4^1/2 ft to inches

Can anyone explain this question to me? My teacher solved it but I didn’t understand how she did it

Amiraneli [1.4K]

Step-by-step explanation:

To find the space a figure takes, we need to find the volume. Volume of a rectangular prism can be found by multiplying the length, width, and height of the figure.

We can start with the green block. The dimensions of this figure are 6cm, 3cm, and 3cm. The 5cm at the bottom is not a dimension of the green figure. Instead, it shows the total width of both blocks. We will use this later.

Back to the first block, we will find its volume by multiplying its dimensions together.

3 · 3 · 6 = 54

So, the volume of the first block is 54 cm³.

To this, we will add the volume of the blue block. We can find its dimensions with some simple deduction.

The picture shows that the height of the figure is 4cm less than the height of the green one, 6cm.

6 - 4 = 2

The height, then, is 2cm.

The width can be found by subtracting the width of the green block from the total width of both figures, 5cm.

5 - 3 = 2

So, the width is also 2cm.

We can see that the length of the blue block is equal to that of the green one, so we know that the length is 3cm.

Now, multiply all the dimensions we have found together.

2 · 2 · 3 = 12

The volume of the blue block is 12cm³.

We have found the volumes of both figures, so now we can add them both together to find the total.

54 + 12 = 66

So, the total volume is 66cm³.

I hope this was a satisfactory explanation ^^ Good luck, mate

7 0

3 years ago

A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At a

zubka84 [21]

Answer:

Z = -1.333

P-value = 0.09176

Decision Rule: Reject $H_o$ if ∝ is greater than the P-value

Conclusion: Since P-value is > the level of significance ∝, we fail to reject the null hypothesis, therefore there is insufficient evidence to conclude that at least half of all voters prefer the Democrat.

Step-by-step explanation:

Given that:

The sample size of the poll = 1068

The proportion of voters that preferred Democratic candidate is $\hat p$ = 0.48

To test the claim that at least half of all voters prefer the Democrat, i.e 1/2 = 0.5

The null hypothesis and the alternative hypothesis can be computed as:

$H_o : p \geq 0.50$

$H_1 : p < 0.50$

Using the Z test statistics which can be expressed by the formula:

$Z = \dfrac{\hat p - p}{\dfrac{\sqrt{p(1-p) }}{n}}}$

$Z = \dfrac{0.48 - 0.5}{\dfrac{\sqrt{0.5(1-0.5) }}{1068}}}$

$Z = \dfrac{-0.02}{\sqrt{\dfrac{{0.5(0.5) }}{1068}}}$

$Z = \dfrac{-0.02}{\sqrt{\dfrac{{0.25}}{1068}}}$

$Z = \dfrac{-0.02}{0.015}$

Z = -1.333

P-value = P(Z< -1.33)

From z tables,

P-value = 0.09176

The level of significance ∝ = 0.05

Decision Rule: Reject $H_o$ if ∝ is greater than the P-value

Conclusion: Since P-value is > the level of significance ∝, we fail to reject the null hypothesis, therefore there is insufficient evidence to conclude that at least half of all voters prefer the Democrat.

5 0

3 years ago

X to the 5th power and y to the 6th power over xy to the 2nd power

never [62]

$\frac{x^5y^6}{(xy)^2}$

$\frac{x^5y^6}{x^2y^2}$

$x^{5-2}y^{6-2}$

$x^3y^4$

6 0

4 years ago

Determine if the function is an even function, an odd function or neither. Y=-6x^6-5x^2- 2

nadya68 [22]

Answer:

Even

Step-by-step explanation:

The function Y=-6x^6-5x^2- 2 is a polynomial. A polynomial function is a function where a whole number exponent greater than 1 is on the variable. All polynomial functions have a degree known as the highest exponent. This degree also determines if the functions is even, odd or neither.

The highest exponent on the polynomial is 6 which is an even number. This polynomial is even.

6 0

3 years ago

I need help please, I am so confused.

vazorg [7]

Answer:

$\begin{tabular}{| c | c | c |}\cline{1-3} Equation & x-intercepts & x-coordinate of vertex\\\cline{1-3} $y=x(x-2)$ & $x=0, x=2$ & $x=1$\\\cline{1-3} $y=(x-4)(x+5)$ & $x=-5, x=4$ & $x=-0.5$\\\cline{1-3} $y=-5x(x-3)$ & $x=0, x=3$ & $x=1.5$\\\cline{1-3} \end{tabular}$

Step-by-step explanation:

x-intercepts are when the curve intercepts the x-axis, so when y =0.

Therefore, to find the x-intercepts, substitute y = 0 and solve for x.

The vertex is the turning point: the minimum point of a parabola that opens upward, and the maximum point of the parabola that opens downward. As a parabola is symmetrical, the x-coordinate of the vertex is the midpoint of the x-intercepts.

Equation: $y=x(x-2)$

$\implies x(x-2)=0$

$\implies x=0$

$\implies (x-2)=0 \implies x=2$

Therefore, the x-intercepts are x = 0 and x = 2

The midpoint of the x-intercepts is x = 1, so the x-coordinate of the vertex is x = 1

Equation: $y=(x-4)(x+5)$

$\implies (x-4)(x+5)=0$

$\implies (x-4)=0 \implies x=4$

$\implies (x+5)=0 \implies x=-5$

Therefore, the x-intercepts are x = -5 and x = 4

The midpoint of the x-intercepts is x = -0.5, so the x-coordinate of the vertex is x = -0.5

Equation: $y=-5x(3-x)$

$\implies -5x(3-x)=0$

$\implies -5x=0 \implies x=0$

$\implies (3-x)=0 \implies x=3$

Therefore, the x-intercepts are x = 0 and x = 3

The midpoint of the x-intercepts is x = 1.5, so the x-coordinate of the vertex is x = 1.5

$\begin{tabular}{| c | c | c |}\cline{1-3} Equation & x-intercepts & x-coordinate of vertex\\\cline{1-3} $y=x(x-2)$ & $x=0, x=2$ & $x=1$\\\cline{1-3} $y=(x-4)(x+5)$ & $x=-5, x=4$ & $x=-0.5$\\\cline{1-3} $y=-5x(x-3)$ & $x=0, x=3$ & $x=1.5$\\\cline{1-3} \end{tabular}$

4 0

2 years ago