If f(x)=x squared +4x-5
show that (x-3) is a factor of the polynomial h(x)=f(x)-f(3)

The function that represent the balance A in the account after t years is f(t) = 13000( 1.013 )^( 2t ).

This question is incomplete, the complete question is:

Rawan deposits $13,000 into an account that pays 2.6% annual interest compounded every 6 months.

Write a function to represent the balance A in the account after t years.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that;

First, convert R as a percent to r as a decimal

r = R/100

r = 2.6/100

r = 0.026

Given that time = t.

A = P( 1 + r/n )^( n × t )

f(t) = 13000( 1 + 0.026/2 )^( 2 × t )

f(t) = 13000( 1 + 0.026/2 )^( 2t )

f(t) = 13000( 1 + 0.013 )^( 2t )

f(t) = 13000( 1.013 )^( 2t )

Therefore, the accrued amount after t years is f(t) = 13000( 1.013 )^( 2t ).

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To the nearest cent, Andy will have $1,322.50 in 2 years.

Interest is the cost of borrowing money, or the return on lending money. It is typically expressed as a percentage of the amount borrowed or lent, known as the principal.

Using the formula [tex]B=p(1+r)^t[/tex], where p=$1,000, r=0.15 (15% expressed as a decimal), and t=2, we can calculate the balance B after 2 years:

[tex]B = $1,000(1+0.15)^2 \\ \\B = $1,000(1.15)^2\\\\B = $1,000(1.3225)\\\\B = $1,322.50\\\\[/tex]

Therefore, to the nearest cent, Andy will have $1,322.50 in 2 years.

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Answer:

Length: 17 cm

Width: 4 cm

Step-by-step explanation:

Let x be the width of the rectangle.

length : 4x+1

x+x+4x+1+4x+1= 42

10x= 40

x= 4

4x+1= 4(4)+1

= 17

Answer:

a. After 4 years, the amount in the account can be found by using the formula for simple interest:

A = P * (1 + r * t), where P is the initial deposit, r is the annual interest rate as a decimal, and t is the number of years.

Plugging in the values, we get:

A = $2,000 * (1 + 0.05 * 4) = $2,000 * 1.2 = $2,400

So after 4 years, there will be $2,400 in the account.

b. After 16 years, the amount in the account can be found using the same formula:

A = $2,000 * (1 + 0.05 * 16) = $2,000 * 1.8 = $3,600

So after 16 years, there will be $3,600 in the account.

c. To find the number of years it will take for the account to contain $2,500, we can use the formula:

t = (A - P) / (P * r), where A is the desired amount.

Plugging in the values, we get:

t = ($2,500 - $2,000) / ($2,000 * 0.05) = ($500) / ($100) = 5 years

So it will take 5 years for the account to contain $2,500.

d. To find the number of years it will take for the account to contain $3,000, we can use the same formula:

t = ($3,000 - $2,000) / ($2,000 * 0.05) = ($1,000) / ($100) = 10 years

So it will take 10 years for the account to contain $3,000.

Step-by-step explanation:

pls mark brainlist

The value of x in the given figure is 31.76.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given triangle, there are two triangles.

Let us find the length of the perpendicular line by using pythagoras theorem.

16² + a² = 22²

256 + a²  = 484

a²  =484-256

a² = 228

a=15.09 = 15

Now let us find the value of x.

Now 44-16= 28

28²+15² = x²

784 + 225 =  x²

1009 = x²

Square root on both sides

x=31.76

Hence, the value of x in the given figure is 31.76.

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The Weight of mini horse is 465 lbs.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

A calf and a mini-horse weigh 705 lbs combined.

The ratio of their weights is 16:31 respectively.

let the Common ratio be x.

So, weight of calf = 16x and Weight of mini horse = 31x

Thus, 16x + 31x = 705

47x = 705

x= 705/ 47

x= 15

Then, the Weight of mini horse = 31x = 31(15)= 465 lbs.

