Here is a pattern made from sticks:
T T 7
LI LV/ LV
시
a)
How many sticks would be in pattern number 6?
28
b)
How many sticks would be in pattern number n?

Answer:

x = 21/5 or x = -2

Step-by-step explanation:

Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

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Answer:

-286

Step-by-step explanation:

45(-6)-16

= -270 - 16

= -286

Step-by-step explanation:

45x - 16

x = -6

45(-6) - 16

-270 - 16

-286

Hope this helps! :)

In the given function H(p) = p/5 + 15, the independent variable is "p" ,

The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.

It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.

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Answer: If the population of mosquitoes was quadrupling each year, then the population in any given year is four times the population of the previous year. Let M0 be the initial population of mosquitoes in 1998, then we can write:

Population of mosquitoes in 1999 = 4 * M0

Population of mosquitoes in 2000 = 4 * (4 * M0) = 16 * M0

Population of mosquitoes in 2001 = 4 * (16 * M0) = 64 * M0

Population of mosquitoes in 2002 = 4 * (64 * M0) = 256 * M0

In general, the population of mosquitoes in the year n (where n is the number of years since 1998) is given by:

Mn = 4^n * M0

Since the population of mosquitoes was 2750 in 1998, we can substitute n = 0 and M0 = 2750 in the above formula to get:

M0 = 2750

Therefore, the population of mosquitoes in the year n is:

Mn = 4^n * 2750

For example, the population of mosquitoes in the year 2002 (which is four years after 1998) is:

M2 = 4^2 * 2750 = 16 * 2750 = 44000

Note that this assumes that the conditions (e.g. weather, presence of predators, etc.) at the beach remain constant over time, which is not necessarily true in reality.

Step-by-step explanation:

Answer:

Step-by-step explanation:

180-90=2b+b

90=3b

90/3=b

30=b

2b=2*30

   =60

180-90=a+a

90=2a

a=90/2

a=45

the answer is 45 degrees

hope it helps!!let me know if it does

Answer:

a= 15°

Step-by-step explanation:

> use the fact that the sum of angles in a triangle is 180°

> based on the picture in the small right triangle we have b° +2b° +90° =180°

b +2b +90 =180° , combine like terms

3b +90 = 180, subtract 90 from both sides of the equation

3b = 90, divide by 3 both sides of the equation

b = 30°

> angle b has a ray that continues as a line so it makes an 180° angle and we have the acute triangle so we can write that

a + a+ (180-b) =180, substitute b

2a + 180-30 =180, subtract 180 from both sides, and add 30 to both sides

2a=30, divide by 2 both sides

a= 15°

Answer:

(3x+2)(x-5)

Step-by-step explanation:

Factor by grouping

\(3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)\)

Answer:

2 liters.

Step-by-step explanation:

These measurement units are part of the metric system. Unlike the U.S. customary system of measurement, the metric system is based on 10s. For example, a liter is 10 times larger than a deciliter, and a centigram is 10 times larger than a milligram.

Hope this helps!!<333

Answer:

a liter is 10 times larger than a deciliter, so yes, it is more.

Answer:

2.25 cups

Step-by-step explanation:

Answer:

2 1/4 (2.25) cups of milk

Step-by-step explanation:

to find out how much milk you needed for 6 servings you first had to figure out how much milk is used for 2 servings because 4+2=6.

Since 2 is half of four all we really have to do is divide the amount of milk used for 4 servings (1 1/2)

1 1/2 ÷ 2= 3/4 (1.5 ÷ 2=0.75)

then you add that to the amount of milk you use for 4 servings and you have your answer

(hope I explained that clearly enough)

The equation of this parabola is Y = -1/2 X². So option C is correct.

