a triangle's base and height are changing. (a) if the base is growing at a rate of 1 cm per second and the height is growing at a rate of 2 cm per second at what rate is the area changing the moment that the base is 4 cm and the height is 7 cm?

Answer:

y=3x+9

Step-by-step explanation:

-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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Answer:

\(u = 8\)

Step-by-step explanation:

The steps are not shown. So, I will solve from scratch

Given

\(7(u -5) = 21\)

Required

Solve, with steps

\(7(u -5) = 21\)

Apply distributive  property

\(7u - 7 * 5 =21\)

\(7u - 35 =21\)

Collect like terms

\(7u = 35 + 21\)

\(7u = 56\)

Divide both sides by 7

\(\frac{7u}{7} = \frac{56}{7}\)

\(u = 8\)

Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

Answer: a - complementary (im not completly sure tho)

Step-by-step explanation: a complementary is either of two angles whose sum is 90°

SOLUTION

Given the question, the following are the steps to solve the problem

Step 1: Write out the question

Step 2: Solve the expression in the first bracket

Step 3: Calculate the tangent of the result in step 2

Hence, the result from the evaluation of tan(sin^-1)(7/9) is approximately 1.2374

Answer: hi

Step-by-step explanation:

Answer:

ANSWER IS C

Step-by-step explanation:

adj = 3

opp = 4

tanx = \(\frac{opp}{adj}\)

tan C = \(\frac{4}{3}\)

35/864 is the probability that the same color is recorded both times .

How does probability explain work?

7/12*1/2 = 7/24

red marbles =  5/12*1/3 ⇒ 5/36

the probability =  7/24*5/36 ⇒ 35/864

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If the distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. the score separating the bottom 81% from the top 19% is 168.24.

 The value of p81, which is the score separating the bottom 81% from the top 19%, can be calculated as follows:

 The given, Mean = μ = 93.2

                    Standard deviation = σ = 87.4

      We are supposed to find the score separating the bottom 81% from the top 19% which is nothing but the 81st percentile.

       Let X be a random variable with a normal distribution, then the z-score of the 81st percentile is calculated as follows:

               z = InvNorm(0.81)

               z ≈ 0.8 (by standard normal distribution tables)

    The 81st percentile in terms of X is given by:

              p81 = μ + zσp81

                     = 93.2 + 0.8(87.4)p81

              p81 = 168.24

   Thus, the score separating the bottom 81% from the top 19% is 168.24.

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320

Step-by-step explanation:

Every time the same instrument is used for a measurement, it produces consistent results, which denotes: -reliability.

The degree to which a measurement tool produces consistent, repeatable estimates of what is believed to be a true score at the core.

The same set of people receives the same instrument again. The correlation between the results on the two instruments is what defines dependability. The scores ought to be comparable if the outcomes remain constant over time. How long to wait between the two administrations is the key to test-retest reliability.

Reliability is defined as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions.

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Answer:

Here's how to subtract 3/8 from 8/12:

8

12

−

3

8

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 8 by 8, and get 64.

Then we multiply 3 by 12, and get 36.

Next we give both terms new denominators -- 12 × 8 = 96.

So now our fractions look like this:

64

96

−

36

96

Step 2

Since our denominators match, we can subtract the numerators.

64 − 36 = 28

So the answer is:

28

96

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

28

96

÷ 2 =

14

48

Let's try dividing by 2 again...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

14

48

÷ 2 =

7

24

Let's try dividing by 2 again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

No good. 11 is larger than 7. So we're done reducing.

There you have it! The final answer is: 0.29166666666

The above equation satisfies the condition of Pr(AnEi).Therefore, Pr(AnEi) is proved for every event A.

For every event A, we have Pr(AnEi)If a partition of the sample space Ω is a collection of disjoint events E1, E2.... En such that Ω-U-1 Ei, then for every event A, we have Pr(AnEi).Given: A partition of the sample space Ω is a collection of disjoint events E1, E2.... En such that Ω-U-1 Ei. The events 1, 2, 4), 13, 6, 5) partition the sample space 1, 2, 3, 4, 5, 6.To prove: Pr(AnEi)

Solution:By the probability of a partition theorem, we can write:Pr(A) = Pr(AE1) + Pr(AE2) + .... + Pr(AEn)...... (1)Since E1, E2, ..... En is a partition of Ω, so we know that:A = AE1 + AE2 + ..... + AEn...... (2)So, substituting equation (2) in equation (1), we get:Pr(AnE1) + Pr(AnE2) + .... + Pr(AnEn)By the definition of disjoint events, we know that if any two events are disjoint, then their intersection is empty.

Hence, we can write:Pr(AnEi) = P(AEi)/P(Ei)...... (3)So, from equation (1), we get:P(AEi) = P(Ei) Pr(AnEi)...... (4)From the definition of the probability of an event A given that another event B has occurred, we can write:P(A/B) = P(A ∩ B)/P(B)...... (5)So, substituting equation (4) in equation (5), we get:P(AEi)/P(Ei) = P(A ∩ Ei)/P(Ei)P(A ∩ Ei) = Pr(AnEi) P(Ei)Hence, the above equation satisfies the condition of Pr(AnEi).Therefore, Pr(AnEi) is proved for every event A.

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Answer: c = 13.96 or \(\sqrt{194.6}\)

Step-by-step explanation:

\(a^{2}+b^{2}=c^{2}\)

a and b = side lengths

c = hypotenuse

\(8.6^{2}+11^{2}=c^{2}\)

\(73.96 + 121=c^{2}\)

\(194.96=c^{2}\)

\(\sqrt{194.6} =c\)

\(c = 13.9628 = 13.96\)

Answer:

YZ = 13.96

m∡Z = 52°

m∡Y = 38°

Step-by-step explanation:

found YZ first by using Pythagorean Theorem:

11² + 8.6² = YZ²

YZ² = 194.56

YZ = √194.56

YZ = 13.96

Used Law of Sines to find m∡Z:

sin 90°/13.96 = sin Z/11

sin Z = 11/13.96

arcsin Z = 52°

180 - (90 + 52) = m∡Y

m∡Y = 38°

Answer:

Step-by-step explanation:

The base ten blocks to show the number 200 in the place value chart is shown below.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The number 200 in the place value.

Now,

Since, the number 200 in the place value.

Hence, The figure for the base ten blocks to show the number 200 in the place value chart is shown in figure.

Thus, The base ten blocks to show the number 200 in the place value chart is shown below.

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The tangent of <S is 8/15

Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

Given:

ST = 68

UT = 60

so, SU = √ST² - UT²

           = √68² - 60²

           = √4624  - 3600

           = √1024

           = 32

So, Tangent of <S = P/ B

tan S = SU / UT

tan S = 32 / 60

tan S = 8/15

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Approximately 19.59% of the rods will have a length less than 22.9 cm. Approximately 4.39% of the rods will be discarded. Approximately 30.85% of the rods will have a length greater than 23.15 cm.

a) The proportion of rods with a length less than 22.9 cm, we can use the z-score formula and the standard normal distribution.

First, we calculate the z-score for 22.9 cm:

z = (x - μ) / σ

z = (22.9 - 23.5) / 0.7

z = -0.857

Next, we look up the corresponding cumulative probability in the standard normal distribution table. From the table, we find that the cumulative probability for a z-score of -0.857 is approximately 0.1959.

Therefore, approximately 0.1959 converting in percentage gives 19.59% of the rods will have a length less than 22.9 cm.

b) The proportion of rods that will be discarded, we need to calculate the proportion of rods shorter than 21.1 cm and longer than 24.7 cm.

First, we calculate the z-scores for both lengths:

For 21.1 cm:

z = (21.1 - 23.5) / 0.7

z = -3.429

For 24.7 cm:

z = (24.7 - 23.5) / 0.7

z = 1.714

Next, we find the cumulative probabilities for these z-scores. From the standard normal distribution table, we find that the cumulative probability for a z-score of -3.429 is approximately 0.0003, and the cumulative probability for a z-score of 1.714 is approximately 0.9564.

The proportion of rods that will be discarded, we subtract the cumulative probability of the shorter length from the cumulative probability of the longer length:

Proportion of rods to be discarded = 1 - 0.9564 + 0.0003 = 0.0439

Therefore, approximately 0.0439, converting in percentage gives 4.39% of the rods will be discarded.

c) The proportion of rods greater than 23.15 cm, we can use the z-score formula and the standard normal distribution.

First, we calculate the z-score for 23.15 cm:

z = (x - μ) / σ

z = (23.15 - 23.5) / 0.7

z = -0.5

Next, we look up the corresponding cumulative probability in the standard normal distribution table. From the table, we find that the cumulative probability for a z-score of -0.5 is approximately 0.3085.