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The inequality that shows the possible amounts of pisquets is 8 < x < 19

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

My friend Vreel has less than 19 pisquets and more than 8 pisquets

Using x for Pisquets, we have:

x < 19 and x > 8

When the inequality is combined, we have

8 < x < 19

Hence, the inequality is 8 < x < 19

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Answer:

18

Step-by-step explanation:

The median of a set of data is the value that separates the lower and upper halves of the data. To find the median, the data must be arranged in numerical order.

The data, arranged in numerical order, is:

5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20

Since the number of data points is an odd number (17), the median is simply the middle value, which is:

18

So the correct answer is A) 18.

Answer: C

Step-by-step explanation:

To find the median, arrange the numbers in sequential order.

5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20

When there are an odd number of data in the set, choose the middle number in the set. For example, see the following data set.

2, 4, 6, 8, 9

The middle number in the data set is 6, so it is the median.

When there is an even number of data in the set, choose the middle two numbers, add them together, and then divide them by 2.

There are 16 numbers in this data set. We need to find the two middle numbers in the set.

5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20

10 and 12 are the two middle numbers in the set.

10 + 12 = 22

22/2 = 11

Median = 11

The measure of central location most often reported for annual income and property value data is the mode.

There are three measures of central tendency of a data-set, which are defined as follows:

Among those three measures, the mode is the one that gives the observation that appears the most often in a data-set, hence the correct option is given by option a.

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100 centimetres make up one metre. 100 centimetres must be multiplied by 0.0328084 to equal one metre in feet. There are 3.28084 feet as a result.

100 cm in one metre

1 cm = 0.0328084 ft

100 cm in 1 metre equals 0.0328084 feet, or 3.28084 feet.

100 centimetres make up one metre. 100 centimetres must be multiplied by 0.0328084 in order to convert 1 metre in cm to feet. This math will show us how many feet are in one metre, centimetre. To proceed step-by-step, we must first multiply one metre by one hundred centimetres. We will get 100 centimetres as a result.Following that, we must multiply 100 centimetres by 0.0328084. This figure represents the number of feet in one centimetre. We can convert 1 metre cm to feet by multiplying these two values, which gives us 3.28084 ft. The length of things can be measured using this conversion in both metric and imperial systems. When attempting to measure objects precisely, it can be helpful to know how to convert between the two systems.

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The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the prism is given as,

Volume = (Base area) x (Height)

The rectangular prism has a volume of 9 cubic inches. The area of the base is 4 square inches.

Then the height of the rectangular prism is given as,

9 = 4 h

h = 9 / 4

h = 2.25 inches

The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.

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Answer:

A) [tex](3,5)[/tex] and [tex](-4,12)[/tex]

Step-by-step explanation:

[tex]x+y=8\\x+(x^2-4)=8\\x^2+x-4=8\\x^2+x-12=0\\(x-3)(x+4)=0\\x_1=3,\,x_2=-4\\\\x_1+y=8\\3+y=8\\y_1=5\\\\x_2+y=8\\-4+y=8\\y_2=12[/tex]

Null hypothesis: The probability of at least two people in each classroom of 25 students sharing a birthday is less than or equal to 40%.

Alternative hypothesis: The probability of at least two people in each classroom of 25 students sharing a birthday is greater than 40%.

Simulation Results:

Simulation 1: 8 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 2: 9 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 3: 7 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 4: 11 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 5: 7 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 6: 6 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 7: 8 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 8: 6 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 9: 10 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 10: 8 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 11: 7 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 12: 11 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 13: 8 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 14: 7 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 15: 10 out of 16 classrooms had at least 2 students sharing a birthday.

Simulation 16: 10 out of 16 classrooms had at least 2 students sharing a birthday.

Proportion of classrooms with at least 2 students sharing a birthday = (8+9+7+11+7+6+8+6+10+8+7+11+8+7+10+10)/16 = 0.7125

The mean number of classrooms with at least 2 students sharing a birthday is 0.7125. We can use this value to calculate the t-statistic.

t-statistic = (0.7125 - 0.4) / (sqrt(0.4 * 0.6 / 16)) = 5.766

Using a one-tailed t-test with 15 degrees of freedom and an alpha level of 0.05, the critical t-value is 1.753. Since the calculated t-statistic is greater than the critical t-value, we can reject the null hypothesis.