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Given that,

The graph of parabola,

the vertex (0, 0)

Y - 0  = 4a (X - 0)²

Y  =  4aX²

It can be seen in the graph it is downward parabola so value a should be  less than zero

So possible equation could be Y = -1/2 X²

Hence, the equation is Y = -1/2 X²

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The graph that represents the solution to the linear inequality −3x − 3y ≥ 6 is given as follows:

The graph shows a solid line, which passes through a point (-2,0) and a point (0,-2), with shading below the line.

The graph is presented at the end of the answer.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The inequality for this problem is given as follows:

−3x − 3y ≥ 6

In slope-intercept format, we have that:

3y ≤ -3x + 6

y ≤ -x - 2.

Hence the intercepts are:

Due to the equal sign, the graph is a solid line, and the shading is below the line, as the inequality is the amounts lower than the line.

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Answer:

P ( Z < 35,2 )  =  0,0122    or   1,22 %

Step-by-step explanation:

Assuming a normal distribution:

μ = 37

σ²  =  49       σ  =  7

Z(s) =  (  x  -  μ  ) / σ /√n

Z(s) = ( 35.2  -  37 ) / 7 / √77

Z(s) =  - 1.8 * 8.77 / 7

Z(s)  =  -  2.25

From z- table we find the area under the bell shape curve and it is:

0,0122

Then  P ( Z < 35,2 )  =  0,0122    or   1,22 %

Answer:

Explained below.

Step-by-step explanation:

Let the random variable X represent the weights​ (lb) of plastic discarded by households.

It is provided that the mean weight is, \(\bar x=2.135\ \text{lb}\) and the standard deviation of the weights is, \(s=2.316\ \text{lb}\).

(a)

Compute the difference between the weight of 5.65 lb and the mean of the​ weights as follows:

\(d=5.65 - \bar x\\\\d=5.65-2.135\\\\d=3.515\)

Thus, the difference is 3.515 lb.

(b)

Compute the number of standard deviations as follows:

\(\text{Number of Standard Deviation}=\frac{d}{s}=\frac{3.515}{2.316}=1.518\)

Thus, the number of standard deviation is 1.518.

(c)

Compute the z-score for the weight 5.65 lb as follows:

\(z=\frac{a-\bar x}{s}=\frac{5.65-2.135}{2.316}=1.517703\approx 1.52\)

Thus, the z-score is 1.52.

(d)

The z-score for the weight 5.65 lb is 1.52.

This  z-score lies in the range -2 and 2.

Thus, the weight of 5.65 lb​ is neither significantly low nor significantly​ high.

Answer

37

Step by Step explanation

replace x with -7

which gives

-(-7)^2-10(-7)+16

= 37

Answer:

8:3

Step-by-step explanation:

read the question carefully

Answer:

8/3 or 8:3

Step-by-step explanation:

It says WATER to DRINK MIX. Therefore, It can't be 3:8 or 3/8. The only thing to make sense is 8/3 or 8:3

Answer:

The null hypothesis is \(H_0: p_1 - p_2 = 0\)

The alternate hypothesis is \(H_a: p_1 - p_2 \neq 0\)

The pvalue of the test is 0.03 < 0.05, which means that we have enough evidence to accept the alternative hypothesis that he proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

Step-by-step explanation:

Before testing the null hypothesis, we need to understand the Central Limit Theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Out of 500 randomly selected people who rode a jet ski, 85% wore life vests.

This means that \(p_1 = 0.85, s_1 = \sqrt{\frac{0.85*0.15}{500}} = 0.016\)

Out of 250 randomly selected boaters, 90.4% wore life vests.

