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3 years ago

5

You have 3 1/2 yards of fabric. You use 2/3 yard to make a pillow cover and 1/3 yard to make a scarf. How much fabric is left af

ter you make both items?

2 answers:

AnnyKZ [126]3 years ago

7 0

You're left with 2 1/2 yards of fabric.

Alexxandr [17]3 years ago

4 0

There is 2 1/2 or 2.5 yards of fabric left

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19/10 rational or irrational ?

yarga [219]

Definition of a rational number:

A rational number is a number that can be written as fraction of integers.

19/10 is a fraction.

19 and 10 are integers.

19/10 follows exactly the definition of a rational number, so it is rational.

3 0

3 years ago

The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of

nignag [31]

Answer:

A. 1.8 × $10^{30}$ Kg

B i. 3.0 × $10^{17}$ seconds

ii. 9.6 × $10^{9}$ years

C. After 9.2 × $10^{9}$ (9.2 billion) years

Step-by-step explanation:

Given that the mass of the Sun = 2× $10^{30}$ Kg.

Mass of hydrogen when Sun was formed = 76% of 2× $10^{30}$ Kg

= $\frac{76}{100}$ ×2× $10^{30}$ Kg

= 1.52 × $10^{30}$ Kg

Mass of hydrogen available for fusion = 12% of 1.52 × $10^{30}$ Kg

= $\frac{12}{100}$ × 1.52 × $10^{30}$ Kg

= 1.824 × $10^{30}$ Kg

A. Total mass of hydrogen available for fusion over the lifetime of the sun is 1.8 × $10^{30}$ Kg.

B. Given that the Sun fuses 6 × $10^{11}$ Kg of hydrogen each second.

i. The Sun's initial hydrogen would last;

$\frac{1.8*10^{30} }{6*10^{11} }$

= 3.04 × $10^{17}$ seconds

The Sun's hydrogen would last 3.0 × $10^{17}$ seconds

ii. Since there are 31536000 seconds in a year, then;

The Sun's initial hydrogen would last;

$\frac{3.04*10^{17} }{31536000}$

= 9.640 × $10^{9}$ years

The Sun's hydrogen would last 9.6 × $10^{9}$ years.

C. Given that our solar system is now about 4.6 × $10^{9}$ years, then;

$\frac{9.6*10^{9} }{4.6*10^{9} }$

= 2.09

So that; 2 × 4.6 × $10^{9}$ = 9.2 × $10^{9}$ years

Therefore, we need to worry about the Sun running out of hydrogen for fusion after 9.2 × $10^{9}$ years.

6 0

3 years ago

From a point 55 feet away from the foot of a tower, the angle of elevation of the top of the

garri49 [273]

Answer:

The height of the tower is approximately 95.263 feet

Step-by-step explanation:

The given parameters are;

The distance from the foot of the tower where the angle of elevation is measured = 55 feet

The angle of elevation to the top of the tower from a point 55 feet from the foot of the tower, θ = 60°

Therefore, by trigonometric ratio, we have;

$tan(\theta )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{The \ height \ of \ the \ tower}{Distance \ from \ foot \ of \ tower}$

Therefore, we have;

$tan(60 ^{\circ} ) = \dfrac{The \ height \ of \ the \ tower}{55 \ feet}$

The height of the tower = 55 feet × tan (60°) = 55 × √3 feet ≈ 95.263 feet.

5 0

3 years ago

Can someone help me fast

djverab [1.8K]

The answer is 1200 hope it helped

4 0

3 years ago

Can someone please help with transformations of parent functions

Anna71 [15]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

that said, compressing vertical |x| by a factor of 4, means A = 4, thus is 4|x|.

8 0

4 years ago