Since 30 of the 40 students said "no", it means 30/40, or 3/4 of the random sample disliked the 8:30am start time. Multiply this by the whole population: 1,000 × (3/4) = 750.

Another way to check this is using 10/40 = .25 and doing 1000x.25 = 250 (the amount of students who liked it). Then subtract from whole population and it's 750.

5 0

1 year ago

Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and AC = 5x - 9, what is x? Round to the nearest tenth.

Aloiza [94]

Similar shapes may or may not be congruent.

The value of x is (a) 9.0

The corresponding sides are:

AB and DE
BC and EF
AC and DF

The side lengths are:

$\mathbf{DE = 41}$

$\mathbf{EF = 23}$

$\mathbf{DF = 36}$

$\mathbf{AC = 5x - 9}$

Because the shapes are congruent, and AC corresponds to DF.

This means that:

$\mathbf{AC = DF}$

So, we have:

$\mathbf{5x - 9 = 36}$

Collect like terms

$\mathbf{5x = 9 + 36}$

$\mathbf{5x = 45}$

Divide both sides by 5

$\mathbf{x = 9.0}$

<em>Hence, the correct option is (a) 9.0</em>

Read more about congruent triangles at:

brainly.com/question/12413243

5 0

2 years ago

the spoke of wheel reaches from the center of the wheel to its rim. If the circumference of the wheel is 42 inches, how long is

xz_007 [3.2K]

If each spoke reaches from the center of the wheel to its rim, then that means that each spoke is as long as the radius.

To calculate radius:

C=2πr

π=3.14
C=42 inches

42=2(3.14)r
2*3.14=6.28
42=6.28r

Divide 42 by 6.28

42/6.28=6.68

length of each spoke is 6.68 inches.

3 0

2 years ago