Identify the factors of x^2 - 4x – 21.

1. (x - 7)(x + 3)

2. (x + 7)(x - 3)

3. (x + 21)(x - 1)

4. (x - 21)(x + 1)

Answer:

D.27

Step-by-step explanation:

This is a question of composite functions.

(fog)(x) = f(g(x)).

We have that:

f(x) = 3x

g(x) = (x+2)²

To find f(g(x)), we replace each x in f(x) by g(x), which is (x+2)². So

f(g(x)) = f((x+2)²)=3(x+2)²

At x = -5

f(g(-5)) = 3(-5+2)² = 3*(-3)²=3*9 = 27

The correct answer is D.27

The probability that at least one of your lights is​ defective is .

The probability of precisely x successes on n repeated trials is known as a binomial probability, and X can only have two possible outcomes.

\(P(X=x)=^nC_rp^x(1-p)^{n-r}\)

Where \(^nC_r\) is the number of different combinations of x objects from a set of n elements and p is the probability.

Now, here 6% lights did not work, so

p=6/100=0.06

n=5

Now, finding the probability that at least one of your lights is​ defective. Either one bulb is defective or no one is defective.

\(P(X=0)+P(x\geq 1)=1\\P(x\geq 1)=1-P(X=0)\)

Now, finding probability of no defective,

\(P(X=0)=^5C_00.06^0(1-0.06)^{5}\\=0.7339\\P(X\geq 1)=1-0.7339\\=0.2661\)

Now, finding the percentage probability,

\(0.2661\times100=26.61\)%

Therefore, the probability that at least one of your lights is​ defective is 26.61%.

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The given question is incomplete here is the complete question:

You purchased a​ five-pack of new light bulbs that were recalled because 6​% of the lights did not work. What is the probability that at least one of your lights is​ defective?.

Answer:

I suck at algebra. your on your own for this one buddy

Answer:

40 minutes

Step-by-step explanation:

I don't think the number of players affect the amount it takes to play the piece. The answer is probably still 40 minutes

40% should be the correct answer! ;D

Please mark brainiest if I'm correct!

Hope this helped!

Answer:

40%

Step-by-step explanation:

40% of 50 shirts would be 20.

To solve you can use 10% of 50, to find 10% of any number simply move the decimal one point to the left. So in this case, 50.0 becomes 5.0. Therefore, 5 is 10% of 50. Then multiply 5 times 4 to get 20. Since 5 is 10% of 50, 20 is four 10% of 50, or simply 40%.

Answer:

distance between -5 to 0 = 5 units

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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Answer:

Step-by-step explanation:This is a standard question which is to be answered according to the definition.If any complex number is written in the form of an ordered pair (a, b), it is written as'z = a + ib.Here, a=3 and b=4Hence, z=3+4i

Answer:

The cost of 7 pens is Rs. 60,  so 2.45

Step-by-step explanation:

find the cost of 7 pens. so 3 divided by 1.05 = 0.35 then multiply by 7 =  2.45 hope this helps can i get brainlyesti tried my best;]

Answer:

the answer is -10 -10+5=-5

Answer and Step-by-step explanation:

We are given the word format of an equation.

Let's right it out in numerical form.

\(\frac{1}{4} (x + 10) = x - 4\)

The first part says One fourth the sum of x and 10

The sum of x and 10 would be shown as x + 10, and one fourth of that means that \(\frac{1}{4}\) is multiplying (x + 10).

In this case, identical would mean equal to.

So, \(\frac{1}{4}\)(x + 10) would be = to something.

It says that it is identical to x minus 4 (x - 4).

\(\frac{1}{4} (x + 10) = x - 4\) is the equation.

#teamtrees #PAW (Plant And Water)

Answer:

\(x < 5\)

Step-by-step explanation:

\(3x + 7 > 4x + 2 \\ 7 - 2 > 4x - 3x \\ 5 > x\)

\(x < 5\)

The total number of different paths which we can have as calculated from the given data is 6.

To know the number of different three-step paths along the edges of a cube are there that take us from vertex a  to vertex b.

For the first path no of different ways = 3

For the second path no of different ways = 2

For the third path no of different ways = 1

Therefore , the total number of ways

= 3 x 2 x 1

= 6

The solid three-dimensional shape also known as a cube has six square faces, eight vertices, and twelve edges. A cube is also known as a hexahedron.

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Answer:

A  The data is proportional and the unit rate per package is $8   This is because y= 8x

Step-by-step explanation:

/y relationship is no of packages = 1                                                                          x/ = total cost to ship = 8    = 8/1  = 16/2 = 24/3 = 32/4 means they are all proportional to 8/1 = 8    y = 8x  see graph attached  

Answer:s=14

Step-by-step explanation:

Based on the given conditions, we can conclude the following:

The number is greater than 40.

The number is not on a red mailbox.

The number has more ones than tens.

