What is the average rate of change for the interval
0

Certainly!

The text is asking how to solve the equation x² - 14x + 9 = 0 using the factoring method. Factoring is a method of finding the roots of a quadratic equation by expressing it as a product of two linear factors. The roots of a quadratic equation are the values of x that make the equation equal to zero. In this case, we are trying to find the values of x that satisfy the equation x² - 14x + 9 = 0.

Note that the lateral area of the right prism is 16cm²

The first step is to convert    the sides of the paralllogram to the same unit

6cm = 60mm

so

Perimeter of base = 2( 60 + 20) = 160 mm

Thus, the lateral area of the prism is

A = p x h = 160 x 0.3dm

But we cant have different units, so we say:

160 mm x 30mm
= 4,800mm

Converting this to centimeters, we have

480cm²

hence, the lateral area of the right prism  480cm²

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Answer: The lateral area of the prism is 48 cm²

Work:

We have,

Lateral area is the surface area of the sides or lateral faces of a three-dimensional object, excluding the surface area of the bases.

Now,

From the figure,

There are 4 rectangular-shaped sides.

And,

1 dm = 10 cm

0.3 dm = 3 cm

Now,

Lateral area of the prism.

= 4 x 3 + 3 x 3 + 4 x 3 + 5 x 3

= 12 + 9 + 12 + 15

= 48 cm²

Thus,

The lateral area of the prism is 48 cm²

The probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.

(a) The probability that exactly 40 of the murders were cleared can be found using the binomial probability formula.  

In this case, n = 50, k = 40, and p = 0.65. Thus, the probability that exactly 40 of the 50 murders were cleared is P(40 successes) = (50C40)(0.65)⁴⁰(0.35)¹⁰ = 0.064.

(b) The probability that between 35 and 37 of the murders, inclusive, were cleared can be found by adding the probabilities of each individual outcome.

For example, the probability of exactly 35 successes is (50C35)(0.65)³⁵(0.35)¹⁵ = 0.069.

Similarly, the probability of exactly 36 successes is (50C36)(0.65)³⁶(0.35)¹⁴ = 0.051.

Adding these two probabilities together gives the probability of between 35 and 37 successes, inclusive, as 0.069 + 0.051 = 0.120.

(c) It would not be unusual if fewer than 20 of the murders were cleared. This is because the probability of this outcome can be calculated using the same formula as before. In this case, if k = 19, then P(19 successes) = (50C19)(0.65)¹⁹(0.35)³¹ = 0.057, which is a relatively high probability.

Therefore, the probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.

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The museum in relation to her hotel is at distance and direction as 3 blocks to the west and 4 blocks to the north.

Given that,

Ruby is visiting San francisco.

The figure representing the situation is given below.

Here it is easier to find the relation of the museum with the hotel.

When Ruby walk a certain distance to the west, she will reach straightly north to the museum.

Distance to the west = 7 - 4 = 3 blocks

Then she can walk 3 + 1 = 4 blocks to reach the museum.

Hence the museum is at a distance of 3 blocks to the west and 4 blocks to the north.

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Answer:

$2,738.89/per month

Step-by-step explanation:

this is a loan shark.  15% is robbery.

The Add on Method is an alternative method of paying interest after it is added onto the principal at maturity. In this method, the interest on the loan is calculated annually and multiplied by the number of years left for repayment.

Calculate the annual interest: Multiply the interest rate by the amount you originally borrowed: 15% x $68,000 = $10,200.

Calculate the add-on interest amount: Multiply the annual interest amount by the number of years in the loan: $10,200 x 3 years = $30,600.

so total she'll have to pay over 3 years = 98600

98600/36 months = 2738.89/per month

Since line segment SP is a diameter, the measure of arc PTS is 180 degrees. 180 - 42 = 138 degrees, which is the measure of arc PT. 97 + 42 + 138 = 277 degrees for the measure of arc PTR

The vertex form of the quadratic equation is:

f(x) = 3*(x - 1)² + 12

Remember that for a quadratic equation whose vertex is at (h, k) and the leading coefficient is a, we can write it in the vertex form as:

y = a*(x - h)² + k

Here we have:

f(x) = (3x-9)(x+1)

We can rewrite that as:

f(x) = (3x - 3*3)(x+1)

f(x) = 3(x - 3)*(x + 1)

Thus the leading coefficient is 3.

The x-value of the vertex is the midpoint the two x-intercepts x = 3 and x = -1, then:

h = (3 - 1)/2

h = 2/2

h = 1

And to get the y-value, we need to evaluate in x = 1.

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

f(2) = 3*-2*2 = -12

So the vertex is (1, 12), then the vertex form is:

f(x) = 3*(x - 1)² + 12

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Therefore, the expression 6r² + 31r + 18 factors completely into (3r + 2)(2r + 9).

