y varies directly as x. If y = 7 when x = 2, find y when x = 3.

As per the given population function, the growth function is written as, P = 13000(1.05)ˣ

Population function:

Population function refers the positive change in a particular population as a function of time. And this growth is not linear, but exponential, and so the formula for population growth can be found by starting with the premise that P (population) multiplies by a rate r over time.

Given,

A population numbers 13,000 organisms initially and grows by 5% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P = abˣ

Now, we have to find the population growth function for this situation.

From the given question, 'we have the following details,

Population numbers = 13,000

So, the value of a in the population function is 13,000

And it grows every year as 5%.

So, in decimal form in can be 0.05.

So, the value of b is calculated as,

=> b = 1 + 0.05

=> b = 1.05

Now, we have to apply these values on the function,

Then we get,

=> P = 13000(1.05)ˣ

Therefore, the population growth function is been identified

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Answer:

[tex]-2x+4[/tex]

Step-by-step explanation:

[tex]g(x)=f(x)+3=-2x+1+3=-2x+4[/tex]

The values can be 4, 25 and -4, -25.

What is a Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

The first number be x and second number be y

Equation 1: x*y = 100

Equation 2: x - y = 21

From equation 2 we can write x = 21 + y

Substituting the value of x in equation 1

(21 + y)*y = 100

21y + y^2 - 100 = 0

y = 4, -25

this implies that x = 25, -4

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The zero of the function f(x) = 3x - 9 is x = 3.

The zero of the function f(x) = -x + 4 is x = 4.

The zero of a function is any replacement for the variable that will produce an answer of zero.

Therefore, let's find the zero of the function f(x) = 3x - 9.

0 = 3x - 9

add 9 to both sides of the equation

0 + 9 = 3x - 9 + 9

9 = 3x

divide both sides by 3

x = 9 / 3

x = 3

The zero of the function is x = 3.

Therefore, let's find the zero of the function f(x) = -x + 4.

0 = - x + 4

subtract 4 from both sides of the equation

0 - 4 = -x + 4 - 4

-4 = - x

x = 4

The zero of the function is x = 4.

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The length of the perpendicular line from side AC to point B is approximately 43cm to the nearest whole number using the trigonometric ratio of sine rule.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratio of sine to be used states that for any triangle say ABC, then (a/sinA) = (b/sinB) = (c/sinC) where a,b, and c are the sides.

Considering right-angled triangle ABC, by Pythagoras rule

AC = √(54² + 72²)

AC = √1800

AC = 90°

so using sine rule;

AC/sinB = AB/sinC

90/sin90 = 72°/sinC

C = sin^-1[(72°×sin90°)/90°] {cross multiplication}

C = 53.13°

The new triangle formed has hypotenuse 54cm with the opposite side as the length of the perpendicular line from side AC to point B(which we can call x)

hence;

sinC = x/54

sin53.13° = x/54

x = 54 × sin53.13° {cross multiplication}

x = 43.2cm

Therefore, the length of the perpendicular line from side AC to point B is approximately 43cm to the nearest whole number, by application the trigonometric ratio of sine and it's rule for triangle.

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The value after differentiate will be;

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

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 function is,

⇒ [tex]y = 3^{x^{3} }[/tex]

Now,

Differentiate the function with respect to x as;

The function is,

⇒ [tex]y = 3^{x^{3} }[/tex]

⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 \frac{d}{dx} (x^3)[/tex]

⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 * 3x^2[/tex]

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

Thus, The value after differentiate will be;

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

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Answer:

C

Step-by-step explanation:

FUNCTION A

21 : 7 = 3

FUNCTION B

8: 4 = 2

3 is greater than 2

All the missing lengths and missing angles of the given right angle triangle are as calculated below

We are given a right angle triangle and as such we can use the trigonometric ratios as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

a) A = 30°, Thus;

B = 180 - (90 + 30)