Let's analyze these conditions:

The number is greater than 40: This means the number could be any number greater than 40, such as 41, 42, 43, and so on.

The number is not on a red mailbox: This condition implies that the number cannot be associated with a red mailbox, but it doesn't provide any specific information about the number itself.

The number has more ones than tens: This condition suggests that the number must have a greater quantity of ones digits compared to tens digits. For example, 41 has more ones than tens, while 14 does not.

Considering all of these conditions, we can conclude that any number greater than 40 that has more ones than tens and is not associated with a red mailbox would satisfy the given criteria.

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An expression which is equivalent to given \(\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }\) is 5 / (z + 5)

The correct answer is an option (B)

Consider given quotient.

\(\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }\)

Consider expression 5z + 15

We can write this expression as 5(z + 3) by  taking out the common factor 5.

So given quotient would be,

\(\frac{\frac{1}{z+5} }{\frac{z+3}{5(z+3)} }\)

As we know a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.

For fraction \(\frac{z+3}{5(z+3)}\) , the common term is z + 3.

So, \(\frac{z+3}{5(z+3)} = \frac{1}{5}\)

We know that for fractions a/b and c/d where b ≠ 0, d ≠ 0, if we take quotient of these fraction then that would be,

(a/b) / (c/d) = (a/b) × (d/c)

So, given quotient would be,

\(\frac{\frac{1}{z+5} }{\frac{1}{5} }\\\\\\=\frac{1}{z+5} \times \frac{5}{1} \\\\\\=\frac{1\times 5}{(z + 5)\times 1}\)

= 5 / (z + 5)

Therefore, an equivalent expression is: 5 / (z + 5)

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You need a score of 72 out of 100 on exam 2 to perform as well as you did on exam 1.

To determine the score you need on exam 2 to perform as well as you did on exam 1, given the mean and standard deviation for exam 2 and the scores for exam 1, you can use the formula for z-scores.

The formula is :z = (X - μ) / σ,

where X is the score you received on exam 1, μ is the mean score for exam 1, and σ is the standard deviation for exam 1.

To find the score you need on exam 2, you can rearrange the formula as follows: X = z * σ + μ, where z is the z-score you calculated for your score on exam 1.

To calculate the z-score for your score on exam 1, you can use the formula: z = (X - μ) / σ = (87 - 79) / 4 = 2.T

o find the score you need on exam 2 to perform as well as you did on exam 1, you can substitute the values you have into the formula:

X = z * σ + μ = 2 * 6 + 60 = 72.

So, you need a score of 72 out of 100 on exam 2 to perform as well as you did on exam 1.

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Answer:

Why do you need a step by step

Step-by-step explanation:

Answer: A. 300 - 70h = 30

Step-by-step explanation:

Rest of the question is:

Which of these following equations represents the hours, h, the bus has travelled.

The driver is going at 70 kilometers per hour meaning that for every hour that passes, 70km has been traveled. Expression to find the distance travelled given hours is:

= 70h

There are 300km between the two cities and 30km are left in the journey. Expression is therefore:

300 - 70h = 30

This shows that when you find the distance travelled so far and deduct it from 300, you will get 30km.

The equation that can represent the distance for which the bus has travelled is 300-70h=30.

The speed can be defined as the rate of change of position of an object with respect to time. It is given by the formula,

\(\rm{Speed = \dfrac{Distance}{Time}\)

The distance travelled by bus is 270 kilometers (300-30), because the distance left between the bus and Orlando is 30 kilometers. while the speed of the bus is 70 kmph.

Let the time for which the bus travelled be h, therefore, the equation that can represent the hours for which the bus has travelled is,

Total distance - distance covered in h hours = distance left between bus and Orlando

\(300-70h=30\)

Thus, the equation that can represent the distance for which the bus has travelled is 300-70h=30.

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a. A speed of 40 mph is 1.5 standard deviations below the mean.

b. The minimum speed of a driver that will be ticketed is approximately 49.36 mph.

The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.

a) We can use the z-score formula to find out how many standard deviations away from the mean a speed of 40 mph is:

z = (40 - 46) / 4 = -1.5

This means that a speed of 40 mph is 1.5 standard deviations below the mean.

b) To find the minimum speed of a driver that will be ticketed, we need to find the z-score that corresponds to the 80th percentile (since we want to find the speed for the upper 20th percentile):

z = invNorm(0.8) ≈ 0.84

Using the z-score formula again, we can solve for the speed:

z = (x - 46) / 4

0.84 = (x - 46) / 4

x - 46 = 3.36

x ≈ 49.36 mph

Therefore, the minimum speed of a driver that will be ticketed is approximately 49.36 mph.

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Answer:

4176 sq. feet

Step-by-step explanation:

Area of one apartment = 1044 sq feet

If all four apartments are equal in area then total area of such four apartments will be ,

1044 * 4 sq feet

= 4176 sq feet

Hence the required answer is 4176 ft².