In mathematics, factoring is the process of finding the factors or divisors of a given number or algebraic expression. When we factor a number or expression, we find the numbers or expressions that can be multiplied together to obtain the original number or expression. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, since these numbers can be multiplied together in different combinations to obtain 12. Factoring is an important skill in algebra, as it helps us to simplify algebraic expressions and solve equations.

Here,

To factor the quadratic expression completely, we need to find two binomials whose product is equal to the given expression. We can start by looking for two numbers whose product is 6 x 18 = 108 and whose sum is 31. After some trial and error, we find that the numbers are 6 and 18.

We can now write the expression as:

=6r² + 31r + 18

18*6=108

27*4=108

27+4=31

= 6r² + 27r + 4r + 18

= 3r(2r + 9) + 2(2r + 9)

= (3r + 2)(2r + 9)

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The slope-intercept form of (y - 4) = 3(x - 5) is expressed as:

y = 3x - 11

The slope-intercept form is expressed as y = mx + b, where we have the variables:

m as the slope

b as the y-intercept.

Given the equation in point-slope form as (y - 4) = 3(x - 5), we can convert as follows:

(y - 4) = 3(x - 5)

y - 4 = 3x - 15

y - 4 + 4 = 3x - 15 + 4

y = 3x - 11

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Step-by-step explanation:

Use a compounding formula like this:

    P (t) = 280 000 (1 + .0725) ^t    

                                      t is years    .0725 is  7.25%  in decimal form

P (12) = 280 000 ( 1.0725)^12 = 648,523 population

Answer:

dont know either

Step-by-step explanation:

dont know either

Answer:

44 butterfly stamps

Step-by-step explanation:

1/8=2/16

2/16+3/16=5/16

16/16-5/16=11/16

64÷16=4

4×11=44

44/64

The probability that all three murders were committed with a gun is: 0.252.

The probability that one murder was committed with a gun is:

P(Gun) = (6368 + 364 + 200 + 3326)/13927 = 0.632

Therefore, the probability that all three murders were committed with a gun is:

P(3 Guns) = P(Gun) * P(Gun) * P(Gun) = [tex]0.632^3[/tex] = 0.252

The probability that a murder was committed with a handgun given that a gun was used is:

P(Handgun | Gun) = P(Handgun and Gun) / P(Gun)

We need to find P(Handgun and Gun). From the table, we see that 6368 murders were committed with a handgun and 6368 + 364 + 200 = 6932 murders were committed with a gun. Therefore:

P(Handgun and Gun) = 6368/13927

And:

P(Handgun | Gun) = (6368/13927) / (6368 + 364 + 200 + 3326)/13927 = 0.542

The probability that two murders involved a gun and two involved a cutting instrument is:

P(2 Guns and 2 Cutting instruments) = (C(4,2) * C(6932,2) * C(1476,2)) / C(13927,4)

Where C(n,r) is the number of combinations of n things taken r at a time.

Thus, calculating this gives: P(2 Guns and 2 Cutting instruments) = 0.150

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The ratio of the sand is 3:7 and it can be write as 6:14 or 7:21 ... They means the same thing.

Now we know that we have 56 bags of sand, the left side of the number should be 56. Like this:

? : 56

Since we know that 3:7 can be write as 6:14 or 7:21 ... we can even write it as 24:56, it's still 3:7.

According to the concept of compound interest, the effective annual yield on your investment of $1800 at a 6.3% interest rate compounded daily is 6.49%.

To find the effective annual yield, we need to use the formula for compound interest:

A = P(1 + r/n)ⁿˣ

Where A is the amount of money at the end of the investment period, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

In this case, we know that the principal amount P is $1800, the annual interest rate r is 6.3%, and the interest is compounded daily, which means that n is 365 (the number of days in a year). We need to find the effective annual yield, which is the total amount of interest earned in one year.

To calculate the effective annual yield, we can use the following formula:

Effective Annual Yield = (1 + r/n)ⁿ - 1

Plugging in the values, we get:

Effective Annual Yield = (1 + 0.063/365)³⁶⁵ - 1

Effective Annual Yield = 0.0649 or 6.49%

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The value of x in the equation is B) None of these.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is 36x+31=535

Now substitute x=1 then,

=> 36(1)+31=535

=> 36+31=535

=> 67 ≠ 535

Now substitute x = 12 then

=> 36(12)+31=535

=> 432+31 = 535

=> 463 ≠ 535

Now substitute x= 17 then

=> 36(17)+31=535

=> 612+31 = 535

=> 643 ≠ 535.

Hence the correct option is B) None of these.

