Dan tries to solve the equation 4x=35. Nadia tries to solve the equation 7.25+y=1034. Their work is shown.

Answer:

\(\dfrac{dA}{dt}+ \dfrac{A}{100}=0\)

A(0) = 70  (i.e the pounds of salt dissolved into the tank)

Step-by-step explanation:

Given that:

a large mixing tank initially holds 400 gallons of water  in which 70 pounds of salt have been dissolved.

The rate at which pure water is pumped into the tank is 4 gal/min

After stirring; the pure water is then pumped out at the same rate.

The objective is to determine the differential equation  for the amount of salt A(t) in the tank at time t > 0. What is A(0)

Taking the differential of:

\(\dfrac{dA}{dt}=R_{in}-R_{out}\)     ---- (1)

where ;

\(R_{in\) = 0

\(R_{out} =\dfrac{A(t)}{400}*4\)

\(R_{out} =\dfrac{A}{100}\)

replacing them into (1) ; we have:

\(\dfrac{dA}{dt}=0 - \dfrac{A}{100}\)

\(\dfrac{dA}{dt}=- \dfrac{A}{100}\)

\(\dfrac{dA}{dt}+ \dfrac{A}{100}=0\)

A(0) = 70 (i.e the pounds of salt dissolved into the tank)

The differential equation for the amount of salt A(t) in the tank at time t > 0 is \(\frac{dA}{dt} + \frac{A}{100} = 0\)

A (0)= 70

Given that,

\(dA\div dt=R_{in}-R_{out}\)

Rin=0

\(R_{out}=A(t)\div 400 \times (4)\\\\ =A\div 100\)

so,

\(dA\div dt=R_{in}-R_{out}\\\\dA\div dt=0- A\div 100\)

So,

\(dA\div dt +A\div 100=0\)

A(0)=70

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Suppose \(-4y+2\ge0\). Then by definition of absolute value,

\(|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}\)

On the other hand, suppose \(-4y+2<0\). Then

\(|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}\)

Recall the definition,

\(|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}\)

Answer:

78

Step-by-step explanation:

13 time 6 equals 78

you get 6 because 4 fits 6 times into 24

Answer:

last one

Step-by-step explanation:

they both whole

Answer:

D

Step-by-step explanation:

Because 12 is greater than -5 and when you divide a postive and a negative you get a negative number. And negative numbers are less than 0 .

The statement that best supports the information in the box plots is: D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

The interquartile range of a data set is the difference between the values that are located on both edges of the rectangular box that is displayed in a box plot.

Interquartile range for the men between 20 - 40 years old = 150 - 110 = 40

Interquartile range for the men between 50 - 70 years old = 125 - 95 = 30

This shows that, D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

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Answer:

1.T

3.T

4.F

5.T

Step-by-step explanation

hope this helps

Answer:

there you go . i couldnt write it so i took a screenshot of it . mark me brainliest plz

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)

The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

No, the two sides are not congruent.

I flipped my whole laptop around to check loll

The tree grew about 3.83 inches between the first and third week.

An equation is an expression that shows the relationship between two or more numbers and variables.

On the first week, the tree was 27 1/2 inches (27.5) tall. On the second week, it was 29 1/4 inches (29.25) tall. On the third week, it was 31 1/3 inches (31.33) tall.

The length grown = 31.33 - 17.5 = 3.83 inches

The tree grew about 3.83 inches between the first and third week.

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The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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I can't see the whole paper the sentences is cut

Answer:

And............ What?

Answer:

-3x -7

Step-by-step explanation:

Add the numbers:

x-12+ 5-4x

x-7 -4x

Combine like terms:

x-7 -4x

-3x -7

Solution:

-3x -7

Answer:

16 dollars

Step-by-step explanation:

114÷6=19-3 is 16

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 6 + c ⇒ c = - 2 + 6 = 4

y = - 2x + 4 ← equation of line in slope- intercept form

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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Dilation is used in eye exams so that the eye doctor can view the patient's eye better. After a while it will slowly reduce in size and return back to normal.

A microscope dilates a specific specimen four times larger. A microscope, a projector, a model boat, or a model of a city. All of these use dilation..

_______________________________

And your question is which one is it? Well it's all of the above.

\(\color{red}{\tt{Hope \ It \ Helps}} \)

The ratio for each product, so that they can be compared to the new brand, is given as follows:

The ratio of an amount A over an amount B is obtained applying the proportion of these amounts, that is, the division of A by B.

Hence, for the products in this problem, the ratio of protein to carbs is applied by the division of the amounts of protein by cards.

For each product, the ratios are obtained as follows:

Hence they can be compared to the new product, as all the ratios have a denominator of one.

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Answer:

It is!

Hope this Helps!

the counting number just before C5F16 is 3,072.

Answer:

We can use the formula for compound interest to solve this problem. The formula is:

A = P * (1 + r/n)^(n*t)

where:

A = the amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:

A = 5000 * (1 + 0.03/12)^(12*10)

A = 5000 * (1.0025)^120

A ≈ $6,621.36

So the investment will be worth approximately $6,621.36 after 10 years.