The p-value is very small (less than 0.0001), indicating strong evidence against the null hypothesis.

Therefore, we can conclude that there is sufficient evidence to suggest that the probability of at least two people in each classroom of 25 students sharing a birthday is greater than 40%.

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Answer:

Step-by-step explanation:

If you got together on December 27, 2021, your 1-month anniversary would be on January 27, 2022, which is exactly 31 days later.

Your 2-month anniversary would be on February 27, 2022, which is exactly 61 days later. Since February has only 28 days in 2022, it means that your 2-month anniversary would fall on the last day of February.

Your 3-month anniversary would be on March 27, 2022, which is exactly 90 days later.

The previous population, of the city is 55,000

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Given that, a city's current population is 40,700, decreased by 26% after it was measured last time, the

Let the previous population, of the city, be x,

Therefore,

x - 26% of x = 40,700

x(1-26%) = 40,700

0.74x = 40,700

x = 55,000

Hence, the previous population, of the city is 55,000

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The symbol of mean is "μ". The population mean, or average score for the population on a certain variable, equation as follows:

μ = ( Σ Xi ) / N

The term "mean" is simply the mathematical average of a set of two or more integers. The arithmetic mean technique, which utilizes the sum of the series' values, and the geometric mean method, which employs the average of a set of products, are only two of the methods available to determine the mean for a given collection of data. Nonetheless, most of the time, the outcomes of the various methods for determining a simple average are essentially the same. The arithmetic mean and the geometric mean are two different types of means that may be determined. By adding all the numbers in a set and dividing by the total number of integers in the set, the arithmetic mean is determined. The equation of mean will be:

μ = ( Σ Xi ) / N.

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All three options involve conducting a survey using random sampling, which is the most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school. The correct answer would be A, B, or C, depending on the availability of resources.

The most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school would likely be a survey using random sampling.

Random sampling is a statistical method in which a representative sample of a larger population is selected, in order to make inferences about the population as a whole. When conducting a survey, random sampling helps to ensure that the sample is representative of the population, reducing the potential for bias.

There are several different types of surveys that could be used to estimate the level of support for a new middle school, including telephone surveys, online surveys, and in-person surveys.

Complete question:

The superintendent of a large school district wants to estimate the percentage of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents. What is the most appropriate method for the superintendent to estimate the percentage of district residents who support the building of a new middle school?

A. Telephone survey using random sampling

B. Online survey using random sampling

C. In-person survey using random sampling

D. Observing the behavior of district residents

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The angles in degree for the given triangle is 74 degrees, 78 degrees and 28 degrees.

In geometry, an angle is the figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are usually measured in degrees or radians and are used to describe the amount of rotation between two intersecting lines or to measure the size of a shape. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees but less than 360 degrees). Angles play an important role in various fields of study such as mathematics, physics, engineering, and architecture.

Here,

To find m23, we need to use the fact that the sum of the angles in a triangle is 180 degrees.

We know that m21 + m23 + m32 = 180 degrees. Rearranging this equation, we get m23 = 180 degrees - m21 - m32.

From the given information, we have:

m21 = (5x + 4) degrees

m32 = 180 degrees - mz2 - mz3 = 180 degrees - (6x - 6) - (10x + 12) = 174 - 4x degrees

Substituting these values into the equation for m23, we get:

m23 = 180 degrees - m21 - m32

= 180 degrees - (5x + 4) - (174 - 4x)

= 6x + 2 degrees

Therefore, m23 is 6x + 2 degrees.

5x+4+6x-6+168-10x=180

x+166=180

x=14

5x+4=5*14+4

=74°

6x-6=6*14-6

=78°

168-10x=168-10*14

=28°

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Answer:  

x = -3

Step-by-step explanation:

I did this before

Answer: √177

Step-by-step explanation:

6²+9²=c²

36+81=c²

117=c²

√117=√c²

√177 = c

(√177 can also be watered down to ±3√13 but √177 is one of the answer choices so yeah)

48 miles per hour is the most accurate rate of speed Morris is traveling

A measurement unit is a standard quantity used to express a physical quantity.

Given that Aneesha's speed is 50 miles per hour.

We need to convert to feet per second.

By given 1 mile = 5,280 feet

50×5280=264000 feet

Now divide by 36000

264000/36000

73.33 feet/second is the Aneeshas speed.

Morris is traveling 3 feet per second less than Aneesha, so his speed is:

73.33 - 3 = 70.33 feet/second

70.33× 3600  = 253,188 feet/hour

253,188 ÷ 5280  = 48 miles/hour

Hence,  Morris is traveling at a speed of 48 miles per hour.

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It is possible for equivalent expressions to make the left and right expressions have the same value

An expression is combination of variables, numbers and operators.

We have to check whether it is  possible to make the left and right expressions have the same value

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

For example 2x+4=2(x+2)

When we plug in x as 2

2(2)+4=2(2+2)

4+4=2(4)
8=8

Hence, its possible to make the left and right expressions have the same value when the expressions are equivalent.

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To convert micrograms (μg) to milligrams (mg), you can divide the number of micrograms by 1000. So, the formula for converting micrograms to milligrams is: mg = μg / 1000.

To convert micrograms to milligrams, divide the number of micrograms by 1000. This is because there are 1000 micrograms in 1 milligram. For example, if you have a measurement of 5000 micrograms and you want to convert it to milligrams, you would divide 5000 by 1000 to get 5 milligrams. This conversion is useful in many fields, including medicine, where medication dosages are often measured in milligrams, and scientific research, where precise measurements of small amounts of substances are necessary.

For example, let's say you have a measurement of 5000 micrograms and you want to convert it to milligrams:

mg = 5000 μg / 1000

mg = 5 mg

Therefore, 5000 micrograms is equal to 5 milligrams.

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Answer:

10[tex]\sqrt{50}[/tex]

Step-by-step explanation:

Since it's a isosceles right triangle, so

x^2+x^2=100^2

2x^2=10000

x^2=5000

x=[tex]\sqrt{5000}[/tex]=10[tex]\sqrt{50}[/tex]

The coordinate from point of intersection is (3, 11)

To find the intersection point of the diagonals of ABCD, we need to find the point where the lines containing the diagonals intersect.

The diagonal connecting A and C has slope:

m₁ = (y₂ - y₁) / (x₂ - x₁)

= (-2 - 6) / (3 - 3)

= undefined

This is because the line is vertical, and so has no slope. However, we can still write an equation for this line using the x-coordinate of point C:

x = 3

The diagonal connecting B and D has slope:

m₂ = (y₂ - y₁) / (x₂ - x₁)

= (-4 - 8) / (1 - 5)

= -3/2

We can write an equation for this line using point-slope form and the coordinates of point B:

y - y₁ = m₂(x - x₁)

y - 8 = (-3/2)(x - 5)

y - 8 = (-3/2)x + 15/2

y = (-3/2)x + 31/2

Now we can find the point of intersection by solving the system of equations given by the two lines:

x = 3

y = (-3/2)x + 31/2

Substituting x = 3 into the second equation, we get:

y = (-3/2)(3) + 31/2

y = 22/2

y = 11

The coordinate is (3, 11)

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Ryan has the faster time when compared to each of their teams,

"Information available from the question"

The time taken by Nick is 10.8 seconds.

The mean time taken by Nick is 11.4 seconds.

The standard deviation of Nick is 0.4 seconds.

The time taken by Ryan is 11.2 seconds.

The mean time taken by Ryan is 11.5 seconds.

The standard deviation of Ryan is 0.1 seconds.

The z-score of Nick is:

[tex]z_1=\frac{10.8-11.4}{0.4}[/tex]

[tex]z_1=-1.5[/tex]

The z-score of Ryan is:

[tex]z_2=\frac{11.2-11.5}{0.1}[/tex]

[tex]z_2=-3[/tex]

Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams.

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Answer:

Step-by-step explanation:

The simple interest formula is given by I = Prt, where P is the principal amount, r is the interest rate (per compounding period), and t is the time in years.

In this case, the interest rate is 5% per month, so we need to convert it to the equivalent annual interest rate, given by r = (0.05 x 12) = 0.6 (since there are 12 months in a year).

The time is 1.5 years, so t = 1.5.

So, the simple interest is:

I = Prt = 1000 x 0.6 x 1.5 = 900

The future value of the investment is the principal amount plus the interest earned, given by:

Future value = P + I = 1000 + 900 = 1900

So, the future value of the investment is $1900.

Answer: the future value of the simple interest investment, where 5% interest is paid monthly for 1.5 years on $1000, is $18074.06.

Step-by-step explanation:

To determine the future value of a simple interest investment, we need to calculate the interest earned over the investment period and add it to the original investment amount. Here's a step-by-step explanation for calculating the future value of a simple interest investment with a 5% interest rate paid monthly for 1.5 years on $1000:

Step 1: Convert the annual interest rate to a monthly rate.

Since the interest rate is 5% per year and the interest payments are made monthly, we need to convert the annual interest rate to a monthly interest rate. We can do this by dividing the annual interest rate by 12:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 5% / 12 = 0.05 / 12 = 0.00417

Step 2: Calculate the interest payment for each month.

For each month, we can calculate the interest payment by multiplying the monthly interest rate by the current balance:

Interest payment = Monthly interest rate * Current balance

Let's calculate the interest payment for the first month:

Interest payment = 0.00417 * $1000 = $4.17

Step 3: Add the interest payment to the current balance to get the new balance.

After each interest payment, we can add it to the current balance to get the new balance:

New balance = Current balance + Interest payment

New balance = $1000 + $4.17 = $1004.17

Step 4: Repeat the steps for each month.

We can repeat steps 2 and 3 for each of the 12 months in the first year and then for the 6 months in the second year.

Step 5: Add up the final balance.

After all 18 interest payments have been made, the final balance will be the sum of all the new balances:

Final balance = $1004.17 + $1004.17 + ... + $1004.17 (18 times) = $1004.17 * 18 = $18074.06

So, the future value of the simple interest investment, where 5% interest is paid monthly for 1.5 years on $1000, is $18074.06.

0700 military time is 7:00 AM in the 24-hour time format used by the military, also known as the 24-hour clock.

The 24-hour clock is a timekeeping system that uses a continuous count of 24 hours, instead of two sets of 12 hours for AM and PM. In this system, each hour of the day is numbered from 0 to 23, and is referred to as "military time" or "24-hour time". So, 0700 military time is equivalent to 7:00 AM, with the "0" indicating the first hour of the day. This system is commonly used in the military, as well as in other fields where precise and standardized timekeeping is important, such as aviation and public transportation.

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The fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

A fraction represents a part of a whole.

1. Let's say Alexa had a total of 5x crayons in the bag.

the number of blue crayons in the bag is 2x,

There is one triangle for every two round crayons,

(1/2) × 2x = x (By condition)

So, the fraction of crayons that are blue triangle is x / 5x = 1/5.

The number of blue round crayons is 2x.

The number of non-blue crayons is 5x - 2x = 3x,

The ratio of blue rounds to non-blue crayons is 2x / 3x = 2/3.

2.

4 out of 5 wall footballs are rubber, 4/5 of the footballs in the bag are rubber.

The fraction of rubber footballs that are brown is 2/3.

The fraction of footballs that are brown rubber footballs is (4/5) × (2/3) = 8/15.

The fraction of non-brown rubber footballs is (4/5) - (8/15) = 4/15.

The ratio of rubber footballs to non-rubber footballs is (4/5) / (1/5) = 4.

So there are 4 times as many rubber footballs as non-rubber footballs

Hence,  the fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

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