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Answer:

h ≥ -14

Step-by-step explanation:

-1h ≤ 14

h ≥ -14

So, the answer is h ≥ -14

The rectangular distribution f(x) = 1/(b-a) for a ≤ x ≤ b is a valid probability density function.

In mathematics and statistics, a distribution refers to the pattern of values or frequencies of a variable within a set of data. It describes the spread and behavior of data and can be represented by graphs, tables, or mathematical functions.

The rectangular distribution is a continuous probability distribution where the probability density function (PDF) is constant over a certain interval and zero elsewhere. In this case, we have a rectangular distribution with parameters a and b, where a is the lower bound of the interval and b is the upper bound of the interval.

The probability density function (PDF) of this rectangular distribution is given by:

f(x) = 1/(b-a) for a ≤ x ≤ b

and f(x) = 0 elsewhere.

To verify that this function is a valid probability density function, we need to check two conditions:

The first condition is satisfied because f(x) is always positive on the interval [a, b]. The second condition is satisfied because the area under the curve of f(x) from a to b is equal to:

[tex]\int\limits^a_b f(x) dx = \int\limits^a_b (1/(b-a)) dx = [x/(b-a)]_b^a= (b-a)/(b-a) = 1[/tex]

Therefore, the rectangular distribution f(x) = 1/(b-a) for a ≤ x ≤ b is a valid probability density function.

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When be graph the functions given, we find that option A is correct.

What is meant by to graph a function?

To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point. Keep plugging in x-values to get coordinates to plot more points on the graph, and then you will see your graphed function once the dots are connected.

Using the graph,

For x < = -2, y = 5.

For -2 < x < 1, the function is a polynomial.

We have two options, either y = x² - 5 or y = x² + 5

The polynomial must have the point (0,-5) on it.

For y = x² - 5 , when x = 0, y = -5.

Hence, it is the correct option.

For x >= 1,

Using graph, we see that when y = 0, x lies between 3 and 4.

For equation, y = 2⁽ˣ⁻²) - 2 , when y = 0, x = 3, so it is not correct.

For equation, y = 2⁽ˣ⁻²) - 3 , when y = 0, x = 3.584, hence it is correct.

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for the first one 225÷5=45. For the second one to do 363÷5 you have to decrease 363 to the closest number divisible by 5 and that number is 360 so 360÷5=72 then for the remaining 3 instead of doing 3÷5 you can do 30÷5 then bring the decimal point 1 digit forward so 30÷5=6 then when you bring the decimal point forward its 0.6 then add both and its 72.6. for the third one its the same thing so 372÷3=124 but since you cant do 10÷3 you have to use fractions so 1÷3 means 1/3 then add both of them together and its 124 1/3

The probability that an American will disapprove or have no opinion on the issue is 13%.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used to describe random phenomena, such as the roll of a dice, the flip of a coin, the occurrence of an earthquake, or the outcome of a hand of poker. It is also used to describe the likelihood of certain events happening based on past data or current conditions.

This can be calculated by subtracting the reported approval rate of 87% from 100%. This means that 13% of Americans disapprove or have no opinion on the issue of human embryonic stem cell research.

It is important to note that this survey's data only pertains to the opinions of Americans and not to any other group of people. Therefore, the probability that any individual randomly selected from the global population will disapprove or have no opinion on the issue may be different.

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Answer:

  500

Step-by-step explanation:

You want to know the total number of plantings if 190 trees comprise 38% of them.

The given relationship can be written as the equation ...

  190 = 0.38 × total

  total = 190/0.38 = 500 . . . . . . . divide by the coefficient of 'total'

There are 500 plantings in the garden.

Yes, the shape can be cut into 3 congruent parts but not 4. This is a whole number division problem. See the attached shape for how to divide the figure into 3 congruent parts.

In mathematics, when two numbers are divided without remainders, it is known as integer division or whole number division.

This specific kind of calculation comes in handy when you desire to find out just the quotient or how many times one number divides into another, disregarding any leftover fraction.

For instance, if we utilize integer division to calculate what happens when ten is divided by two; we're left with five as our answer since two divides equally into ten precisely five times without remaining any leftovers.

Conversely speaking though and in regards to regular arithmetic calculations; dividing ten by three amounts up to three with a remainder value attached since three cannot do so equally.

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a) Assuming no withdrawals are made, the future value in Kareem's account after 3 years is $1,768.74.

b) After 3 years, the interest earned on Kareem's investment is $68.74.

The future value and the interest are determined by the investment (present value) and the interest rate, including the compounding periods.

The future value of a present-value investment can be determined using an online finance calculator, including the total interest earned on the investment.

