Which of the following are mathematical sentences?
Check all that apply.

Let a(t) and b(t) denote the amounts of salt in tanks A and B, respectively.

The volume of liquid in tanks A and B after t minutes are

A: 50 L + (5 L/min + 3 L/min - 8 L/min)t = 50 L

B: 40 L + (7 L/min + 8 L/min - 3 L/min - 12 L/min)t = 40 L

so the amount of solution in the tanks stays constant.

Salt flows into tank A at a rate of

(2 g/L)*(5 L/min) + (b(t)/40 g/L)*(3 L/min) = (10 + 3/40 b(t)) g/min

and out at a rate of

(a(t)/50 g/L)*(8 L/min) = 4/25 a(t) g/min

so the net flow rate is given by the differential equation

[tex]\dfrac{\mathrm da(t)}{\mathrm dt}=10+\dfrac{3b(t)}{40}-\dfrac{4a(t)}{25}[/tex]

We do the same for tank B: salt flows in at a rate of

(3 g/L)*(7 L/min) + (a(t)/50 g/L)*(8 L/min) = (21 + 4/25 a(t)) g/min

and out at a rate of

(b(t)/40 g/L)*(3 L/min + 12 L/min) = 3/8 b(t) g/min

and hence with a net rate of

[tex]\dfrac{\mathrm db(t)}{\mathrm dt}=21+\dfrac{4a(t)}{25}-\dfrac{3b(t)}8[/tex]

Replace a(t) and b(t) with x and y. Then the system is (in matrix form)

[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\end{bmatrix}=\dfrac1{200}\begin{bmatrix}-32&15\\32&-75\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}+\begin{bmatrix}10\\21\end{bmatrix}[/tex]

with initial conditions x(0) = 60 g and y(0) = 80 g.

Answer:

x > 25

Step-by-step explanation:

x+25> 50

Subtract 25 from each side

x+25-25 >50-25

x > 25

Answer:

x>25

Step-by-step explanation:

x+25>50

1. Subtract 25 from both sides of the equation

x+25>50

  -25  -25

x>25

Answer:

Which expression can you use to find 23% of 52? "0.23 x 52"

23% of $52 is $. "11.96"

An easy way to check your answer is to use the friendly 25% and divide 52 by 4 to get 13.

Step-by-step explanation:

just did it good luck everyone

23% of $52 is $11.96.

In order to determine the value of 23% of $52, we would multiply 23% by $52. Multiplication is a basic mathematical operation that entails adding a certain number by itself a certain number of times. The sign used to represent multiplication is ×.

23% x 52

= 0.23 x 52 = $11.96

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Answer:

Octagon regular.

Step-by-step explanation:

This shape has 8 sides to it is an octagon. A octagon irregular doesn't have equal sides while this one does. The best way to tell is if it looks like a stop sign which are octagon regular.

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: hourly wage of a high school student

X~N(μ;σ²)

X[bar]= $8.25

σ= $0.25

For a 95% CI for the average hourly wage for 1 high school student:

For this exercise you have to consider the sample size n=1

a) The margin of error of the CI is calculated as:

d= [tex]Z_{1-\alpha /2}[/tex] * σ

1-α: 0.95 ⇒ α:0.05

1-α/2:0.975

[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

d= 1.96 * 0.25= 0.49

b)

The formula for the interval is

X[bar] ± [tex]Z_{1-\alpha /2}[/tex] * σ

[8.25 ± 0.49]

[7.76; 8.74]

With a 95% you'd expect the interval $[7.76; 8.74] to include the average hourly wage of one high school student in Illinois.

c)

Te calculated interval is $ [7.76; 8.74] the value $9.15 does nor fall within that acceptable range.

I hope this helps!

Answer:

27

Step-by-step explanation:

Input 5 for all x-values.

If that is an equal sign...

1/9*(3^5)

With PEMDAS, exponents are done before multiplication.

1/9*243

= 27

Answer:

4x-7>13

add 7

4x>20

divide by 4

x>5

Step-by-step explanation:

Answer:350000

Step-by-step explanation:

The number is 350000

350000 rounded to the nearest hundred thousand is 400000

350000 rounded to the nearest ten thousand is 350000

Answer:

The perimeter of the lake is 314m. The perimeter of the park is 339 m. Paul should win the debate.

Step-by-step explanation:

Answer:that’s a lot of numbers.            

Step-by-step explanation:

Answer:

The attendance was 198 children, 90 students and 99 adults.

Step-by-step explanation:

We define:

c: children attendance

s: students attendance

a: adult attendance

The equation that describes the total ticket sales is:

[tex]5c+7s+12a=2808[/tex]

We also know that the children attendance doubles the adult attendance:

[tex]c=2a[/tex]

The third equation is the seating capacity, which we assume is full:

[tex]c+s+a=387[/tex]

We start by replacing variables in two of the equations:

[tex]c=2a\\\\s=387-c-a=387-2a-a=387-3a[/tex]

Then, we solve the remaining equation for a:

[tex]5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99[/tex]

Then, we solve for the other two equations:

[tex]c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90[/tex]

The attendance was 198 children, 90 students and 99 adults.

Answer:

the angle is acute angle

Answer:

The type of angle shown is an acute angle

Step-by-step explanation:

there are 4 main types of angles. this is an acute angle as it is less than 90°.

Types of angles:

The 4 main types of angles are: acute, obtuse, right angles, reflex angles.

Acute angles- Acute angles are angles less than 90°.

Obtuse Angles-Obtuse angles are angles greater than 90° but less than 180°.

Right Angles- Right angles are angles of 90°.

Reflex Angles- Reflex angles are angles greater than 180° but less than 360°.

Answer:

Which expression is equivalent to 3 over 175

I would say try - C or D

Answer:

22,950 units³

Step-by-step explanation:

All you have to do is:

[tex]\frac{3}{4} *60*15*34=\\45*15*34=\\675*34=\\\\22,950[/tex]

The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.

Here, we have,

To estimate the proportion of all shrubs of this species that will resprout after fire with 96% confidence, we will use the formula for a confidence interval for a proportion.

The formula for the confidence interval for a proportion (p) is given by:

CI = p ± Z * √(p * (1 - p) / n)

where:

CI is the confidence interval

p is the sample proportion (resprouted specimens / total specimens)

Z is the critical Z-score corresponding to the desired confidence level (96% confidence level corresponds to a Z-score of approximately 1.750)

n is the sample size (total number of specimens)

Given information:

Total number of specimens (n) = 19

Number of specimens that resprouted after fire = 6

Now, calculate the sample proportion (p):

p = (number of specimens that resprouted) / (total number of specimens)

p = 6 / 19 ≈ 0.3158 (rounded to four decimal places)

Now, calculate the critical Z-score for a 96% confidence level (use a Z-table or calculator):

Z ≈ 1.750

Now, calculate the margin of error (E):

E = Z * √(p * (1 - p) / n)

E = 1.750 * √(0.3158 * (1 - 0.3158) / 19)

E ≈ 0.1884 (rounded to four decimal places)

Finally, calculate the confidence interval:

CI = p ± E

CI = 0.3158 ± 0.1884

The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.

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The answer in length

The length is used to measure the distance between to end points or edges. so 17 meters measurement represent the length.

Its the sum of length of the sides used to made the given figure.

Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters.

Area is what is on the inside.

The perimeter is the outside of the hole thing.

Hence, the length is used to measure the distance between to end points or edges.

so 17 meters measurement represent the length.

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Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 10

For the alternative hypothesis,

µ > 10

The inequality sign indicates that It is a right tailed.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 35,

Degrees of freedom, df = n - 1 = 35 - 1 = 34

t = (x - µ)/(s/√n)

Where

x = sample mean = 14.44

µ = population mean = 10

s = samples standard deviation = 4.45

t = (14.44 - 10)/(4.45/√35) = 5.9

We would determine the p value using the t test calculator. It becomes

p < 0.00001

Since alpha, 0.01 > than the p value, then we would reject the null hypothesis. Therefore, At a 1% level of significance, we can conclude that the true mean is greater than 10.

