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konstantin123 [22]

3 years ago

9

A soccer ball is made of 32 pieces of leather: white hexagons and black pentagons. Each black piece borders only with white piec

es, each white piece borders with three black pieces and three white pieces. How many black pieces are needed to manufacture the ball?

1 answer:

zlopas [31]3 years ago

4 0

Answer:

24

Step-by-step explanation:

1+3=4

4 divided by 32 is 8

8 white ones

then 8-32 is 24

24 black ones

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P(x) =2x3 -11x2 -4x +1 g(x) =2x +1

icang [17]

Answer:

see explanation

Step-by-step explanation:

If (2x + 1) is a factor then x = - $\frac{1}{2}$ is a root and P(- $\frac{1}{2}$ ) = 0 ← Factor theorem

P(- $\frac{1}{2}$ )

= 2(- $\frac{1}{2}$ )³ - 11(- $\frac{1}{2}$ )² - 4(- $\frac{1}{2}$ ) + 1

= - $\frac{1}{4}$ - $\frac{11}{4}$ + 2 + 1

= - $\frac{12}{4}$ + 3

= - 3 + 3

= 0

Since P(- $\frac{1}{2}$ ) = 0 then g(x) is a factor of P(x)

5 0

3 years ago

A newspaper reports that the population mean annual salary of a full-time college professor in a certain region is exactly $127,

Leya [2.2K]

Answer:

Option B) Fail to reject the null hypothesis that the true population mean annual salary of full-time college professors in the region is equal to $127,000.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $127,000

Sample mean, $\bar{x}$ = $126,092

Sample size, n = 160

Alpha, α = 0.10

Sample standard deviation, σ = $8,509

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 127000\text{ dollars}\\H_A: \mu \neq 127,000\text{ dollars}$

We use Two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

$t_{stat} = -1.35$

Now, $t_{critical} \text{ at 0.10 level of significance, 159 degree of freedom } = \pm 1.654$

Since,

The calculated t-statistic lies in the acceptance region, we fail to reject and accept the null hypothesis.

Option B) Fail to reject the null hypothesis that the true population mean annual salary of full-time college professors in the region is equal to $127,000.

8 0

3 years ago

Abscissa and ordinate

kipiarov [429]

Abscissa - perpendicular distance from the y- axis

ordinate - perpendicular distance from the x- axis

In a point P(x,y)
x is abscissa and y is ordinate

7 0

3 years ago

Find AC and BC. <br><br> Answers: <br> 14.94<br> 13.46<br> 11.10<br> 10<br> Please help.

anzhelika [568]

Step-by-step explanation:

Use Sine rule.

$\frac{ac}{ \sin(b) } = \frac{ab}{ \sin(c) } \\ \frac{ac}{ \sin(90) } = \frac{10}{ \sin(42) } \\ ac \sin(42) = 10 \sin(90) \\ ac = \frac{10 \sin(90) }{ \sin(42) } \\ ac = 14.9 \: units \: (3s.f)$

Angle A + angle B + angle C = 180 (sum of angles in triangle)

Angle A + 90 + 42 = 180

Angle A + 132 = 180

Angle A = 180 - 132

= 48

$\frac{bc}{ \sin(a) } = \frac{ab}{ \sin(c) } \\ \frac{bc}{ \sin(48) } = \frac{10}{ \sin(42) } \\ bc \sin(42) = 10 \sin(48) \\ bc = \frac{10 \sin(48) }{ \sin(42) } \\ = 11.1units (3sf)$

3 0

3 years ago

Write the equation of the line that passes through the points (1, -6) and (8, 9). Put

ZanzabumX [31]

Answer:

$y-9 = \frac{15}{7} (x-8)$

Step-by-step explanation:

Point-slope form is represented by $y-y_1 = m (x-x_1)$ . To write an equation with it, we need the slope of the line and a point the line crosses through. We already have at least one point the line crosses through, so let's figure out the slope.

To find the slope, use the slope formula $\frac{y_2-y_1}{x_2-x_1}$ . $x_1$ and $y_1$ represent the x and y values of one point the line crosses, and $x_2$ and $y_2$ represent the x and y values of another point the line crosses. So, using the x and y values of (1, -6) and (8, 9), substitute them into the formula and solve:

$\frac{(9)-(-6)}{(8)-(1)} \\= \frac{9+6}{8-1} \\= \frac{15}{7}$

Thus, the slope is $\frac{15}{7}$ .

2) Now, using the point-slope form of $y-y_1 = m (x-x_1)$ , substitute $m$ , $x_1$ , and $y_1$ for real values in order to write an equation in point-slope form. The $m$ represents the slope, so substitute $\frac{15}{7}$ in its place. The $x_1$ and $y_1$ represent the x and y values of one point on the line. So, choose any one of the points given - either one is fine - and substitute its x and y values for $x_1$ and $y_1$ . (I chose (8,9)). This gives the following equation and answer:

$y-9 = \frac{15}{7} (x-8)$

5 0

3 years ago