N (# of periods) = 3 years

I/Y (Interest per year) = 1.33%

PV (Present Value) = $1,700

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $1,768.74

Total Interest = $68.74

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The students that are correct in their approach to solving the problem are Nico, Raj and Sandra.

It should be noted that we can start by simplifying the left side of the equation by distributing the two-fifths:

(2/5)(5) + (2/5)x = 8

2 + (2/5)x = 8

Next, the next thing is that we can isolate the variable term on one side of the equation by subtracting 2 from both sides:

(2/5)x = 6

x = 6 / (2/5)

x = 6 * (5/2)

x = 15

Therefore, the solution to the equation is x = 15.

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Sasha buys 5 boxes crackers for 12.25 if each box cost the same amount  one box of crackers costs $2.45.

To find the cost of one box of crackers, we can use the concept of unit rate, which is the cost per one unit. In this case, we want to find the cost per one box of crackers.

If Sasha bought 5 boxes of crackers for a total of $12.25, we can set up a proportion to find the cost of one box of crackers:

5 boxes / $12.25 = 1 box / x

Here, "x" represents the cost of one box of crackers. We can solve for "x" by cross-multiplying the proportion:

5 boxes * x = $12.25 * 1 box

5x = $12.25

x = $12.25 / 5

x = $2.45

To check our answer, we can multiply the cost of one box by the number of boxes Sasha bought:

$2.45 * 5 boxes = $12.25

This confirms that our answer is correct.

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Complete question is:

Sasha buys 5 boxes crackers for 12.25, if each box cost the same amount, then how much does 1 box of the crackers cost?

The formula for how far the rocket travels in t seconds is d(t) = 8,000t.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Making distance the subject of formula, we have:

Distance, d(t) = speed × time

Distance, d(t) = 8,000 × t

Distance, d(t) = 8,000t

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Answer:

Your answer is 90% of 60 = 54.

a. It should be noted that about 10.56% of pregnancies last more than 267 days.

b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.

c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.

d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.

In this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:

z = (239 - 257) / 8 = -2.25

To the left of 239, there is:

P(X < 239) = P(Z < -2.25) = 0.0122

This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.

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a. It should be noted that about 10.56% of pregnancies last more than 267 days.

b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.

c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.

d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.

In this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:

z = (239 - 257) / 8 = -2.25

To the left of 239, there is:

P(X < 239) = P(Z < -2.25) = 0.0122

This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.

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Answer:  B, C, B

Step-by-step explanation:

see images for explanation

Answer:

[tex]\textsf{11)} \quad \text{b.}\;\;2\frac{3}{4}[/tex]

[tex]\textsf{12)} \quad \text{c.}\;\;7\frac{1}{2}[/tex]

[tex]\textsf{13)} \quad \text{b.}\;\;\dfrac{2}{3}x+4=10[/tex]

Step-by-step explanation:

To find the answer to the given equation when y = 4, substitute y = 4 into the equation:

[tex]\begin{aligned} y=4 \implies \dfrac{3}{4}+\dfrac{2(4)}{4}&= \dfrac{3}{4}+\dfrac{8}{4}\\\\&= \dfrac{3}{4}+2\\\\&= 2\frac{3}{4}\end{aligned}[/tex]

Therefore, the answer is 2³/₄.

[tex]\hrulefill[/tex]

To find the answer to the given equation when y = 8, substitute y = 8 into the equation:

[tex]\begin{aligned}y=8 \implies \dfrac{12}{8}+\dfrac{3(8)}{4}&= \dfrac{12}{8}+\dfrac{24}{4}\\\\&= \dfrac{12}{8}+6\\\\&= \dfrac{8+4}{8}+6\\\\&= \dfrac{8}{8}+\dfrac{4}{8}+6\\\\&= 1+\dfrac{1}{2}+6\\\\&=7\frac{1}{2}\end{aligned}[/tex]

Therefore, the answer is 7¹/₂.

[tex]\hrulefill[/tex]

To determine which equation is true if x = 9, substitute x = 9 into each equation.

[tex]\begin{aligned} \text{a)} \quad \dfrac{2}{3}(9)-6&=12\\\\\dfrac{18}{3}-6&=12\\\\6-6&=12\\\\0&=12\end{aligned}[/tex]

[tex]\begin{aligned} \text{b)} \quad \dfrac{2}{3}(9)+4&=10\\\\\dfrac{18}{3}+4&=10\\\\6+4&=10\\\\10&=10\end{aligned}[/tex]

[tex]\begin{aligned} \text{c)} \quad 3(9)-12&=21\\27-12&=21\\15&=21\end{aligned}[/tex]

[tex]\begin{aligned} \text{d)} \quad 3(9)+12&=19\\27+12&=19\\39&=19\end{aligned}[/tex]

Therefore, the only equation that holds true is option b.