B = 60°

Using sine rule;

a/sin A = b/sin B

a/sin 30 = 6/sin 60

a = 3.464

c/sin 90 = 6/sin 60

c = 6.928

b) a = 13 and b = 13

Using Pythagoras theorem;

c = √(13² + 13²)

c = 18.385

Since a = b, it means it is an isosceles triangle and so;

A = B = 45°

c) B = 30°, c = 10

A = 180 - (30 + 90)

A = 60°

10/sin 90 = b/sin 30

b = 5

10/sin 90 = a/sin 60

a = 8.66

d) A = 45°, c = 12

B = 45°

c/sin 90 = b/sin 45 = a/sin 45

b = a = 12 * sin 45 = 8.485

e) c = 1, b = 1/√2

c/sin 90 = b/sin B

1/sin 90 = (1/√2)/ sin B

B = 45° = A

a = √(1² - (1/√2)²)

a = 0.7071

f) c = 4 and b = 4;

a = √(4² - (4)²)

a = 0

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The inverse element of the binary operation is given by  (20-7a)/9 .

The binary operation is defined by a * b = 2a + 3b - 5

Now let us first find the identity element of the operation.

let e be the identity element.

Hence we know that a * e = a

Therefore a * e = 2a + 3e - 5

or, a = 2a + 3e - 5

or, a - 2a = 3e - 5

or, -a = 3e - 5

or, e = (5-a) / 3

Now we know that the inverse of the operation will be such that

a * a⁻¹ = e

or,  a⁻¹ = (20-7a) / 9

Therefore the inverse of the operation is given by (20-7a) / 9  .

A binary operation or dyadic operation is a rule that combines two elements (referred to as operands) to produce a third element. Formally, a binary operation is a two-arity operation.

An internally binary operation on a set is a binary action with the same set as its two domains or codomain. Examples include addition, multiplication, and other basic mathematical operations.

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Answer:

See attached file

Step-by-step explanation:

See attached file for the answer!

If you need help with more like these, I would suggest checking out Khan Academy.

They provide great free videos on every topic you could imagine!

Hope this helped!

The probability that a randomly selected firm will earn less than 22 million dollars is 0.8557

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = 20 million dollars = 20 m

standard deviation, σ = 11 million dollars = 11 m

The probability

differ from the population proportion by less than 22 m

X < 22 m

z score

z = (22 - 20) / 11

= 0.181818

p value for z < 0.181818 = 0.85573

The probability required = 0.8557

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Answer:

[tex]3^{7/2}[/tex]

Step-by-step explanation:

[tex]3^3 \sqrt{3} \\ \\ =3^3 \cdot 3^{1/2} \\ \\ =3^{3+\frac{1}{2}} \\ \\ =3^{7/2}[/tex]

The amount of points of each question in each part are given as follows:

It is stated in the problem that:

Hence the amount of points of each part is the least common multiple of 6 and 8, obtained by factoring by prime factors as follows:

6 - 8|2

3 - 4|2

3 - 2|2

3 - 1|3

1

Hence:

lcm(6,8) = 2³ x 3 = 24.

Meaning that each part was worth 24 points, and the number of questions is given as follows:

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The value of x for which (-1, 4) and (x, -2) make a slope of m = 5/4 is - [tex]\frac{29}{5}[/tex]

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

equation of straight line is y = mx + c

when x = -1, y = 4, m = 5/4

so that

4 = -1(5/4) + c

c = 4 + 5/4

4 can be written as fraction as 16/4

c = 16/4 + 5/4

Adding the numerator

c = 12/4

at x = x, y = -2

substituting

-2 = x( 5/4) + 21/4

-2 = 5x/4 + 21/4

-2 = [tex]\frac{5x + 21}{4}[/tex]

cross multiplying

5x + 21 = -8

collect like terms

5x = -8 - 21

5x = -29

x = -29/5

In conclusion, the value of x is -29/5

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Answer:

[tex]g(x)=(x+4)^2-5[/tex]

Step-by-step explanation:

The graph of [tex]f[/tex] was shifted 4 units left and 5 units down,

The cost of each friend's meal in terms of a is 35/a.  