Answer: Yes

Step-by-step explanation:

It isn't an

1 an improper fraction

Less than the denominator

Therefore, three thirds or 3/3 is one whole fraction

Rly hope I helped!

☆꧁Ashlin꧂☆

Answer:yes he his correct

Step-by-step explanation:

3/3=1

Answer:

26.3%

Step-by-step explanation:

5 is divided by 19

That answer is then multiplied by 100.

You may round your answer to the nearest whole number.

Answer:440

Step-by-step explanation:

F=440(2)h/12 h=6

F=440 x 2 x 6/12

F=(440 x 2 x 6) ➗ 12

F=5280 ➗ 12

F=440

Answer:

2.4c = 3.24

Step-by-step explanation:

Answer:

it is 4 ounces + 18 ounces

Answer:

x=5

Step-by-step explanation:

x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.

Answer:

5

Step-by-step explanation:

Because this is a right triangle, you know that by the Pythagorean theorem:[tex]\sqrt{(x+7)^2+x^2}=x+8[/tex]

Squaring both sides to get rid of the square root:

[tex](x+7)^2+x^2=(x+8)^2[/tex]

Expanding all of the parentheses:

[tex]x^2+14x+49+x^2=x^2+16x+64[/tex]

Combine like terms:

[tex]x^2-2x-15=0[/tex]

Factor:

[tex](x-5)(x+3)=0[/tex]

Since x cannot be negative, it is equal to 5. Hope this helps!

Answer:

17.9

Step-by-step explanation:

Answer:

i think ...

Step-by-step explanation:

symmetric distribution  usually be a bell shape distribution .

most likely the median = mean = 60

The required value of 60 could be the median of the distribution. Option B is correct.

The mean of the values is the ratio of the total sum of values to the number of values.

When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top 50% of data.

Here,
The mean of a symmetric distribution is 60.
Since for the symmetric data and rational data, the mean is equal to the median,
So Mean = Median
Median = 60

Thus, the required value of 60 could be the median of the distribution.

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Answer

the answer is -56

Step-by-step explanation:

Answer:

[tex]k-m=b[/tex]

[tex]b-m=diff[/tex]

Step-by-step explanation:

If there are total of k students in a class, and m of those students are girls, the total amount of boys would be:

[tex]k-m=b[/tex]

(Where k, m, b are variables that represent the total number of students, the amount of girls and the amount of boys respectively)

As the amount of girls subtracted from the total amount would leave you with the amount of boys.

There would be:

[tex]b-m[/tex] more boys than girls.

If there were 10 total students in the class and 3 of those students were girls, lets use our above equations to see if they are correct - and if we get the expected amounts of:

7 boys in the class, and 4 more boys than there are girls.

[tex]k-m=b\\10-3=7\\7=7[/tex]

This is correct, as we expected this amount.

[tex]b-m=diff\\7-3=4[/tex]

The difference between them is 4, so this is correct.

y=10x

x= how many candles

Answer:

B.

Step-by-step explanation:

Answer:b

Step-by-step explanation:you need to add both

Answer:<1=126° <2=54°

Step-by-step explanation:

sum of angles in a =180°

<2+90+36=180

<2+126=180

Collect like terms

<2=180-126

<2=54°

<2 and <1 are supplementary angles therefore their sum is equal to 180

<2 + <1=180

54 + <1=180

Collect like terms

<1=180-54

<1=126

Answer:

  about 5.613 seconds

Step-by-step explanation:

Using the quadratic formula to find the value of t when h = 0, we have ...

  at² +bt +c = 0

  t = (-b±√(b²-4ac))/(2a)

  t = (-72±√(72² -4(-16)(100)))/(2(-16))

  t = (-72±√11584)/-32 = (9±√181)/4

Only the positive value of t is of interest.

  The coin will hit the stream after (9+√181)/4 seconds ≈ 5.613 seconds.