Therefore, approximately 30.85% of the rods will have a length greater than 23.15 cm.

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Answer: 155 anos

agregue 12 anos a la edad mas avanzada, que es 30.

obtienes 42

encontrar las edades de los otros ninos, restar 3, 4, 6

42-3 = 39

42-4 = 38

42-6 = 36

sumarlos todos

39 + 38 + 36 + 42 = 155

EXPLANATION.

When the mean and median are of the same value, the data are said to be symmetric or to form a symmetric set.

therefore the answer is: the option B.

Answer:

x = 1.25

Step-by-step explanation:

-3x+10 = 5x-8

+3x        +3x

10 = 8x - 8

+8           +8

18 = 8x

x = 18/8

x = 1 1/4 = 1.25  

Therefore, the top of the ladder is sliding down the wall at a rate of 3.75 ft/sec (negative rate) when the bottom is 15 feet from the wall.

To solve this problem, we can use related rates and the Pythagorean theorem.

Let's denote the distance between the bottom of the ladder and the wall as x, and the height of the ladder (distance from the ground to the top of the ladder) as y. We are given that dx/dt = -2 ft/sec (negative because the bottom is sliding away from the wall).

According to the Pythagorean theorem, x^2 + y^2 = 17^2.

Differentiating both sides of the equation with respect to time t, we get:

2x(dx/dt) + 2y(dy/dt) = 0.

Substituting the given values, x = 15 ft and dx/dt = -2 ft/sec, we can solve for dy/dt:

2(15)(-2) + 2y(dy/dt) = 0,

-60 + 2y(dy/dt) = 0,

2y(dy/dt) = 60,

dy/dt = 60 / (2y).

To find the value of y, we can use the Pythagorean theorem:

x^2 + y^2 = 17^2,

15^2 + y^2 = 289,

y^2 = 289 - 225,

y^2 = 64,

y = 8 ft.

Now we can substitute y = 8 ft into the equation to find dy/dt:

dy/dt = 60 / (2 * 8) = 60 / 16 = 3.75 ft/sec.

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The solution to one half cubed − 2 ÷ square root of 64 is negative one eighth

The expression is given as:

one half cubed − 2 ÷ square root of 64

Rewrite the expression properly as follows:

(1/2)^3 − 2/√64

Take the square root of 64

(1/2)^3 − 2/8

Evaluate the quotient of 2 and 8

(1/2)^3 − 1/4

Take the cube of 1/2

1/8 - 1/4

Evaluate the difference

-1/8

Hence, the solution to one half cubed − 2 ÷ square root of 64 is negative one eighth

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- 1/8

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

First you have to organize your information:

3 Teach.= 70 children

There are 14700 children 210 times 70.

You multiply 3*210 =70*210 because if you multiple one side you have to do the other to.

This equals 630= 14700. They need 630 teachers.

They have 612 so you only have to subtract 630 -612 =18

They need 18 teachers more.

An example of a tiered observation when measuring temperature would be measurements rounded off to the nearest degree.

This means that when you observe and measure the temperature, you would round the values to the nearest whole degree, providing a concise and uniform set of data points for analysis or comparison.

One example of a tiered observation when measuring temperature could be only considering those temperatures in a certain range, such as only observing temperatures that fall within the range of 60-70 degrees Fahrenheit. This would be a tiered observation because it is limiting the range of data being observed.

However, it's important to note that measurements rounded off to the nearest degree could also be considered a tiered observation because it's grouping data into discrete categories based on the rounding method used.
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Answer:

Step-by-step explanation:

To solve this problem, you have to combine like terms of x and b from one side of the equation.

Combine like terms.

3(2x+5b)+4x-2x-4b+6

Solve.

4x-2x=2x

Rewrite the problem down.

3(2x+5b)+2x-4b+6

Expand the form.

Use a distributive property.

Distributive property:

A(B+C)=AB+AC

3(2x+5b)

Multiply.

3*2x=6x

3*5b=15b

Rewrite the problem.

6x+15b

6x+15b+2x-4b+6

Combine like terms.

6x+2x+15b-4b+6

Add the numbers from left to right.

6x+2x=8x

8x+15b-4b+6

Then, you add again.

15b-4b=11b

= 8x+11b+6

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

8x+11b+6

Step-by-step explanation: