The polynomial 10x3 35x2 â’ 4x â’ 14 is factored by grouping. 10x3 35x2 â’ 4x â’ 14 5x2(____) â’ 2(____) What is the common factor that is missing from both sets of parentheses? â’2x â’ 7 2x 7 â’2x2 7 2x2 7.

Answer:

6 is 1/2 of 12

6 is 1/4 of 24

12 × 1/2 = 6

6 × 4 = 24

24

18 is 1/3 of 24

12 is 1/2 of 24

6 is 1/4 of 24

In the given case, where data was collected for a city that indicates that crime increases as median income decreases, and the relationship was moderately strong, an appropriate value for the correlation is the Pearson correlation coefficient. Pearson's correlation coefficient is a measure of the strength of a linear relationship between two variables.

It is a statistical measure that quantifies the degree of association between two variables, in this case, crime and median income. The Pearson correlation coefficient is a number between -1 and 1, where -1 indicates a perfectly negative correlation, 0 indicates no correlation, and 1 indicates a perfectly positive correlation. In the given case, as the relationship was moderately strong, the appropriate value for the correlation would be close to -1.

To find the Pearson correlation coefficient between crime and median income, we use the following formula:

r = (NΣxy - (Σx)(Σy)) / sqrt((NΣx² - (Σx)²)(NΣy² - (Σy)²))

Where,r = Pearson correlation coefficient, N = Number of pairs of scores, x = Scores on the independent variable (Median Income), y = Scores on the dependent variable (Crime), Σ = Sum of the values in parentheses

The correlation coefficient will be between -1 and 1. The closer the value is to -1 or 1, the stronger the correlation. The closer the value is to 0, the weaker the correlation.

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Answer: 28

Step-by-step explanation:

To find the number, we need to use the fact that 4/7 of a number is 84 to set up an equation that we can solve. Since 4/7 of a number is 84, we can write the following equation:

(4/7) * x = 84

To solve this equation, we need to first get rid of the fraction by multiplying both sides of the equation by 7/4:

(4/7) * x * (7/4) = 84 * (7/4)

This gives us the equation:

(4/7) * (7/4) * x = 84 * (7/4)

Since (4/7) * (7/4) = 1, we can simplify the equation as follows:

1 * x = 84 * (7/4)

We can then simplify the right side of the equation by multiplying the numerator and denominator of the fraction by 4:

1 * x = 84 * (7/4) = 84 * (28/28) = 28

Finally, we can solve for x by dividing both sides of the equation by 1:

1 * x / 1 = 28 / 1

This gives us the final equation:

x = 28

Therefore, the number is 28.

Answer:

y=1 (including the algebra itself)

Step-by-step explanation:

Answer:

132.

Step-by-step explanation:

There are a total of 12 entries.

A total of 12 people can be awarded first place. After first place has been awarded, there are 11 people remaining.

\(12*11 = 132.\)

Therefore, there is a total of 132 different ways the prizes can be given.

Answer:

yes

Step-by-step explanation:

Answer:

its 15

Step-by-step explanation:

i took the test and got it right

good luck!!

Answer:

1) There are 100 carbon-14 atoms in the wood when it died

2) A function that models the number 'N' of carbon-14 atoms present in the wood (t) years after it died is  presented as follows;

\(N = 100 \times \left (\dfrac{1}{2} \right )^{\dfrac{t}{5,730} }\)

Step-by-step explanation:

The given parameters are;

The number of carbon-12 for each carbon-14 atom ≈ 10¹² carbon-12 atoms

The number of carbon-12 in the piece of wood = 10¹⁴ carbon-12 atoms

The number of carbon-14 in the piece of wood = 40 carbon-14 atoms

The number of carbon-12 in an organism = Constant

The number of carbon-14 in an organism = Decays

1) Given that the number of carbon-12 in an organism is constant, and there are 10¹² carbon-12 atoms per each carbon-14 atom, therefore, we have;

The number of carbon-12 atoms in the wood when it died = 10¹⁴ carbon-12 atoms

The number of carbon-14 atoms in the wood when it died = (10¹⁴ carbon-12 atoms)/(10¹² carbon-12 atoms/(carbon-14 atom)) = 100 carbon-14 atoms

The number of carbon-14 atoms in the wood when it died = 100 carbon-14 atoms

2) The half life of a radioactive isotope is given by the following formula;

\(N(t) = N_0 \cdot \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{\frac{1}{2} }} }\)

The half life of carbon-14 atoms, \(t_{\frac{1}{2} }\) ≈ 5,730 years

N₀ = The amount of carbon-14 present in the wood when it died = 100 carbon-14 atoms

Therefore, we have;

The number, N, of carbon-14 atoms present in the wood (t) years after it died is given as follows;

\(N = 100 \times \left (\dfrac{1}{2} \right )^{\dfrac{t}{5,730} }\)

Answer:

Step-by-step explanation:

The formula for electrical power, P, is P = I2R , where I is current and R is resistance. The formula for I in terms of P and R is 1 I= P/R 2 3 I=P-R2 2 I= square root of P/R 4 I= square root of P-R.

Answer:

Step-by-step explanation:

(4^2/5)^1/4

first multiply the exponent

2/5*1/4=2/20=1/10

4^1/10= 10√4(the ten is on the top to the square root)

Answer:

Step-by-step explanation:

To increase the difference between 456.674 and 234.458 by 345.856, we follow the following steps :

Step 1: Subtract 456.674 from 234.458 and,

Step 2:  Add 345.856 to the result.

so,  456.674 - 234.458 = 222.216

222.216 + 345.856 = 568.072

Therefore, the increased difference between 456.674 and 234.458 by 345.856 is 568.072

Answer:

4 to the power of 13

Step-by-step explanation:

A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.

A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).

A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria:

Linearity: The graph must shοw a straight line passing thrοugh the οrigin (0,0). This means that as οne variable increases, the οther variable increases in prοpοrtiοn.

Cοnstant ratiο: The slοpe οf the line (i.e., the change in the y-variable divided by the change in the x-variable) must be cοnstant thrοughοut the entire graph.

This cοnstant ratiο represents the prοpοrtiοnality cοnstant between the twο variables.

Hence,  A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.

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The measure of the central angle m ∠JIK is 160°.

Given that the circle I, in which IJ is the radius of 9 units, the area of shaded sector = 36π, we need to find the m ∠JIK, the central angle.

Area of the sector = central angle / 360° × π × radius²

∴ 36π = m ∠JIK / 360° × π × 9²

m ∠JIK = 360° × 4 / 9

m ∠JIK = 160°

Hence, the measure of the central angle m ∠JIK is 160°.

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Answer:

Se vendieron 700 boletos para adultos y 1,150 boletos para niños.

Step-by-step explanation:

Primero tenemos que definir dos variables:

x = número de boletos de niños vendidos

y = número de boletos de adultos vendidos.

Entonces podemos escribir la recaudación total como:

x*$4 + y*$6

Y sabemos que la recaudación total fue $8,800, entonces:

x*$4 + y*$6 = $8,800

También sabemos que se vendieron 1,850 boletos, entonces:

x + y = 1,850

Entonces tenemos el sistema de ecuaciones:

x*$4 + y*$6 = $8,800

x + y = 1,850

En este caso podemos utilizar el método de sustitución, para ello primero debemos aislar una de las variables en una de las ecuaciones.

Si aislamos x en la segunda ecuación tenemos:

x = 1,850 - y

Ahora podemos sustituir esto en la otra ecuación para obtener:

(1,850 - y)*$4 + y*$6 = $8,800

Ahora podemos resolver esto para y.

$7,400 - y*$4 + y*$6 = $8,800

y*$2 = $8,800 - $7,400 = $1,400

y = $1,400/$2 = 700

Entonces se vendieron 700 boletos para adultos.

Ahora podemos usar la ecuación x = 1,850 - y para obtener el valor de x.

x = 1,850 - y

x = 1,850 - 700 = 1,150

Se vendieron 1,150 boletos para niños.

Answer:

6 i think

Step-by-step explanation:

30+6ft=11ft

    -6     -6

   30=5

30/5=6  5/5=1

6=1

Answer:

a and b*

Step-by-step explanation:

it's kinda self explanatory. she isn't very good at communicating with others. she is rude and disrespectful.

Answer:

Step-by-step explanation:

The sum of two irrational numbers is always still irrational.

5√3 + 6√5 is still going to be irrational. You cannot find two such numbers adding to rational.

Answer:

The sum of two rational numbers is always rational

Step-by-step explanation:

The sum of numbers always terminate and ends.

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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The t-shirts she sell is 24.

What is profit and selling price?

Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.

The selling price is the price that the buyer pays to buy a product or goods. This is a price above cost and includes a profit ratio.

According to Question, Christine sold the t- shirts at $4 each and she earned a profit of $71 and his total expenses were $25

Let the total number of t- shirts sold by Christine be "x"

Profit = Selling price – Expenses

Selling price is given as:

selling price = total number to t-shirt sold ×price of each t shirt

selling price = n ×4

71 = (n×4) -24

71 + 25  = n×4

96/4 = n

n = 24

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Answer:

There are 18 choices for first place, 17 for second, and 16 for third.

Therefore, there are 18 x 17 x 16=4896

So there are 4,896 ways possible

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may God bless you:)

The greatest number of flowers Tina can place in each vase is 8.

Given: Total number of roses: 64

Total number of tulips: 72

Each vase hold same number of flowers. To find the greatest number of flowers that can be placed in each vase.

What is highest common factor?

Highest common factor or HCF between two or more numbers is the process of finding the highest number which can divide all the numbers in a given or the highest number by which all the numbers in the given set are divisible.

The highest common factor HCF is also called greatest common divisor or GCD.

Now, let's solve the given question:

Total number of roses = 64

Total number of tulips = 72

Now it is said that each vase should contain the same number of flowers.

So we have to find the highest possible number which can completely divide 64 and 72 with remainder 0. (divisible)

So, to find the greatest possible number than can divide 64 and 72 we need to find the HCF or GCD of 64 and 72.

Therefore, HCF(64, 72) is 8.

The maximum or greatest number of flowers that can be placed in each vase is 8.

Hence the greatest number of flowers Tina can place in each vase is 8.

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Answers:

===============================================

Explanation:

We're told that

cos(B) = 9/41

Since the cosine ratio involves adjacent/hypotenuse, we can see that the adjacent side is 9 and the hypotenuse is 41. For angle B, the adjacent side is the leg closest to the angle in question. So that would be side AB.

Therefore, AB = 9 and BC = 41 are the adjacent and hypotenuse for reference angle B.

Apply the pythagorean theorem to solve 9^2+x^2 = 41^2, and you should get x = 40. This is the other leg of the triangle. Or you could note how tan(C) = 9/40 to imply that AC = 40 is the adjacent side for reference angle C.

Answer:

BCDA is equivalent to FGHE

A is equivalent to angle E

B is equivalent to angle F

C is equivalent to angle G

D is equivalent to angle H

Step-by-step explanation:

1st step is just figuring out which sides corresponds with which.

A is equivalent to angle E

B is equivalent to angle F

C is equivalent to angle G

D is equivalent to angle H

On the last one I am confused by what it is asking, but here is what I think:

The scale factor from the big figure to the small figure is 1.5 because of 15/10=1.5

12/8=1.5 and so on.

When the radius of the cup is 3 cm, the rate of change of the radius is approximately -0.214 cm/sec. This means that the radius is decreasing at a rate of about 0.214 cm/sec.

We can use related rates to find the rate of change of the radius of the cup when the radius is 3cm. Let's begin by finding an equation that relates the height and the radius of the cone.

We know that the cup is a right circular cone, so the formula for the volume of a cone is:

V = (1/3)π\(r^2\)h

where V is the volume, r is the radius, and h is the height.

We are given that the cup is 16 cm deep and has a radius of 4 cm, so we can use these values to find the constant of proportionality in our equation. Plugging these values in, we get:

V = (1/3)π(\(4^2\))(16)

V = 64π

Now we can take the derivative of both sides of the equation with respect to time:

dV/dt = (1/3)π(2r)(dr/dt)h + (1/3)π\(r^2\)(dh/dt)

We are given that water is poured into the cup at a constant rate of 2 cm^3/sec. This means that dV/dt = 2. We are also given that the radius is changing at a certain rate when it is 3 cm, so dr/dt = ? and r = 3. We need to find dh/dt, the rate of change of the height.

We can plug in the values we know and solve for dh/dt:

2 = (1/3)π(2(3))(dr/dt)h + (1/3)π(\(3^2\))(dh/dt)

2 = 2π(3)(dr/dt)h + 3π(dh/dt)

2 = 6π(dr/dt)h + 3π(dh/dt)

2 = 2π(3)(dr/dt)(16/r) + 3π(dh/dt) (substituting h in terms of r using the similar triangles)

2 = 32π(dr/dt)/r + 3π(dh/dt)

2 = 32π(dr/dt)/3 + 3π(dh/dt) (substituting r=3)

Now we can solve for dh/dt:

2 = 32π(dr/dt)/3 + 3π(dh/dt)

2 - 32π(dr/dt)/3 = 3π(dh/dt)

dh/dt = (2 - 32π(dr/dt)/3) / (3π)

Substituting the given values, we get:

dh/dt = (2 - 32π(dr/dt)/3) / (3π)

dh/dt = (2 - 32π(0.2)/3) / (3π) (since the volume of a cone is (1/3)π\(r^2\)h, taking the derivative of this equation gives dh/dt = 0.2(dr/dt))

dh/dt ≈ -0.214 cm/sec

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The term "arc" is used to describe units of measure for angular distance because it refers to the length of an arc on a circle.

Angular distance is the measure of the separation between two points on a circle or an arc. The term "arc" is used to describe this measure because it refers to the length of the arc connecting the two points on the circle.

