Let f(x)=5x and g(x)=sinx and h(x)=g(f(x))=sin(5x) What is h’(x)?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

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To find the inverse of a function, you can follow these steps:

Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.

Solve the equation for y. In this case, you would get:

x = √y + 8

y = x - 8

Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:

f^-1(x) = x - 8

This is the inverse function of y = √x + 8.

Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.

The two changes that would Karl earn more money are "Karl increases his initial investment" and "Karl deposits more money into the account every year" (options B and D).

In this case, the amount of money Karl can get depends on both the amount of money he invest and the interest rate. Here are some examples:

If he invest $100 and the interest rate is 10% he will get $10

If the invest $1000 and the interst rate is the same (10%) he will get $1000

Moreover, if the interste rate increases he can get more money: If the invest $100 but the interst rate is 12% he gets $12

This means he can get more profit if the investment is higher or the rate increases. Based on this, the two options that would increase his amount of money are increasing the initial investment or depositing more money (option B and D).

Note: This question is incomplete; here is the missing section:

A. The bank decreases the interest rate.

B. Karl increases his initial investment.

C. The bank adds a fee to keep the account active.

D. Karl deposits more money into the account every year.

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Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:

Odds against = (1 - probability of event occurring) / probability of event occurring

In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:

Odds against = (1 - 0.16) / 0.16

= 0.84 / 0.16

= 5.25

So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.

It means that there are 5.25 times more likely that it will not happen compare to happen.

Step-by-step explanation:

Therefore, N2 and 2N are not equal, they are different mathematical expressions.

A finite collection of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

A mark, sign, or term that denotes, denotes, or is taken to denote a concept, an item, or a connection is known as a symbol. By connecting seemingly unrelated ideas and events, symbols let individuals look beyond the known and the visible.

No, N2 and 2N are not the same.

N2 is the square of N, which means it is N multiplied by itself. For example, if N = 5, then N2 = 5*5 = 25.

2N, on the other hand, is N multiplied by 2. For example, if N = 5, then 2N = 5*2 = 10.

So, N2 and 2N are not equal, they are different mathematical expressions.

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The area of the quarter of the circle is 78.50 squared centimeters.

A circle is a 2 dimensional plane shape that is bounded by a curve. Its area can be determined by;

area of a circle = [tex]\pi r^{2}[/tex]

where r is the value of the radius of the circle.

The radius of a circle is given as the half of its diameter.

Thus, a quarter of a circle is the 4th part of a given circle. This implies of fraction selected when a circle is divided into 4 equal part.

So that;

area of quarter of a circle = area of a circle/ 4

                                          = [tex]\pi r^{2}[/tex]/ 4

The area of quarter of then given circle = ((22/7)*(10)^2)/ 4

                                                       = 78.50 squared centimeters

Therefore, the answer to the area of the quarter circle was found as explained above.

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No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.

To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.

In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.

10^2 + 12^2 = 100 + 144 = 244

244 ≠ 15^2

Therefore, 10 12 15 is not a Pythagorean triple.

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Answer:

[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]

Rewrite the third fraction:

[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]

Apply the difference of two squares to the denominator of the third fraction:

[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]

Therefore the expression can be written as:

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).

Adjust the fractions based on the LCM:

[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]

[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]

Factor out 3 from the numerator:

[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]

Cancel the common factor (a + 6):

[tex]\implies \dfrac{3}{a-6}[/tex]

Therefore:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

The Slope of log - log graph  represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .

What is Logarithm ?

The Logarithm is defined as  power to which a number must be raised to get some other number .

A log-log plot is the plot in which  both the x-axis  and y-axis use a log scale.

The plot of  logarithms of variables helps in extracting  the information about the power relationship. The case of  freely falling object is  used to illustrate a log - log plot.

A plot of the logarithm of freefall distance as a function of logarithm of time gives  a straight line of slope 2.

Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.

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Answer:

u = 8

Step-by-step explanation:

calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )

m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives

[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )

10(u - 5) = 30 ( divide both sides by 10 )

u - 5 = 3 ( add 5 to both sides )

u = 8

Step-by-step explanation:

(u - 5)/(5 + 5)= 3/10

(u - 5)/10= 3/10

10u - 50 = 30

10u = 80

u = 8

If 1 inch represents 1.5 feet, we can use this conversion factor to find the length of the actual airplane in feet. Thus 12 inches of model airplane represents an actual length of the actual airplane of 18 feet.

Therefore the answer is 18 feet.

To convert the length of the model airplane (12 inches) to feet, we can multiply it by the conversion factor (1 inch = 1.5 feet)

= 12 inches × 1.5 feet/inch

= 18 feet

So the length of the actual airplane is 18 feet.

