The volume of a rectangular box is 343 ft3. If the width is 4 times longer than the height, and the length is 16 times longer than the height, find the dimensions of the box.

Answer:

it is a positive number because she was rising if she had been going down then the number would have become negative.

Step-by-step explanation:

Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

B. 7b3 + 4ab + 4a2

Step-by-step explanation:

35b5/5b2 + 20ab3/5b2 + 20a2b2/5b2  

7b3 + 4ab + 4a2

Answer:

B = 7b³ + 4ab + 4a²

Step-by-step explanation:

35b^5 + 20ab³ + 20a²b² by 5b² ÷ 5b²

= 35b^5 + 20ab³ + 20a²b² by 5b²

_________________________

5b²

= 7b³ + 4ab + 4a²

Step-by-step explanation:

for me u need to change in grams

so

3kg=3000g

1.5kg+850g=2350g

so take

(3000-2350)g

ans=650g

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

277.67pi

Step-by-step explanation:

The formula of volume of a cone is V=π r^2 h/3

So, put the values in

V= PI 7 sqruared 17/3

3.14159*49*17/3

That is equal to

872.32

Then divide by pi and its 277.67Pi

Explanation:

The 0.5+8 simplifies to 8.5

It might help to think of 8 as 8.0

So,

y(0.5+8)

y(8.5)

8.5y

Or you could say it like this

y(0.5+8)

0.5y+8y

8.5y

the second step results from the distributive property.

The two inequalities that define the shaded region in the diagram are:

y ≥ 4 and y < x

For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥"  because the shaded region is to the left and the boundary line is solid.

The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:

y ≥ 0(x) + 4

y ≥ 4

For the dashed line:

m = change in y / change in x = 1/1 = 1

b = 0

the inequality sign to use is: "<"

Substitute m = 1 and b = 0 into y < mx + b:

y < 1(x) + 0

y < x

Thus, the two inequalities are:

y ≥ 4 and y < x

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Yes it is.

Please give me brainliest i need it ;)

Answer:

  14 ohms

Step-by-step explanation:

The resistance varies directly with length, so increasing the length by a factor will increase the resistance by the same factor.

__

The length of the wire increased by a factor of 1.4 from 100 ft to 140 ft. That means the resistance will increase by a factor of 1.4 from 10 ohms to 14 ohms. (The diameter did not change.)

The longer wire will have a resistance of 14 ohms.

In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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A) This is a linear function and the equation of the graph is conventionally y = mx + c where m is gradient and c is intercept on y axis

In this function, the equation of the graph is

y = 4x + 1

B) This is a quadratic function and it takes the form:

where a = -1, b = 4 and c = -2. Thus the equation of this line is:

C) This is an exponential function. The c(x) value increases with the increasing powers of 3.

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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The FV is $107 for the simple interest.

The formula to calculate simple interest is given as:

I = P × R × T

Where,I is the simple interest, P is the principal or initial amount, R is the rate of interest per annum, T is the time duration.

Formula to find FV:

FV = P + I = P + (P × R × T)

where,P is the principal amount, R is the rate of interest, T is the time duration, FV is the future value.

Given that P = $100, R = 7%, and T = 1 year, we can find the FV of the investment:

FV = 100 + (100 × 7% × 1) = 100 + 7 = $107

Therefore, the FV of $100 invested at 7% for one year (simple interest) is $107.

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Answer:

y=5x+3

Step-by-step explanation:

First, we need to find the slope. Remember that the slope equation is \(m=\frac{y2-y1}{x2-x1}\).

If we plug in the given points we get m=5. (let me know if you need further elaboration on this step)

So now that we have a slope, we can plug it into the slope-intercept equation.

y=mx+b

y=5x+b

We still need to find b (y-intercept), but luckily, we were given two points that we could plug in. I'm going to use (1,8) here.

8=5(1)+b

8=5+b

b=3

Now we have all of our parts and can put them into the equation.

y=5x+3

Hope this helped!

Answer:

y = 4x + 1

Step-by-step explanation:

y = -1/4 x + 8

Slope: -1/4

Slope of the perpendicular line is the negative inverse: 4

y = 4x + a

Point (0,1)

1 = (4)*(0)+a

1 = a

y = 4x + 1

Answer:

8x-(-4x-6)=42

8x+4x+6=42

12x=42-6

12x=36

x=36/12

x=3

substitute in an equation of your choice

8(3)-y=42

24-y=42

24-42=y

-18=y

Step-by-step explanation:

Answer:

x= 4 y= -10

Step-by-step explanation:

8x - y = 42

-4x - 6 = y

rearrange -4x - 6 =y to -4x -y = 6

8x - y = 42

-4x - y = 6

4x = 48

48/4 = 12

x=4

subsitute x with 4 adn solve for y = -22

y= -10

Answer:

14. 1. would u be mine?

Step-by-step explanation:

LHS :-

Answer:

The y intercept is 6

Step-by-step explanation:

the "b" in the equation is the y-intercept

Answer:

Step-by-step explanation:

The best answer to submit for (515 x 0.0025) + 24.57 is 25.8575.

A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. Decimal notation is the name for the method used to represent numbers in the decimal system. The Hindu-Arabic numeral system has been expanded to include non-integer values.

To find the answer to the expression (515 x 0.0025) +24.57, we can simplify it by performing the multiplication and addition in the correct order:

(515 x 0.0025) + 24.57 = 1.2875 + 24.57 = 25.8575

Therefore, the best answer to report is C. 25.8575.

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Answer:

An irrational number is a real number that can't be written as a fraction.

Ex. \(\sqrt{5}\)

A rational number is a real number such as a whole number, fraaction, decimal, or integer.

Answer:

multiply 16-y this is correct

Step-by-step explanation:

it is a square.

so, all sides are equally long.

that means e.g.

y - 3 = 2y - 11

-3 = y - 11

8 = y

and then

3x - 10 = 3y - 19 = 3×8 - 19 = 24 - 19 = 5

3x = 15

x = 15/3 = 5

so the length of all 4 sides is by using e.g.

y - 3 = 8 - 3 = 5

each side is 5 units long.

Answer:

x = 8

Step-by-step explanation:

44x = 432

divide both sides by 44

\(\frac{44x}{44} = \frac{432}{44}\)

x = 9.8

since 8 is the closest number, that would be your answer

Answer: No, because in order for two or more numbers to combine, both or all of them need to have the same variables, or else they are not like terms and you cannot combine them.

Step-by-step explanation:

hope it helped!!!

This is False in light of the stated statement. Due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

How is regression calculated?

Y = mX + b, where X is the predictive (independent) factor, m is really the approximately slope, and b is the expected intercept, is the methodology for simple linear regression.

The relationship between scattered data points in any set is shown by a regression line. When there is a linear pattern, it displays the relationship between the dependent y variable and independent x variables.

The correlation between the independent variables (IVs) and the dependent variable is described by a linear regression equation (DV). The DV for the IV values you indicate can also be predicted for new values.

Hence we get the required answer.

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Answer:

12

Step-by-step explanation:

2/3f=8

f = (8 times 3)/2

8 times 3 = 24

24/2 = 12

Answer:

#14) x is 95 (155-180= 25, 180-25-60= 95)

#19) my best guess is 4 (DE=7 -> AB=11, a 4 unit increase)

Answer:

B. IS correct

Step-by-step explanation:

Answer:

last one option D

Step-by-step explanation: