What is 38 percent of 10 oranges

Answer:

A. 0.00008

Explanation:

Given the scientific notation:

To write the number in standard form:

Step 1: Write the number of zeros (5) before number 8.

Step 2: Place the decimal point after the first zero.

The correct choice is A.

Answer: 13 1/3 Ibs

Step-by-step explanation:

20 x 2/3 = 13.3333333 (repeating)

Simplified that’s 13 1/3

The amount of the dog food in the bag will be 40/3 or 13.33.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

I have 20 pound bag of dog food if it is 2/3 full right now.

Then the amount of the dog food in the bag will be

⇒(2/3) x 20

⇒ 40 / 3

⇒ 13.33

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Answer:

\(\displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

Step-by-step explanation:

We are given a function:

\(\displaystyle \large{y = t^2 \sin (2t)}\)

To differentiate a function, we are going to use the product rules since there are two functions which are t^2 and sin(2t) multiplying together.

From the product rules, \(\displaystyle \large{y = f(x)g(x) \to y\prime = f\prime (x) g(x)+f(x) g\prime (x)}\)

Therefore, \(\displaystyle \large{y = t^2 \sin (2t) \to y\prime = (t^2)\prime \sin (2t) + t^2 (\sin (2t))\prime}\)

Before we start differentiating, I’d like you to look at [sin(2t)]’. A function like this, you cannot just directly derive and answer. You need to use chain rules.

We know that, \(\displaystyle \large{y = \sin (x) \to y\prime = \cos (x)}\) but what if the “x” is another function? Like sin(3x), sin(x^2) as examples. The insides are another function, can be expressed as fog(x) or gof(x) is composite function.

Basically, chain rule is a rule or formula for composite function and it’s the most common and useful as well as being always used in differentiation.

Chain Rules

\(\displaystyle \large{\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}}\)

where u is another function in a bracket. From the formula above, it can be also written as:

\(\displaystyle \large{[f(g(x))]\prime = f(g(x))\prime \cdot g(x)\prime\)

To simply say, you differentiate the whole function first then multiply with the chain or inner derived function.

So from the function, we obtain:

\(\displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot (2t)\prime}\\ \displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot 2}\\ \displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

The factored form would be:

\(\displaystyle \large{y\prime = 2t ( \sin (2t) + t \cos (2t))}\)

From above, for polynomial function, to differentiate, you can do by using the power rules.

Power Rules

\(\displaystyle \large{y = ax^n \to y\prime = nax^{n-1}}\)

Answer:

1. 3 + 2 = 2 + 3

2. 5 + 2 = 3 + 4

3. 6 + 0 = 3 + 3

4. 8 + 2 = 9 + 1

5. 2 + 2 = 4 + 0

6. 5 + 3 = 6 + 2

u basically just fill in the blank with a number that would add up to the number u already have that would equal the same as the other side. also pls give brainliest haha

Answer:

Step-by-step explanation:

We use the known identity:

sin (A + B)  sin A cos B + cos A sin B.

8 sin x cos 3x + 8 sin 3x cos x

= 8 (sin x cos 3x + sin 3x  cos x)

= 8sin (x + 3x)

= 8 sin 4x

Identity :

sin (A + B)  sin A cos B + cos A sin B

= 8 sin x cos 3x + 8 sin 3x cos x

= 8 (sin x cos 3x + sin 3x  cos x)

= 8sin (x + 3x)

= 8 sin 4x

Answer:

  sin(θ-φ) = -(21/1105)√85

Step-by-step explanation:

There are a few relations among trig functions that are useful here.

Using the above relations, we observe that ...

  tan(θ)cot(φ) = sin(θ)cos(φ)/(cos(θ)sin(φ))

Subtracting 1 gives ...

  tan(θ)cot(φ) -1 = (sin(θ)cos(φ) -cos(θ)sin(φ))/(cos(θ)sin(φ))

  = sin(θ-φ)/(cos(θ)sin(φ))

We can find the values of the denominator terms:

  cos(θ) = √(1/(tan²(θ)+1)) = √(1/((12/5)² +1)) = √(25/169) = 5/13

  sin(φ) = √(1/(cot²(φ)+1)) = √(1/((2/9)² +1)) = √(81/85) = (9√85)/85

Then the desired sine value is ...

  sin(θ-φ) = (tan(θ)cot(φ) -1)(cos(θ)sin(φ)) = ((12/5)(2/9) -1)(5/13)(9√85/85)

  = -21√85/(13·85)

  sin(θ-φ) = -(21/1105)√85

__

Check

  θ = arctan(12/5) ≈ 67.3801°

  φ = arccot(2/9) ≈ 77.4712°

  θ -φ ≈ -10.0911°

  sin(θ -φ) ≈ sin(-10.0911°) ≈ -0.175213

  -(21/1105)√85 ≈ -0.175213

_____

Additional comment

Perhaps more straightforward would be the computation of the sine and cosine of each angle, then find the difference of products according to the sine formula for the difference of angles. This takes more explanation, but doesn't require as much working of individual trig functions. The straightforward approach would give ...

     sin(θ -φ) = (12/13)(2/√85) -(5/13)(9/√85) = -21/(13√85) . . . same as above

You'd have to develop the other two trig functions of θ and φ to get this.

Answer:

Is it 11.6%?

