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tensa zangetsu [6.8K]

2 years ago

7

a piece of stained glass in the shape of a right triangle has sides measuring 8 cm, 15 cm, and 17cm. what is the area of the pie

ce

1 answer:

Hoochie [10]2 years ago

6 0

Area:LW
8*15=180
<span>8 is the length,15 is the Width,17 is the hieght </span>

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The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 1600 vo

Arturiano [62]

Answer:

Test statistic = -2.44

There is enough evidence to support the strategist's claim.

Step-by-step explanation:

H0 : p = 0.41

H1 : p < 0.41

pˆ = 0.38

Test statistic :

z=pˆ−p/√p(1−p)/n

Z = (0.38 - 0.41) / √(0.41(1 - 0.41) / 1600

Z = - 0.03 / √0.0001511875

Z = - 0.03 / 0.0122958

Z = - 2.4399

Test statistic = -2.44

The Pvalue :

P(Z < -2.44) = 0.0073436

α - level = 0.02

If Pvalue < α ; Reject H0

0.0073436 < 0.02 ; We reject H0

Since Pvalue < α ; Hence, There is enough evidence to support the strategist's claim.

8 0

2 years ago

An object launched vertically from a point that is 37.5 feet above ground level with an initial velocity of 48.6 feet per second

Elis [28]

Answer: 3.675 seconds

Step-by-step explanation:

Hi, when the object hits the ground, h=0:

h=−16t^2+48.6t+37.5

0=−16t^2+48.6t+37.5

We have to apply the quadratic formula:

For: ax2+ bx + c

x =[ -b ± √b²-4ac] /2a

Replacing with the values given:

a=-16 ; b=48.6; c=37.5

x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)

x = [ -48.6 ± √ 4,761.96] /-32

x = [ -48.6 ± 69] /-32

Positive:

x = [ -48.6 + 69] /-32 = -0.6375

Negative:

x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)

Feel free to ask for more if needed or if you did not understand something.

8 0

2 years ago

A football is thrown by a quarterback to a receiver. The points in the figure show the height of the football, in feet, above

nevsk [136]

Answer:

Coordinates of the point B will be (14, 3.5).

Step-by-step explanation:

From the graph attached,

Distance between the Quarterback and Receiver = x-coordinate of the point B = 14 yards

Similarly, height of the football from the ground at point B = y-coordinate of the point B = 9 + $\frac{12-9}{2}$

= 9 + 1.5

= 10.5 feet

Since, 1 feet = $\frac{1}{3}$ yards

10.5 feet = $\frac{10.5}{3}$

= 3.5 yards

Therefore, coordinates of the point B will be (14, 3.5).

6 0

3 years ago

Multiplying Powers with the Same Base

Luda [366]

Applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. $5 \times 5^3 = 5^4$

2. $5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3} = 5^{10}$

To multiply the powers having the same base, we will apply the product rule for exponents.

<h3>What is the Product Rule for Exponents?</h3>

Base on the product rule for exponents, we have, $a^m \times a^n = a^{m + n} = a^{mn}$ .
In order to find the products of two given numbers that have the same base, the exponents would be added together.

1. $5^6 \times 5^{-4$

Add the exponents together

$5^6 \times 5^{-4} = 5^{(6) + (-4)}$

$5^6 \times 5^{-4} = 5^2$

2. $5 \times 5^3$

Add the exponents together

$5 \times 5^3 = 5^{(1 + 3)}$

$5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3}$

Add the exponents together

$5^{-3} \times 5^{-3} = 5^{(-3) + (-3)$

$5^{-3} \times 5^{-3} = 5^{-6$

$5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0$

Add the exponents together

$5^{-4} \times 5^{4} \times 5^0 = 5^{(-4) + (4) + (0)$

$5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3}$

Add the exponents together

$5^{7} \times 5^{3} = 5^{10}$

In summary, applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. $5 \times 5^3 = 5^4$

2. $5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3} = 5^{10}$

Learn more about product rule of exponents on:

brainly.com/question/847241

5 0

1 year ago

If f(x)=x-7 and g(x)=x^3, what is G(f(x))?

lesya692 [45]

Replace the 'x' in the formula for g(x) by f(x):-

g(f(x)) = (x-7)^3

Its D

8 0

3 years ago

Read 2 more answers