According to the stem-and-leaf plot above, how many trees are less than 640

How do you find the measure of ECF?

tigry1 [53]

Answer:

37°

Step-by-step explanation:

∠ECF= ∠ACG

∠ACG= 90° - ∠GAC= 90° - 53°= 37°

6 0

3 years ago

Graph the following equations<br> - y = 2 x - 1

zalisa [80]

Answer:

f(x)= 1 - 2x

Step-by-step explanation:

7 0

3 years ago

A car has mass 1500 kg and is traveling at a speed of 35 miles/hour. what is its kinetic energy in joules? (Be sure to convert m

photoshop1234 [79]

Answer:

Factor by which kinetic energy increase = 4 times

Step-by-step explanation:

Given,

Mass of the car, v1 = 1500 kg

initial speed of car = 35 miles/h

$=\dfrac{35\times 1609.34}{3600}\ m/s$

= 15.64 m/s

Initial kinetic energy of the car is given by,

$k_1\ =\ \dfrac{1}{2}.m.v_1^2$

$=\ \dfrac{1}{2}\times 1500\times (15.64)^2\ joule$

= 183606.46 J

Final velocity of car v2 = 70 miles/hour

$=\dfrac{70\times 1609.34}{3600}$

= 31.29 m/s

So, final kinetic energy of car is given by

$k_2\ =\ \dfrac{1}{2}.m.v_2^2$

$=\ \dfrac{1}{2}\times 1500\times (31.29)^2$

= 734425.84 J

Now, the ratio of final to initial kinetic energy can be given by,

$\dfrac{k_2}{k_1}=\ \dfrac{734425.84}{183606.46}$

$=>\ k_2\ =\ 4k_1$

Hence, the kinetic energy will increase by 4 times.

7 0

3 years ago

Arrange the geometric series from least to greatest based on the value of their sums.

son4ous [18]

Answer:

80 < 93 < 121 < 127

Step-by-step explanation:

For a geometric series,

$\sum_{t=1}^{n}a(r)^{t-1}$

Formula to be used,

Sum of t terms of a geometric series = $\frac{a(r^t-1)}{r-1}$

Here t = number of terms

a = first term

r = common ratio

1). $\sum_{t=1}^{5}3(2)^{t-1}$

First term of this series 'a' = 3

Common ratio 'r' = 2

Number of terms 't' = 5

Therefore, sum of 5 terms of the series = $\frac{3(2^5-1)}{(2-1)}$

= 93

2). $\sum_{t=1}^{7}(2)^{t-1}$

First term 'a' = 1

Common ratio 'r' = 2

Number of terms 't' = 7

Sum of 7 terms of this series = $\frac{1(2^7-1)}{(2-1)}$

= 127

3). $\sum_{t=1}^{5}(3)^{t-1}$

First term 'a' = 1

Common ratio 'r' = 3

Number of terms 't' = 5

Therefore, sum of 5 terms = $\frac{1(3^5-1)}{3-1}$

= 121

4). $\sum_{t=1}^{4}2(3)^{t-1}$

First term 'a' = 2

Common ratio 'r' = 3

Number of terms 't' = 4

Therefore, sum of 4 terms of the series = $\frac{2(3^4-1)}{3-1}$

= 80

80 < 93 < 121 < 127 will be the answer.

4 0

3 years ago

Read 2 more answers

Divide 25/11 by 5/22<br>

Igoryamba

Answer:

25/11 divided by 5/22 = 10

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 11 on the left side and the dividend 25 on the right side like this:

1 1 ⟌ 2 5

Step 2:

The divisor (11) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:

0

1 1 ⟌ 2 5

Step 3:

Multiply the divisor by the result in the previous step (11 x 0 = 0) and write that answer below the dividend.

0

1 1 ⟌ 2 5

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.

0

1 1 ⟌ 2 5

- 0

2

Step 5:

Move down the 2nd digit of the dividend (5) like this:

0

1 1 ⟌ 2 5

- 0

2 5

Step 6:

The divisor (11) goes into the bottom number (25), 2 time(s). Therefore, put 2 on top:

0 2

1 1 ⟌ 2 5

- 0

2 5

Step 7:

Multiply the divisor by the result in the previous step (11 x 2 = 22) and write that answer at the bottom:

0 2

1 1 ⟌ 2 5

- 0

2 5

2 2

Step 8:

Subtract the result in the previous step from the number written above it. (25 - 22 = 3) and write the answer at the bottom.

0 2

1 1 ⟌ 2 5

- 0

2 5

- 2 2

3

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 25 divided by 11 calculated using Long Division is:

7 0

3 years ago