This means that \(p_2 = 0.904, s_2 = \sqrt{\frac{{0.904*0.096}{250}} = 0.019\)

Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

At the null hypothesis, we test that the proportions are the same, that is, the subtraction between them is zero. So

\(H_0: p_1 - p_2 = 0\)

At the alternate hypothesis, we test that the proportions are different, that is, the subtraction between them is different of zero. So

\(H_a: p_1 - p_2 \neq 0\)

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \(\mu = 0\)

From the two samples, we have that:

\(X = p_1 - p_2 = 0.85 - 0.904 = -0.054\)

\(s = \sqrt{s_1^2+s_2^2} = \sqrt{0.016^2 + 0.019^2} = 0.0248\)

Test statistic:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{-0.054 - 0}{0.0248}\)

\(z = -2.17\)

Pvalue of the test and decision:

The pvalue of the test is the probability that the difference differs from 0 by at least 0.054, which is P(|Z| > 2.17), which is 2 multiplied by the pvalue of z = -2.17

Looking at the z-table, z = -2.17 has a pvalue of 0.015

2*0.015 = 0.03

The pvalue of the test is 0.03 < 0.05, which means that we have enough evidence to accept the alternative hypothesis that he proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

Answer:

Between 6 and 7

Step-by-step explanation:

6^2 = 6 × 6 = 36

7^2 = 7 × 7 = 49

45 is between 36 and 49

The answer is below., the town's tax status should change within the next 3 years.

An exponential decrease can be represented by the formula:

y = ab^x

where a is the initial amount and b < 1.

Let p represent the population after t years, hence:

p = ab^t

Since the population decreases exponentially at a rate of 14.3% each year, hence:

b = 100% - 14.3% = 85.7% = 0.857

b = 0.857

Also, a = 9400 people

Therefore the equation is:

p = 9400(0.857)^t

The town's tax status will change once the population is below 6,000 people, therefore:

9400(0.857)^t < 6000

for the tax status to change.

At t = 3 years:

p = 5917

so, 5917< 6000

the town's tax status should change within the next 3 years.

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The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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Question:

"Convert F2 from hexadecimal to binary."

Answer:

11110010

Step-by-step explanation:

Hex F2 to decimal explained:

The value of HEX F2 in decimal is 242.

The value of HEX F2 in binary is 11110010.

2 2 X 160 = 2

F 15 X 161 = 240

HEX F2 = 242

The binary value is: 11110010

A hexadecimal number has base 16 (0,1,2,3,4,5,6,7,8,9 A,B,C,D,E,F).

basic hex to a decimal conversion table

Hex 0 1 2 3 4 5 6 7 8 9 A B C D E F

Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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Answer: y=-3/4x+2

Step-by-step explanation:

y=mx+b

y=-3/4x+b

-4=-3/4(8) +b

-4=-6+b

b=2

y=-3/4x+b

y=-3/4x+2

Answer:

there is no graph maybe post again

Answer:

20=20

Step-by-step explanation:

40-20=-20+40 or, 20=20

Answer:

1218

(14x25)x3=1050

because you have three sides

14x12=168 then 168+168=336

then add al together 1050+336=1 386

Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer:

A (8, -7)

Step by step explaination:

The reflection of point J on the coordinate plane is J(8,-7).

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected.

Given that the point (8,.7) is reflected on the x-axis. The reflected coordinates are,

J(8,7) ⇒ j'(8,-7)

Therefore, the reflection of point J on the coordinate plane is J(8,-7).

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According to the solving this equation  the total number of votes was 6897.

An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.

If the ratio of yes votes to no votes was 4 to 7, that means that for every 4 yes votes, there were 7 no votes. Let's call the number of yes votes 4x and the number of no votes 7x. Then we have:

4x + 7x = total number of votes

Simplifying the left side, we get:

11x = total number of votes

We also know that there were 2508 yes votes, so we can set up the equation:

4x = 2508

Solving for x, we get:

x = 627

Now we can plug this value of x into the equation for the total number of votes:

11x = total number of votes

11(627) = total number of votes

6897 = total number of votes

the total number of votes was 6897.

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Answer:

I=P0r  

A=P0+I=P0+P0r=P0(1+r)  

I  is the interest

A  is the end amount: principal plus interest

P0  is the principle (starting amount)

r  is the interest rate (in decimal form. Example: 5%=0.05)

Step-by-step explanation:

Answer:

Step-by-step explanation: