all observations then square its value:

$SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\$ $= \sqrt{ \frac{339.2308}{13-1}}$

$= \sqrt{ \frac{339.2308}{12}}\\\\= \sqrt{28.269}\\\\=5.31$

please find attached file

In point b:

New $x_i = 1 x_i + 0.05 x_i = 1.05 x_i$

Calculate new mean:

$\to \bar{x} = \frac{\sum x}{n} \\$

$=\frac{567}{13} \\\\= 43.62$

calculating the standard deviation:

$SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\$ $= \sqrt{ \frac{374.0022}{13-1}}$

$= \sqrt{ \frac{374.0022}{12}}\\\\= \sqrt{31.16}\\\\=5.58$

please find attached file

In point C:

Calculate new mean:

$\to \bar{x} = \frac{\sum x}{n} \\$

$=\frac{47.25}{13} \\\\= 3.46$

calculating the standard deviation:

$SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\$ $= \sqrt{ \frac{2.5975}{13-1}}$

$= \sqrt{ \frac{2.5975}{12}}\\\\= \sqrt{0.216}\\\\=0.46$

please find attached file

In point d:

for b,

New $\bar{x}= 1.05 \bar{x}= 1.05(41.54) =43.62$

New $s= 1.05s= 1.05(5.31)=5.57$

for c,

New $\bar{x}= \frac{ \bar{x}}{12}= \frac{41.54}{12} = 3.46$

New $s = \frac{s}{ 12} = \frac{5.31}{12}= 0.44$

4 0

4 years ago

Explanation/Answer would be appreciated please

Gwar [14]

Answer: The solution for the system is (2, -7)

Step-by-step explanation:

Ok, here we have linear relationships.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, we have two lines:

ya, that passes through:

(-8, -5) and (-3, -6)

Then the slope is:

a = (-6 - (-5))/(-3 - (-8)) = (-6 + 5)/(-3 + 8) = -1/5

now, knowing one of the points like (-3, - 6) we can find the value of b.

y(x) = (-1/5)*x + b

y(-3) = -6 = (-1/5)*-3 + b

-6 = 3/5 + b

b = -6 - 3/5 = -33/5

then the first line is:

ya = (-1/5)*x -33/5

For the second line, we know that it passes through the points:

(-8, -15) and (-3, -11)

Then the slope is:

a = (-11 - (-15))/(-3 -(-8)) = (-11 + 15)/(-3 + 8) = 4/5

The our line is:

y(x) = (4/5)*x + b

and for b, we do the same as above, using one of the points, for example (-3, -11)

y(-3) = -11 = (4/5)*-3 + b

b = -11 + 12/5 = -(55 + 12)/5 = -43/5

then:

yb = (4/5)*x - 43/5.

Ok, our system of equations is:

ya = (-1/5)*x -33/5

yb = (4/5)*x - 43/5.

To solve this, we suppose ya = yb

then:

(-1/5)*x + -33/5 = (4/5)*x - 43/5.

-33/5 + 43/5 = (4/5)*x + (1/5)*x

10/5 = 2 = (4/5 + 1/5)*x = x

2 = x

now we evaluate x = 2 in one of the lines:

ya = (-1/5)*2 -33/5 = -2/5 - 33/5 = -35/5 = -7

Then the lines intersect at the point (2, - 7), which is the solution for the system.

6 0

3 years ago

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