The cost of each friend's meal when the number of friends is 5 is $7.

We are given that;

Total amount that they can spend on food bill = $41 including delivery charge of $6

The equation is given as;

6 + ax = 41

Where;

a is the number of people

x is the cost of each friend's meal.

Thus;

ax = 41 - 6

ax = 35\

x = 35/a

So it will be the cost of each friend's meal in terms of a.

Now,

If the number of friends = 5

Then,

a = 5

Thus;

x = 35/5 = $7

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Complete question is;

A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6. The equation below represents the situation, where x is the cost of each friend's meal.

The cost of each friend's meal in terms of a is

.

The cost of each friend's meal when the number of friends is 5 is $

The unit price for A is 3.57 ounce per dollar and the unit price for B is 3.4 ounce per dollar and A is better than B.

According to the question,

We have the following information:

A certain shampoo is available in two sizes. A 14.2 - ounce bottle costs $3.98. A 33.9 -ounce bottle costs $9.98.

Unit price of A:

14.2 ounce = $3.98

1 dollar = 14.2/3.98 ounce

Unit price for A = 3.57 ounce per dollar

Unit price for B:

33.9 ounce = $9.98

1 dollar = 33.9/9.98

Unit price for B = 3.4 ounce per dollar

Now, the unit price for A is greater than the unit price for B. So, size A is better.

Hence, the unit price for A is 3.57 ounce per dollar and the unit price for B is 3.4 ounce per dollar and A is better than B.

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when y equals zero, x equals -2

or, at y = 0, the function touches the x-axis at -2

A. The. part

B. The. whole

C. The. People

D. Benchmark. percent

The amount of mango juice you need is 8 litres

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

Orange juice = 3 parts

Mango juice = 6 parts

When these parameters are represented as ratio, we have the following expression

Ratio = Orange : Mango

This is then represented as

Orange : Mango = 3 : 6

When the litres of orange juice is 4, we have

4: Mango = 3 : 6

Express as fraction

Mango/4 = 6/3

Multiply through by 4

Mango = 4 * 6/3

Evaluate

Mango = 8

Hence, the mango juice is 8 litres

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Answer:

Chips are $0.80 a bag

A bottle of water is $1.60

A gallon of milk costs $3.80

Step-by-step explanation:

Answer:

$3.80 = cost of one gallon of milk.

$1.60 = cost of one bottle of water.

$0.80 = cost of one snack-size bag of chips.

Step-by-step explanation:

Define the variables:

Total items purchased:

Given information:

Create a system of equations with the given information:

[tex]\begin{cases}3x+4y+7z=23.40\\y=2z\\x=y+2.20\end{cases}[/tex]

Rearrange the second equation to make z the subject:

[tex]\implies z=0.5y[/tex]

Substitute the found expression for z and the third equation into the first equation and solve for y:

[tex]\implies 3(y+2.20)+4y+7\left(0.5y\right)=23.40[/tex]

[tex]\implies 3y+6.6+4y+3.5y=23.4[/tex]

[tex]\implies 10.5y+6.6=23.4[/tex]

[tex]\implies 10.5y=16.8[/tex]

[tex]\implies y=1.60[/tex]

Substitute the found value of y into the third equation and solve for x:

[tex]\implies x=1.60+2.20[/tex]

[tex]\implies x=3.80[/tex]

Substitute the found value of y into the second equation and solve for z:

[tex]\implies 1.60=2(z)[/tex]

[tex]\implies z=0.80[/tex]

Conclusion:

The solutions of the absolute value equations are:

1) |3x - 1| - |2x + 5 - 5 + x| = 0

x = 1/6

2) |2*(x + 1) - 4| = |2 - 2*(2 - x)|

x can be any real number.