It is important to pay attention to the units of measurement when performing conversions and make sure to use the correct conversion factor. And also it's a good practice to always check your answer to make sure it makes sense in the context of the problem.

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To find the missing side length of the acute angled triangle apply the cosine law as follow:

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = b² + a² - 2abcosC

As given in the question,

Given triangle is acute angled triangle.

Let us consider the measure of two sides and its included angle of the acute angled triangle is given.

Let the triangle be ABC,

Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.

Apply cosine law to find the measure of the missing side in the acute angled triangle:

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = b² + a² - 2abcosC

Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.

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Therefore , the solution of the given problem of surface area comes out to be Felix is required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.

Its surface area is a gauge of the space it takes up overall. A three-dimensional shape's entire environment is considered part of its surface area. Surface area is the total area of a thing. By adding up the faces on each of its six rectangle sides, a cuboid's volume of water can be calculated. The following formula could be used to calculate the dimensions of the box: Surface is the same for 2lh, 2lw, and 2hw (SA). The muti shape's surface area serves as a representation of the entire region.

Here,

Given: One parallelogram-shaped tile has a base of 4 cm and a height of 2 cm.

4 x 2 cm is the area of a single parallelogram-shaped tile.

8 cm2 is the size of one parallelogram-shaped tile.

The total area of the five black and five white tiles is 10 8cm2.

Total tile area is 80cm2 for the 5 black and 5 white tiles.

Felix is therefore required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.

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The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.

Given that,

In the picture we have a circle with an angle AOB is a central angle with a measure of 110°.

We have to find the measure of the ACB arc.

We know that,

Suppose that AB is the minor arc that is m(arc AB) = 110°

We know that measure of the major arc is 360°-  measure of minor arc.

m(arc ACB)= 360- m(arc AB)

m(arc ACB)= 360-110

m(arc ACB)= 250°

Therefore, The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.

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Answer:

[tex]\frac{d}{c}[/tex]

Step-by-step explanation:

[tex]\frac{cxcxdxdxd}{cxcxcxdxd}[/tex]  You can cross out 2 c's from the top and the bottom and 2 d's from the top and the bottom.  It now looks like this

[tex]\frac{d}{c}[/tex]

The third side of the triangle can be found out by using the Pythagoras theorem or the Heron's formula.

When there is a right angle triangle (A triangle whose on angle is of 90 degrees) then we use the Pythagoras theorem to find the third side.

The relation says that the sum of the square of the base and perpendicular is equal to the square of the hypotenuse.

In case of the scalene triangle the heron's formula is used to find out the value of the third side of the triangle.

There are several methods also present to find the value of the third side of the triangle.

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For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.

For a=-1/2 and b=6, the expression with the largest value is a+b, which is equal to 5.5. The expression with the smallest value is a-b, which is equal to -7.5. The expression closest to zero is a+b, which is equal to 5.5.

For a=12 and b=-6, the expression with the largest value is a+b, which is equal to 6. The expression with the smallest value is a-b, which is equal to 18. The expression closest to zero is a-b, which is equal to 18.

For a=-6 and b=-12, the expression with the largest value is a+b, which is equal to -18. The expression with the smallest value is a-b, which is equal to 6. The expression closest to zero is a+b, which is equal to -18.

For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.

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Answer: Acute

Step-by-step explanation:

The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex]. A and b are legs while c is hypotenuse. Hypotenuse is also the longest side. Let's plug them in and see if they are equal to each other.

[tex]46^2+61^2=68^2[/tex]            [exponent]

[tex]2116+3721=4624[/tex]      [add]

[tex]5837\neq4624[/tex]

Since they are not equal, then it is not a right triangle.

To tell is a triangle is acute, if the sum of the two shorter sides squared is greater than the longest side squared, then the triangle is acute.

At the end of the Pythagorean Theorem, we got 5837≠4624. 5837>4624, so that tells us that the triangle is acute.

Based on the question above, the patient pays $600 and the insurance company pays $2400.

To calculate how much the patient pays, we first need to calculate how much the insurance pays. We can do this by taking the total cost of the treatment ($3000) and multiplying it by the percentage that the insurance pays:

(90% = 0.9).

$3000 x 0.9 = $2700

This means that the insurance pays $2700 of the cost of the treatment. But we also need to subtract the $300 deductible from this amount.

$2700 - $300

= $2400

So the insurance pays $2400 for the medical treatment.

To find out how much the patient pays, we can subtract the amount paid by the insurance from the total cost of the treatment:

$3000 - $2400

= $600

Therefore, the  mathematics involved in solving this problem is very straightforward. We used basic arithmetic operations such as multiplication and subtraction to find the amounts paid by the insurance company and the patient.

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Therefore , the solution of the given problem of triangle comes out to be  ΔA"B"C "≅ ΔABC is congruent.

