the surface area of a cuboid whose 6 faces have 10cm
​

The fourth term in the sequence is:

f(4) = -76

Here we have a sequence where we know the first term:

f(1) = 8

And the recursive formula is:

f(n) = -2*f(n - 1) - 4

Using the recursive formula we can get the next terms:

f(2)  = -2*f(2 - 1) - 4

      = -2*f(1) - 4 = -2*8 - 4 = -20

f(3) = -2*f(3 - 1) - 4

      = -2*-20 - 4 = 40 - 4 = 36

f(4) = -2*f(4 - 1) - 4

     = -2*36 - 4 = -76

That is the value of the fourth term.

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Answer: The answer is x²+2x-8

Step-by-step explanation:

The exponential function from the decay function given is y = 30.5(0.7)ˣ

An exponential function is a mathematical function that models the growth of a quantity as a power of another quantity, typically as the exponent of a constant called the base. The general form of an exponential function is given by:

f(x) = a^x

where "a" is the base and "x" is the input. The value of "a" must be positive and greater than zero. When "a" is greater than 1, the exponential function grows very quickly, and when "a" is between 0 and 1, the exponential function decreases very quickly.

In this problem, we can find the exponential function by;

when x = 0

f(0) = 30.5

The function can be written as;

f(x) = 30.5(b)ˣ

To find the value of b,

We can take another point and solve;

f(0) = 30.5

f(1) = (21.35)

Looking at the graph, this is a decay function and we can easily find the value as 0.7.

The function is given as y = 30.5(0.7)ˣ

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The area of the figure is solved to be

The area of a kite is solved using the formula

= P * q / 2

Where

p = length of long diagonal

q = length of short diagonal

Using the figure the length can be traced to be

p = 3 - -5 = 3 + 5 = 5

q = 6 - 2 = 4

Area of the figure

= 5 * 4 / 2

= 20 / 2

= 10 square units

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Answer: The equation 20x³-25x²+4x-5 can be factored by finding its roots, which are the values of x that make the equation equal to zero.

To find the roots, you can use one of the following methods:

Rational Root Theorem

Synthetic Division

Factor Theorem

Binomial Expansion

I would recommend using the Rational Root Theorem, which states that if a polynomial has a rational root, then it can be expressed as a product of linear factors with rational coefficients.

First, list out the possible rational roots of the equation: ±1, ±2, ±5, ±1/2, ±1/5.

Next, test each root by dividing the equation by (x-root), using synthetic division. If the remainder is zero, then the root is a factor of the equation. Repeat this process until you have found all of the roots.

Finally, factor the equation by grouping the roots into pairs and multiplying each pair to obtain a quadratic factor. Factor each quadratic and simplify the expression.

It is important to note that this is a rather advanced topic in algebra and finding the roots of polynomials can be quite challenging. If you need further assistance, I recommend seeking help from a tutor or textbook on algebra.

Step-by-step explanation:

Answer:

x= 1/27

Step-by-step explanation:

the correct answer is : X = 1/27

Answer:

- 1/2

Step-by-step explanation:

To solve for x in the equation 3^2x = 1/3, we can start by taking the logarithm of both sides with base 3:

log3 (3^2x) = log3 (1/3)

Using the logarithmic property logb (a^n) = n * logb (a), we can simplify the left side:

2x * log3 (3) = log3 (1/3)

Since log3 (3) = 1, we can simplify further:

2x = log3 (1/3)

To find the value of the logarithm on the right side, we can use the definition of logarithms: logb (a) = c if and only if b^c = a. Since 1/3 = 3^-1, we have:

2x = log3 (3^-1) = -1

Finally, to solve for x, we divide both sides of the equation by 2:

x = -1/2

So the solution to the equation 3^2x = 1/3 is x = -1/2.

The explanation of each statement in each given situation is given below:

a. B(0) = 0

depth in inches 0 minutes after filling began is 0; that is at time =0; depth =0

b. B(1) < B(7)

B(1) represents the function one minus after filling began

c. B(9) = 11

depicts that the depth in inches of water 5 minutes after filling is 11

d. B(10) = B(22)

depicts that the depth in inches of water 10 minutes after filling began is 22.

e. B(20) > B(40)

represents the function 20 minutes after filling began

These are the required answers

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The question translated in English is: "#7. Tyler filled his tub, took a shower, and then drained the tub. Function B gives the depth of the water,

inches, t minutes after Tyler started filling the tub.