This length is a fraction of the circumference of the circle and is proportional to the angle between the two points. The use of the term "arc" in this context is a nod to the geometric origins of angular measurement, which is based on the properties of circles and their angles.

The most common units of angular measurement are degrees, minutes, and seconds, which are all based on the division of a circle into 360 equal parts (degrees) and further subdivisions (minutes and seconds).

Other units of angular measurement, such as radians and gradians, are also based on the properties of circles and their angles.

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To find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, we can use the concept of the Poisson distribution and the probability of repairability.

Step 1: Calculate the probability of producing exactly 15 defective components.
Using the Poisson distribution formula, we can plug in the mean (19) and the desired value (15) to calculate this probability:
\(P(X = 15) = (e^(-19) * 19^15) / 15!\)

Step 2: Calculate the probability of 10 out of the 15 defective components being repairable.
Given that each defective component has a probability of 0.62 of being repairable, we can calculate the probability of 10 being repairable out of the 15 defective components using the binomial distribution formula:
\(P(X = 10) = (15 choose 10) * (0.62^10) * (0.38^5)\)

Step 3: Multiply the probabilities from Step 1 and Step 2 to get the desired probability:
\(P(X = 15 and X = 10) = P(X = 15) * P(X = 10)\)

Alternatively, we can directly calculate the probability that 15 defective components are produced and 10 out of the 15 are repairable:
\(P(X = 15 and X = 10) = (e^(-19) * 19^15) / 15! * (15 choose 10) * (0.62^10) * (0.38^5)\)

Note: To obtain the actual numerical value of the probability, you will need to substitute the values into the formulas and perform the calculations.

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a- The probability that exactly 15 defective components are produced is approximately 0.0310.
b- The probability that exactly 10 of the 15 defective components are repairable is approximately 0.1064.
c- The probability that exactly 15 defective components are produced and 10 of them are repairable is approximately 0.0033.

The probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, can be calculated using the Poisson distribution and the given information.

The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space, given the average rate of occurrence. In this case, the average rate of defective components produced by the process is 19.

To calculate the probability, we need to use the formula for the Poisson distribution:

\(\[ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \]\)

where P(X = k) is the probability of exactly k events occurring, λ is the average rate of occurrence, e is the base of the natural logarithm (approximately 2.71828), and k! represents the factorial of k.

First, let's calculate the probability that exactly 15 defective components are produced:

\(\[ P(X = 15) = \frac{e^{-19} \cdot 19^{15}}{15!} \]\)

To simplify the calculation, we can use a calculator or software that can evaluate exponentials and factorials. The result is approximately 0.0310.

Next, let's calculate the probability that exactly 10 of the 15 defective components are repairable. We can use the binomial distribution, since each defective component has a probability of 0.62 of being repairable.

The formula for the binomial distribution is:

\(\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \]\)

where P(X = k) is the probability of exactly k successes, n is the number of trials, p is the probability of success, and (nCk) represents the number of ways to choose k successes from n trials.

In this case, we have n = 15 (the number of defective components) and p = 0.62 (the probability of a defective component being repairable).

\(\[ P(X = 10) = \binom{15}{10} \cdot 0.62^{10} \cdot (1-0.62)^{15-10} \]\)

Again, using a calculator or software to evaluate combinations, exponents, and subtraction, the result is approximately 0.1064.

Finally, to calculate the probability that exactly 15 defective components are produced and 10 of them are repairable, we can multiply the two probabilities together:

P(15 defective components and 10 repairable) = P(X = 15) * P(X = 10)

Multiplying the two probabilities, we get approximately 0.0033.

So, the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, is approximately 0.0033.

Please note that the calculations and results provided are based on the information given in the question.

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}\)

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

\(\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}\)

After using the test statistic z, P(3.6<X<53.5) = 0.967.

In the given question, suppose X is a normal random variable with mean 35 and sdev 10.

We have to find P(3.6<X<53.5).

Fro the given question,

Mean x = 35

sdev s = 10

Z = X - mu / sd

P(3.6<X<53.5) = P ( 3.6-35/10 < Z < 53.5-35/10 )

P(3.6<X<53.5) = P ( -31.4/10 < Z < 18.5/10 )

P(3.6<X<53.5) = P ( -3.14 < Z < 1.85 )

P(3.6<X<53.5) = P ( Z < 1.85) - P ( Z < -3.14)

left tail of both

P(3.6<X<53.5) = 0.9678 - 0.0008

P(3.6<X<53.5) = 0.967

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The right answer is:

Suppose X is a normal random variable with mean 35 and sdev 10. Find P(3.6<X<53.5)