10x - 15x + 3 group like terms with parentheses then combine like terms as final answer

the 2nd term in a geometric sequence is 20 the 4th term in the same sequence is 45/4 or 11.25 what is the common ratio?

lbvjy [14]

Let x be the common ratio and y be the 3rd term

11.25/x=y This means the fourth term divided by the common ratio will get the third term
20x=y This means the second term multiplied by the common ratio will get the third term

11.25/x=20x Set the two y's equal to each other, and solve for x!
20x^2=11.25
x^2=.5625
x=+-√.5625
x=.75 or -.75

5 0

3 years ago

Read 2 more answers

A colony of 21,300 bacteria doubles in size every 260 hours. What will the population be 520

bonufazy [111]

Answer:

85,200

Step-by-step explanation:

21,300*2=42,600

42,600*2 = 85,200

7 0

3 years ago

you have 4500 cubic centimeters of wax. how many cylindrical candles can you make from the wax if each candle is 15 cm tall and

ira [324]

Use the formula for the volume of a cylinder to work out how much wax you need to make one candle.

π×5²×15 = 375π

Then divide the amount of wax you have by the amount of wax you need to produce one candle to work out how many candles you can make.

4500 ÷ 375π = 3.82

However, you can't produce 82% of a candle, so you have to round down to 3 candles.

8 0

3 years ago

Ten college students were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 a

solong [7]

Answer:

The 95% confidence interval for the true slope is (0.03985, 0.14206).

Step-by-step explanation:

For the regression equation:

$\hat y=\alpha +\hat \beta x$

The (1 - <em>α</em>)% confidence interval for the regression coefficient or slope $(\hat \beta )$ is:

$Ci=\hat \beta \pm t_{\alpha/2, (n-2)}\times SE(\hat \beta )$

The regression equation for current GPA (Y) of students based on their GPA's when entering the program (X) is:

$\hat Y=3.584756+0.090953 X$

The summary of the regression analysis is:

Predictor Coefficient SE t-stat p-value

Constant 3.584756 0.078183 45.85075 5.66 x 10⁻¹¹

Entering GPA 0.090953 0.022162 4.103932 0.003419

The regression coefficient and standard error are:

$\hat \beta = 0.090953\\SE (\hat \beta)=0.022162$

The critical value of <em>t</em> for 95% confidence level and 8 degrees of freedom is:

$t_{\alpha/2, n-2}=t_{0.05/2, 10-2}=t_{0.025, 8}=2.306$

Compute the 95% confidence interval for $(\hat \beta )$ as follows:

$CI=\hat \beta \pm t_{\alpha/2, (n-2)}\times SE(\hat \beta )\\=0.090953\pm 2.306\times 0.022162\\=0.090953\pm 0.051105572\\=(0.039847428, 0.142058572)\\\approx (0.03985, 0.14206)$

Thus, the 95% confidence interval for the true slope is (0.03985, 0.14206).

6 0

3 years ago

A flower bed has the shape of a rectangle 5 yards long and 4 yards wide. What is its area in square feet?

aalyn [17]

To find the area, use A= bh (base x height), or A = lw (length x width)

There are 3 feet in 1 yard

3 x 5 = 15
4 x 3 = 12

15 x 12 = 180

The flower bed is 180 ft²

hope this helps

3 0

3 years ago