Explain the meaning of each statement in this situation.

to. B(0) = 0

b. B(1) C.B(9) = 11

d. B(10) = B(22)

and. B(20) > B(40)"

The solution of units problem is   Suzy has 5 toy trucks by using the equation 15 = 3 * Suzy's number of toy trucks

According to the given information:

If Patricia has 3 times as many toy trucks as Suzy, we can set up an equation where:

Patricia's number of toy trucks = 3 * Suzy's number of toy trucks

We know that Patricia has 15 toy trucks, so we can substitute that value into the equation:

15 = 3 * Suzy's number of toy trucks

Now we can solve for Suzy's number of toy trucks:

Suzy's number of toy trucks = 15 / 3

Suzy's number of toy trucks = 5

Therefore, Suzy has 5 toy trucks.

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The left Riemann Sum approximation for the integral of 20(4x² - 2x)dx over the interval [0, 20] with four equal subintervals is 165250.

In calculus, the integral is a mathematical tool that allows us to find the area under a curve. It is an important concept that is used in many fields of science and engineering. One way to estimate the value of an integral is by using a Riemann Sum, which involves dividing the region under the curve into small rectangles and adding up their areas.

In this case, we will be using a left Riemann Sum with four equal subintervals to estimate the integral of 20(4x² - 2x)dx.

To use a left Riemann Sum, we need to first divide the interval of integration into equal subintervals. In this case, we have four subintervals of width

=> (b - a)/n = (20 - 0)/4 = 5.

The left endpoint of each subinterval will be used as the height of the rectangle that represents the area under the curve in that subinterval.

Next, we need to evaluate the function 20(4x² - 2x) at the left endpoints of each subinterval. These values will be used as the heights of the rectangles. The left endpoints are 0, 5, 10, and 15, so we have:

f(0) = 20(4(0)² - 2(0)) = 0

f(5) = 20(4(5)² - 2(5)) = 1900

f(10) = 20(4(10)² - 2(10)) = 7200

f(15) = 20(4(15)² - 2(15)) = 15150

We can now find the area of each rectangle by multiplying its height by its width (5). The total area is the sum of these areas:

(0)(5) + (1900)(5) + (7200)(5) + (15150)(5) = 165250

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The missing value is given as follows:

x = 11.3 cm.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The parameters for this problem are given as follows:

Hence the missing value is obtained as follows:

14² + x² = 18²

x = sqrt(18² - 14²)

x = 11.3 cm.

We have a triangle in which:

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The unknown number's variable w is equal to -10.

In mathematics, a variable is an alphabet or phrase that represents an unknown quantity, unknown value, or unknown number. The variables are used, particularly when dealing with algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.

The following information can be written as an equation to express it:

4 + w/5 = 2

By deducting 4 from both sides of the equation, we may isolate the variable on one side and solve for w:

w/5 = -2

Then, to find w, we can multiply both sides by 5.

w = -10

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The data is symmetric because some students have phones and some do not. The correct option is B.

A histogram is a simplified representation of the distribution of numerical data. The phrase was first used by Karl Pearson at the outset.

Rectangles are used in a histogram, a type of visual representation of statistical data, to show how frequently data points occur throughout a range of subsequent numerical intervals of equal width.

In the most common sort of histogram, the independent variable and dependent variable are shown along the horizontal axis and the vertical axis, respectively.

The histogram is a frequently used graphing tool. It is used to summarize data that is measured on an interval scale, whether it be continuous or discontinuous.

It is widely applied to give the primary properties of the data distribution a practical way to be illustrated.

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Answer: B. The data is symmetric because some students have phones and some do not.

Step-by-step explanation:

Ken total annual income is $ 55,401.98.

What has compounded annually?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.

The completely randomized design, in which participants are assigned to treatment groups at random, is the most basic type of experimental design. The main benefit of using this method is that it minimizes the influence of chance and eliminates bias. This approach makes use of probability theory, which gives statistical analysis a strong foundation.

Given that Roth IRA has a present value of $524,856.00. The rate of interest is 3.4% per annum.

A = P(1+r)^t

A = amount

P = principal

r = rate of interest

t = time

The amount after 15 years is

A = 524,856.00(1+3.4%)¹⁵

A = 866658.9925

The total interest is  866658.9925 - 524,856.00 = $341802.99

The average interest per annum is (341802.99 /15) =22786.866

The annual income is 22786.866 + 32,615.12 = 55,401.986

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The mean score of all the ninth graders in the city is equal to 81.84 ( round to two decimal places )

Number of schools in the city = 3

Result of the mean score of the ninth grade students are

Glenwood     78       269

Central City   93       321

Lincoln High  66       161

Given mean score by PR manager = 81

Correct mean score is calculated as

= ( 78 × 269 + 93 × 321 + 66 × 161 ) / ( 269 + 321 + 161 )

= ( 20982 + 29853 + 10626 ) / 751

= 61461 / 751

= 81.84 ( round to two decimal places )

Therefore, the mean score of the ninth grade students of all the schools in the city is given by 81.84 ( round to two decimal places ).