3) | (x - 2)/4 | - 1/3 = x

This absolute value equation has two solutions, these are:

x = 2/15

x = -10/9

Here we need to solve some absolute value equations, the first one is:

|3x - 1| - |2x + 5 - (5 - x)| = 0

First, we need to simplify the arguments of both absolute values, then we get:

|3x - 1| - |2x + 5 - 5 + x| = 0

|3x - 1| - |3x| = 0

|3x - 1| = |3x|

Now we can remove the absolute value parts, obviusly this is ony true if the right part is negative:

3x - 1 = -3x

-1 = -3x - 3x

-1 = -6x

-1/-6 = x

1/6 = x

That is the solution of the first equation.

2) The second part is:

|2*(x + 1) - 4| = |2 - 2*(2 - x)|

Simplify this:

|2x + 2 - 4| = |2 - 4 + 2x|

|2x - 2| = |2x - 2|

this is true for all values of x, we have the same thing in both sides.

3)

| (x - 2)/4 | - 1/3 = x

|(x - 2)/4| = x + 1/3

We can separate the absolute value part in two equations:

(x - 2)/4 = x + 1/3

(x - 2)/4 = -(x + 1/3)

The first equation gives:

(x - 2) = 4*x + 4/3

x - 4x = 4/3 + 2

-3x = 4/3 + 6/3

x = (10/3)*(-1/3) = -10/9

The second equation gives:

(x - 2)/4 = -(x + 1/3)

(x - 2) = -4*(x + 1/3)

x - 2 = -4x - 4/3

x + 4x = 2 - 4/3

5x = 2/3

x = 2/3/5 = 2/15

This equation has two solutions, x = 2/15 and x =  -10/9

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Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

The standard errors for the sample sizes of 440, 230, and 1200 are 1.2, 1.65, and 0.72, respectively.

The mean of the population is μ = 90. The standard deviation of the population is σ = 25. We are given three sample sizes. We need to compute the standard error for each sample size.

The standard error is computed by dividing the standard deviation by the square root of the sample size. It calculates the accuracy of a sample mean by factoring in sample-to-sample variability.

Let S1, S2, and S3 represent the standard errors for the sample sizes of 440, 230, and 1200, respectively.

S1 = σ/√n

S1 = 25/√440

S1 = 1.2

S2 = σ/√n

S2 = 25/√230

S2 = 1.65

S3 = σ/√n

S3 = 25/√1200

S3 = 0.72

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AP Statistics students generally scored very well on questions about Units 1, 2, and 3, with 18% of students answering all such questions correctly.” “The most challenging units were 4 (Probability, Random Variables, and Probability Distributions) and 5 (Sampling Distributions).

Hope it helps you.

The hardest part of AP stats is Physics 1, AP U.S. History and AP Chemistry.

The course and exam for AP Statistics frequently prove to be difficult, especially for students who have not previously taken algebra II or calculus.

Newtonian mechanics, electrical charge and force, and other subjects are covered in AP Physics 1, which is regarded as one of the hardest AP courses. Students also complete college-level lab experiments and write reports for around 25% of the class period.

In general, AP Statistics students  do find it hard or difficult in "Probability, Random Variables, and Probability Distributions Unit 4 and Unit 5.

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The length of the hypotenuse is (c) 9.9 yards

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

Legs = 7 yards

This means that

Opposite = 7

Adjacent = 7

The hypotenuse is then calculated using the following Pythagoras theorem

Hypotenuse = √(Opposite² + Adjacent²)

Substitute the known values in the above equation, so, we have the following representation

Hypotenuse = √(7² + 7²)

Evaluate

Hypotenuse = 9.9

Hence, the hypotenuse is 9.9 yards

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Answer:

its right

Step-by-step explanation:

Answer: Its right i just got the same question

Step-by-step explanation: