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3 years ago

Round 478.54 to the nearest tenth

2 answers:

8 0

A tenth is the number that occurs after the decimal
If the number after the tenth is five or higher, then you round up
If the number after the tenth if four or lower, then the tenth stays the same value as it is
In this case, the Ume after the tenth is exactly four, so the value of the tenth stays the same
So your answer is 478.5

vaieri [72.5K]3 years ago

7 0

478.5 is the answer

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Diagram shows two perpendicular straight lines,OB and CBD,drawn on a Cartesian plane.

Tems11 [23]

Answer: (a) y = -3x + 10

$\bold{(b)\x=\bigg(\dfrac{10}{3},0\bigg)}$

<u>Step-by-step explanation:</u>

The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.

Step 1: Find the slope of OB using the formula: $m=\dfrac{y_2-y_1}{x_2-x_1}$

(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)

$m=\dfrac{1-0}{3-0} = \dfrac{1}{3}$

Step 2: Find the slope of CD (opposite and reciprocal of OB)

$m = \dfrac{1}{3}\qquad m_\perp=-\bigg(\dfrac{3}{1}\bigg) = -3$

Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)

(x₁, y₁) = (3, 1) because it is the point the line will pass through

y - 1 = -3(x - 3)

y - 1 = -3x + 9 <em>distributed -3 into (x - 3)</em>

y = -3x + 10 <em>added 1 to both sides</em>

***********************************************************************

The x-intercept of DQ is the same x-intercept as CD. The x-intercept is when y = 0

y = -3x + 10

0 = -3x + 10

-10 = -3x subtracted 10 from both sides

$\dfrac{10}{3}=x$ <em>divided both sides by -3</em>

3 0

3 years ago

What is the balance after 15 years in a savings account that earns 2% interest compounded bimonthly when the initial deposit is

motikmotik

The amount will be equal to $1348.07. The correct option is A.

<h3>What is compound interest?</h3>

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

$\rm A = P(1+\dfrac{r}{n})^{nt}$

Compound Interest Formula:

A = Account Balance

P = Principle/Initial Amount

r = Rate of Interest (decimal)

n = Number of times compounded (per year)

t = Number of Years

Given Information

Account Balance = ?

It is given that the balance after 15 years in a savings account earns 2% interest compounded bi-monthly when the initial deposit is 1000.

This is because we are gaining money, so the multiplier should be greater than 1. We already added 1, which is 100% so you simply add the 0.02 for the extra 2%.

Number of times compounded per year = 6

This is because it is being compounded bi-monthly, or once every 2 months. 12 months divided by 2 months is 6 months, so 6 times a year.

Number of years = 15

Solve by plugging the given values into the formula.

$\rm A = P(1+\dfrac{r}{n})^{nt}$

$\rm A = 1000(1+\dfrac{0.02}{6})^{6 \times 15}$

A = 1000 x (1.14)

A = $1348.07.

Therefore, the amount will be equal to $1348.07. The correct option is A.

To know more about Compound interest follow

brainly.com/question/24924853

#SPJ1

3 0

2 years ago

A certain semiconductor device requires a tunneling probability of T = 10-5 for an electron tunneling through a rectangular barr

Goryan [66]

Answer:

Generally the barrier width is $a = 1.9322 *10^{-9} \ m$

Step-by-step explanation:

From the question we are told that

The tunneling probability required is $T = 1 * 10^{-5}$

The barrier height is $V_o = 0.4 eV$

The electron energy is $E = 0.08eV$

Generally the wave number is mathematically represented as

$k = \sqrt{ \frac{2 * m [V_o - E]}{\= h^2} }$

Here m is the mass of the electron with the value $m = 9.11 *10^{-31} \ kg$

h is is know as h-bar and the value is $\= h = 1.054*10^{-34} \ J \cdot s$

$k = \sqrt{ \frac{2 * 9.11 *10^{-31 } [0.4 - 0.04] * 1.6*10^{-19}}{[1.054*10^{-34}^2]} }$

=> $k = 3.073582 *10^{9} \ m^{-1}$

Generally the tunneling probability is mathematically represented as

$T = 16 * \frac{E}{V_o } * [1 - \frac{E}{V_o} ] * e^{-2 * k * a}$

$1.0 *10^{-5} = 16 * \frac{0.04}{0.4 } * [1 - \frac{0.04}{0.4} ] * e^{-2 * 3.0736 *10^{9} * a}$

=> $6.944*10^{-6}= e^{-2 * 3.0736 *10^{9} * a}$

Taking natural log of both sides

$ln[6.944*10^{-6}] = -2 * 3.0736 *10^{9} * a}$

=> $-11.8776 = -2 * 3.0736 *10^{9} * a}$

=> $a = 1.9322 *10^{-9} \ m$

4 0

2 years ago

Bottles of grape soda are assumed to contain 300 milliliters of soda. There is some variation from bottle to bottle because the

Pie

Answer:

Because the p-value of 0.0828 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of soda in all the bottles filled that day does not differ from the target value of 300 milliliters.

Step-by-step explanation:

The null hypothesis is that the sample mean does not differ from the population mean.

If p < α, we reject the null hypothesis.

If p > α, we do not reject the null hypothesis.

p values are between 0 and 1.

4 0

3 years ago

Someone plz help T^T

Ulleksa [173]

Answer:

The answer is 157 1/2 ( ╹▽╹ )

5 0

3 years ago