The fact that a triangle has sides or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not collinear. Any triangle that has three sides and three corners is a polygon.

Here,

Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.

Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".

Find the right answer for the triangles ABC and A"B"C."

So,

We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.

As a result, after reflection, figures always match their pictures.

"ABC," "A'B'C," etc (i)

The process of dilation is flexible. Although the size is changed, the shape is still the same.

Figures after dilatation therefore always resemble their photographs.

ΔA'B'C' ≅ ΔA "B"C" ... (ii)

With I and (ii), we obtain

ΔA"B"C "≅ ΔABC

Similar triangles include ABC and ABC.

As a result, choice A is the right one.

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According to the exponential function,

a) The function that models the given situation is f(rabbits) = 65000(√500/13)ˣ

b) The number of rabbits in 1870 is 6.5

c) According to your model, the first pair of rabbits introduced into Australia is 19th century

Here we have given that during the 19th century, here rabbits were brought to Australia.

And here we also know that the rabbits had no natural enemies on that continent, their population increased rapidly.

And we have given that there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.

Then according to the exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is to be determined.

Then the exponential function can be written as,

=> f(rabbits) = 65000(√500/13)ˣ

When we plot these on the graph then we get the graph like the following.

Through the graph we have identified that the value of rabbits in 1870 is 6.5

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Answer:

FALSE

Step-by-step explanation:

It is not necessarily true that ƒ(5)=8 just because ƒ(1)=0, ƒ(3)=0, and ƒ(4)=0. In fact, it is possible for ƒ(x) to be a cubic function and for ƒ(5) to equal any number, depending on the specific form of the function and the values of its coefficients.

On solving the provided question, we can say that - in the linear equation here the value will be

The algebraic equation y=mx+b is known as a linear  equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here,

y = 4x + 11

x = 8

y = 32 + 11

y = 43

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2.25×10 times greater is the weight of the elephant than the weight of the lion.

Two or more expressions with an Equal sign is called as Equation.

Given that a zookeeper  weighted an African elephant to be 9 x 10³ pounds.

An African lion to be 4 x 10² pounds

We need to find how many times greater is the weight of the elephant than the weight of the lion

Now, Divide the weighed an African elephant with weighed an African lion to determine times greater is the weight of the elephant than the weight of the lion,

N=9×10³/4×10²

=2.25×10

Hence, 2.25×10 times greater is the weight of the elephant than the weight of the lion.

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Answer: The statement "if sin 0 < 0 and cos 0 > 0" is not true, as both the sine and cosine of an angle of 0 degrees are equal to 0. Therefore, the statement is not meaningful and the question cannot be answered.

It is important to note that sine, cosine, and all the trigonometric functions are defined in radians and not degrees and the value of sin(0) and cos(0) is not zero but 1

Please provide more context or specify what you are asking about in order to give a more accurate answer.

Step-by-step explanation:

The average monthly salary of all the staff is going to be 19,333.34 ₹.

Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,

So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that

No. of males=10

No. of females=5

So, the total no. of figures = 15

Sum total of  set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be

=(20,000 × 10 + 18,000 × 5) ₹/15

=(200,000+90,000)/15₹

=290,000/15 ₹

=19,333.34 ₹

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Edna's phone can operate for up to 12 more hours without running out of battery. ​

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

fully charged

T = 18Hr

It has been 6 hours since Edna's phone was fully charged.

remaining battery =18- 6= 12Hr

x=12Hr

6 + x < 18

6 +x > 18

neither nor.

both equations are wrong.

6 +x = 18

Edna's phone can operate for up to 12 more hours without running out of battery. ​

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Answer:     -0.2      hope this answer helps you good luck                                

Answer:

-0.2

Step-by-step explanation:

[tex] \frac{ {5}^{ - 1} }{ { - 9}^{0} } = \frac{ \frac{1}{5} }{ - 1} = \frac{1}{5} \times \frac{ - 1}{1} = \frac{ - 1}{5} = - 0.2[/tex]

The margin of error and the sample mean of the confidence interval are given as follows:

The confidence interval is defined as follows:

(12.7, 19.5).

The definition of a confidence interval is that it is obtained as the sample mean plus/minus the margin of error.

Hence the sample mean is calculated as the mean of the bounds of the interval, hence:

(12.7 + 19.5)/2 = 16.1.

The margin of error is calculated as the absolute value of the difference of each bound from the sample mean, hence:

|19.5 - 16.1| = |12.7 - 16.1| = 3.4.

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On solving the provided question, we can say that by linear equation  $249.67  money was raised from the raffle

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here,

the linear equation that can be formed is

200x + 24 y = 3.50

125 x + 20y = 5

ratio = 8:1

so,  $249.67  money was raised from the raffle

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