Step-by-step explanation:

I divided 290/250

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Answer: The total volume of milk would be \(\dfrac{1}{2}\ gallon\)

Step-by-step explanation:

Since we have given that

Volume = \(\dfrac{1}{4}\ gallon\)

Number of weeks = 2

So, Total volume of milk that Gino's family drank would be

\(\dfrac{1}{4}\times 2=\dfrac{1}{2}\ gallon\)

Hence, the total volume of milk would be \(\dfrac{1}{2}\ gallon\)

Answer:

6 gallons

Step-by-step explanation:

Answer:

Step by step proof shown below.

Step-by-step explanation:

To prove the equation, you need to apply the Logarithm quotient rule and the Logarithm power rule. Here's how the quotient rule looks like.

\(log_b(x/y) = log_b(x) - log_b(y)\)

And here's how the power rule looks like

\(log_a(x)^n = nlog_a(x)\)

First let's apply the quotient rule.

\(\frac{f(x+h)-f(x)}{h} = \frac{log_a(x+h)-log_a(x) }{h} = \frac{log_a(\frac{x+h}{x} )}{h}\)

Now we can do some quick simplification, and apply the power rule.

\(\frac{1}{h} log_a(1 + \frac{h}{x} ) = log_a(1+\frac{h}{x} )^\frac{1}{h}\)

There is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range

To calculate the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school, you would need to follow these steps:

Calculate the mean of the sample by adding up all the hours of sleep reported and dividing by the sample size (n).

Calculate the standard deviation (σ) of the sample by taking the square root of the sum of squares of the differences between the sample values and the mean divided by n1.

Calculate the standard error (SE) by dividing the standard deviation by the square root of n.

Calculate the margin of error (ME) by multiplying the standard error by the critical value of 1. 96.

Calculate the confidence interval by adding and subtracting the margin of error from the mean. This will give you the lower and upper bounds of the confidence interval.

Therefore, the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school is (6. 73, 7. 67). This means that there is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range

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The y-coordinate of -3f(x-1) when x = 0 is -63

From the question, we have the following parameters that can be used in our computation:

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

From the question, we have the following parameters that can be used in our computation:

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

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Answer:

hamburger =282 calories

soda=212 calories

Step-by-step explanation:

2h+5c=1624 ...............×3

3h+2c=1270 ................×2

use eliminate method: multiply the first equation by 3, and second one by 2 to eliminate h first:

6h+15c= 4872

6h+4c=2540

subtract the two equations

6h+15c-6h-4c=4872-2540

11c=2332

c=2332/11

c=212 calories in soda

substitute c in any equation to get h

2h+5c=1624

2h+5(212)=1624

2h=1624-1060

2h=564

h=564/2=282

h=282 calories

check :

2(282)+5(212)=

564+1060=1624

3h+2c=1270

3(282)+2(212)=1270

After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.

To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.

Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.

Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.

Experimental probability of heads: 160/300 = 0.5333

Experimental probability of tails: 140/300 = 0.4667

Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.

In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.

To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.

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The question probable may be:

Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.

Answer:

slope is -3

it is the only one that makes sense because the line goes through -3

Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

For the given parallelogram, the measure of angle B is 65° and the measure of angle D is 65°. The answer is the third option.

There are different types of quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, for a parallelogram, its the opposite sides are equal and parallel. For a parallelogram is noted too that the opposite angles are equal.

The question gives the values of the angle B and D in function of n.

Therefore, considering that the opposite angles of the  parallelogram (ABCD)  are equal, so D=B.  Thus,

6n-25=3n+20

6n-3n=20+25

3n=45

n=15°

Replacing the value of n in each angle (B and D). Then,

D=6n-25= 6*15-25= 90-25= 65°

B=3n+20= 3*15+20= 45+20 = 65°

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Answer:

-1.5

Step-by-step explanation:

First, find the slope of these points.

-8-4/5-(-3)= -12/8= -3/2= -1.5

The slope of a line parallel to another, always has the same slope as the line that it is parallel to.

Answer:

\(2.375\,\,miles\)

Step-by-step explanation:

Given: Length of a hiking trail is \(3\frac{4}{5}\,\,miles\)

Terence travels \(\frac{5}{8}\) of the length of a hiking trail

To find: Distance travelled by Terence

Solution:

Whole numbers refer to natural numbers together with 0.

A fraction represents a part of a whole.

A whole number and a fraction combined into mixed fraction.

Distance travelled by Terence = \(\frac{5}{8}(3\frac{4}{5})=\frac{5}{8}(\frac{19}{5})=\frac{19}{5}=2.375\,\,miles\)

Answer:

The answer is 3

Step-by-step explanation:

20% of 15 can be written as 20% × 15

= 20/100 × 15

= 3

Thus, 20% of 15 is 3.

hope this helps

Answer:

the second one

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

a – 17 = 15

collect like terms

a=15+17

a=32

Answer:

y=2x+5

Step-by-step explanation:

This is a proportional relationship.The other one's are not true.

PLS Mark brainlist

Hope this helps:)

Answer:

y = -4x + 1

Step-by-step explanation:

→ First as the gradient is sloping downwards, we can eliminate 2 options

B and C

→ Then substitute x = 1 into  \(y=-\frac{1}{4}x+1\)  and  \(y=-4x+1\\\)  and see if you get 3 as the answer

y = -4x + 1

Answer:

y=2/5x+3

Step-by-step explanation:

brainliest pls

Answer:

D

Step-by-step explanation:

because the estimate of 52 is 50 and the estimate of 11 is 10 so there.