The above question is incomplete , the complete question is:

In a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean score on test Number of ninth graders

Glenwood     78       269

Central City   93       321

Lincoln High  66       161

The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81 . Of course, that is incorrect.

a. What is the mean score for all ninth graders in the city? Round to two decimal places.

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The solution of the system of equations is (4, -3)

Here we want to solve the next system of equations:

y = -(1/2)x - 1

y = (1/4)x - 4

Graphically.

To do so, we just need to graph both of these lines on the same coordinate axis and find the point where the lines intersect. Below is the graph of the system of equations, there we can see that the lines intersect at the point (4, -3), so that is the solution of the system.

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Answer:

None

Step-by-step explanation:

Let's clarify that a radical symbol beside a number means what number squared (or to the power of 2) can give me the number in the symbol.

In this case it would be 4 because

[tex]4*4=16[/tex]

A method I use is to find the square root is dividing the number in the radical symbol 2 times

First by the original number, and then by the product of the last equation. It will not always work, but it works in some cases like this one.

[tex]\frac{16}{2} = 8\\ \\\frac{8}{2}=4\\ \\\sqrt{16}=4[/tex]

Second step, multiply 4 by 4, which equals 16.

Since the square root of 16 is 4, you can substitute 4 in the rest of the equations instead of the radical expression.

None of the following equations equal 16, which means none of the following equations if equal to [tex]\sqrt{16} *4[/tex]

The general equation of a circle is (x-h)² + (y-k)² = r²

Where,

Here we are given the equation (x+4)² + (y+5)² = 64 and given this we are asked to find the diameter as well as the coordinates of the center.

Finding the center

If (h,k) = center, then the coordinates of the center are the given values of h and k but negative. This is because the values are being subtracted from x and y. (x-h)² + (y-k)² = r²

This means that, (x+4)² + (y+5)² = 64 is the same as saying (x-(-4))² + (y-(-5))² = 64 based off of the general equation of a circle.

Notice how the plugged in values are negative rather than positive.

In conclusion, we can say that the center is at (-4,-5) (see attached image below to check answer)

In the equation, 64 takes the place of r²

So r² = 64

Taking the square root of both sides we get r = 8

So the radius is 8.

To convert to diameter we multiply by 2

So diameter = 8 * 2 = 16

In conclusion, a circle with the equation (x+4)² + (y + 5)² = 64, has a center  at (-4,-5) and a diameter of 16

Answer: The least number that can be made using each digit exactly once is 123456789. The value of 4 is greater than the value of 6 because in the decimal system (base 10), the position of a digit determines its value. The leftmost digit represents the greatest place value (ones, tens, hundreds, etc.) and each subsequent digit represents a smaller place value. In the number 123456789, the 4 is in the thousands place, which has a greater value than the 6, which is in the tens place.

Therefore, the 4 has a greater value than the 6 because it represents a larger place value.

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

an exponential function modelling the situation has the form

y = a [tex](b)^{x}[/tex]

to find a and b use ordered pairs from the table

using (0, 11000 )

11000 = a [tex](b)^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then

a = 11000 , so

y = 11000 [tex]b^{x}[/tex]

using (1, 9350 )

9350 = 11000 [tex]b^{1}[/tex] = 11000b ( divide both sides by 11000 )

[tex]\frac{9350}{11000}[/tex] = b

b = 0.85

then exponential function is

y = 11000 [tex](0.85)^{x}[/tex]

Option C. the least squares method is a procedure for using sample data to find the estimated regression equation.

The procedure for using sample data to find the estimated regression equation is called the least squares method. This method involves finding the line that minimizes the sum of the squared vertical distances between the observed data points and the line. The estimated regression equation is used to predict the value of the dependent variable based on the value of the independent variable. This method is commonly used in regression analysis to model the relationship between two variables. It is a useful tool for making predictions and understanding the relationship between variables.

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Answer:

the number of shirts sold

Step-by-step explanation:

that's what the question is asking

The rays that are opposite are:

TX and TL

A ray is a line that points in one direction. It has one starting point and no end point.

It is important that we know the difference between a line and a ray.

A line has no endpoints or a starting point.

We have,

From the figure,

The rays are:

TS

TL

TV

TZ

All have a common starting point, T.

We see that,

TX and TS are perpendicular rays.

TS and TL are perpendicular rays.

TX and TL are opposite rays.

Now,

The rays that are opposite are:

TX and TL.

Thus,

TX and TL are opposite rays.

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The probability of selecting three numbers in increasing order is 1/3, which means that in one out of every three trials, we will select three numbers in increasing order.

Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. In this problem, we are asked to find the probability of selecting three numbers in increasing order from a range of 0 to 1.

Let's compute the probability of selecting three numbers in increasing order. Since the total number of possible outcomes is infinite, we need to use a continuous probability distribution to compute the probability. In this case, we can use the uniform distribution, which assumes that each number between 0 and 1 is equally likely to be selected.

The probability of selecting "a" as the smallest number is a/1 = a.

The probability of selecting "a" as the largest number is (1-a)/1 = 1-a.

The probability of selecting "a" as the middle number is 2(1-a)a, which is the product of the probability of selecting "a" and the probability of selecting "b" or "c" from the remaining range.

Therefore, the probability of selecting three numbers in increasing order is the sum of these probabilities:

P(increasing order) = ∫₀¹ (a * (1 - a) + (1 - a) * a + 2a(1 - a))da

P(increasing order) = ∫₀¹ 2a(1 - a)da

P(increasing order) = 2∫₀¹ a - a²da

P(increasing order) = 2[(a²/2) - (a³/3)] from 0 to 1

P(increasing order) = 2[(1/2) - (1/3)] = 1/3

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answer is

5(-1) = -5 +23 = 18

A two-tailed test is a hypothesis test in which the rejection region is option (B) in both tails of the sampling distribution

The hypothesis test is defined as the statistic approach checking the results of a research study support a particular theory when we apply that result to population

A two-tailed test is a hypothesis test that defined in which the critical area of the distribution is two sided, so the sample will be greater than or less than a certain range of values

Therefore, the rejection region of a two-tailed test is a hypothesis test is in both tails of the sampling distribution.

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The relation:

{x = y : x, y ε A}.

And this relation is a function.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A={2,4,6} and B={135}

R={(2,2), (4,4), (6,6)} is a relation on A.

That means, each value of set A connects to the same point.

The relation:

{x = y : x, y ε A}

Hence, {x = y : x, y ε A}.

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In  ΔABC, we can conclude that m∠A < m∠C and m∠B < m∠A < m∠C. Hence, options a. and d. are the accurate solutions.

The angle opposite to the longest side of the triangle is the largest angle of the triangle, similarly, the angle opposite to the smallest side of the triangle is the smallest angle of the triangle.

In the given ΔABC, we have,  

The longest side = AB = 3.1

The angle opposite to side AB = m∠C

The smallest side = AC = 2.9

The angle opposite to side AC = m∠B

side CB = 3

The angle opposite to side CB = m∠A

We have,

side AC < side CB < side AB

m∠B < m∠A < m∠C

From the given relations in the options provided, we get,

a. m∠A < m∠C

d. m∠B < m∠A < m∠C

are correct interpretations.

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The complete question is -

Select all the angle relationships in △ABC that are correct.

The company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.

To predict the number of T-shirts with problems in a shipment of 3,000 short-sleeved and 3,000 long-sleeved T-shirts, we can use the proportion of T-shirts with problems in the random sample as an estimate of the proportion of T-shirts with problems in the population.

For short-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 4/60 = 0.067. For long-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 1/60 = 0.017.

To estimate the number of short-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of short-sleeved T-shirts in the shipment:

Estimated number of short-sleeved T-shirts with problems = 0.067 x 3,000 = 201

Similarly, to estimate the number of long-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of long-sleeved T-shirts in the shipment:

Estimated number of long-sleeved T-shirts with problems = 0.017 x 3,000 = 51

Therefore, the company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.

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The total cost of the computer is $2418.75.

The total cost of the computer in sale $2,056.

The computer is regularly priced at $2250.

With the 15% discount, Jerome would save = $2250 × 15%

With the 15% discount, Jerome would save = $2250 × 15/100

With the 15% discount, Jerome would save = $337.50 on the computer

The sales tax is 7.5%.

So the tax on the computer would be = $2250 × 7.5%

The tax on the computer would bee = $2250 × 7.5/100

The tax on the computer would be = $168.75

The total cost for the computer on sale would be = $2250 - $337.50

The total cost for the computer on sale would be = $1,912.5

If the tax is 7.5% .

So he has to pay = $1,912.5 + $1,912.5 × 7.5% = $2,056

Therefore, the total price for the computer on sale would be $2,056,

The price of the computer not on sale = $2250 + $168.75 = $2418.75.

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