Using visual interpretation of the plot trend, the scatter plot shows positive correlation.

A positive correlation is depicted by a positive slope or trend line on a scatter plot. The trend of the scatter plot slopes upward which establishes a positive association.

If the slope is otherwise negative, such that the trend line slopes downward, then we have a negative association or relationship.

Therefore, the scatter plot shows positive relationship.

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To solve this problem, we need to use the concepts of probabilities, distribution, and events.

(a) The probability of all children being of the same sex is the sum of the probabilities of having all boys and having all girls. Each child has a 50% chance of being a boy or a girl, so the probability of having all boys or all girls is (0.5)^5 = 0.03125. Therefore, the probability of all children being of the same sex is 0.03125 + 0.03125 = 0.0625.

(b) The probability of the first 3 children being boys and the last 2 girls is the product of the probabilities of each child being a boy or a girl, in the specified order. The probability of having a boy on the first child is 0.5, the probability of having a boy on the second child is also 0.5, and the probability of having a boy on the third child is also 0.5. The probability of having a girl on the fourth child is 0.5, and the probability of having a girl on the fifth child is also 0.5. Therefore, the probability of the specified event is (0.5)^5 = 0.03125.

(c) The probability of exactly 3 children being boys can be calculated using the binomial distribution. There are 10 possible ways to choose which 3 out of 5 children are boys, and each of these ways has a probability of (0.5)^3 * (1-0.5)^2 = 0.125. Therefore, the probability of exactly 3 children being boys is 10*0.125 = 1.25.

(d) The probability of the first 2 children being girls and the other 3 being boys is the product of the probabilities of each child being a boy or a girl, in the specified order. The probability of having a girl on the first child is 0.5, the probability of having a girl on the second child is also 0.5. The probability of having a boy on the third child is 0.5, and the probability of having a boy on the fourth child is also 0.5. The probability of having a boy on the fifth child is also 0.5. Therefore, the probability of the specified event is (0.5)^5 = 0.03125.

(e) The probability of at least 1 girl can be calculated by subtracting the probability of having all boys from 1. The probability of having all boys is 0.03125, so the probability of having at least 1 girl is 1-0.03125 = 0.96875. In summary, the probabilities of the specified events are: (a) 0.0625 (b) 0.03125 (c) 1.25 (d) 0.03125 (e) 0.96875

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Answer:

220.5

Step-by-step explanation:

I am pretty sure

7 x 5 ÷ 2 = 17.5

12 x 14 = 168

Add them up to get 220.5

Formula of trapezoid:

Base 1 + Base 2 times height times half (basically dividing by 2)

Formula of parallelogram:

height times width

If the mass m of the wrecking ball is 3620 kg, 902 N is the tension TB in the cable that makes an angle of 40∘ with the vertical

70.51kg is the tension TA in the horizontal cable, derived by static equilibrium

According to the static equilibrium condition, the net force on the object in the horizontal and vertical direction must be zero along the moment about any point. If an object follows the above three condition then it can be said into an equilibrium position.

If the mass m of the wrecking ball is 3620 kg, what is the tension TB in the cable that makes an angle of 40∘ with the vertical 902 N.

70.51 kg  is the tension TA in the horizontal cable

Let’s write the conditions of the equilibrium for the wrecking ball:

∑\(F_{x} = 0 ,\) ∑\(F_y = 0\)

Let’s consider the forces that act on the wrecking ball in the horizontal x- and vertical y-direction:

\(T_a - T_b sin\)∅ = 0, (1)

\(T_b cos\)∅ \(- mg = 0. (2)\)

a) We can find the tension \(T_b\) in the cable that makes an angle of 40° with the vertical from the first equation:

\(T_b = \frac{T_a}{sin}\) = \(\frac{580 N}{sin 40} = 902 N\)

b) We can find the mass of the wrecking ball from the second equation:

\(T_b cos\)∅ \(= mg\)

\(m = \frac{T_b cos}{g} = \frac{902 N * cos 40 }{9.8 m/s^2} = 70.51 kg\)

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The sine function of an any angle has a maximum value of 1 and a minimum value of -1.

These values are reached when the angle is at 90 degrees and 270 degrees, respectively. The sine function is periodic, with a period of 360 degrees, and its values repeat every cycle. so it have also same value at 360+θ. where θ is any angle.

When the angle is 0 degrees or 360 degrees, the sine value is 0. The sine function is often used in trigonometry and engineering to describe wave-like behavior, such as alternating current and sound waves.

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Complete question:

What is maximum and minimum value of a sin of an angle?

Answer:

a). 3/4 kg de papa

Step-by-step explanation:

Given that,

Patata colocada en balanza = 1 1/4 Kg

Flor de papa total quiere = 2 kg

Encontrar,

Se agregará más peso en la báscula para que sea de 2 kg =?

Procedimiento:

Peso requerido para ser colocado = Peso total - peso colocado

= 2 - \(1\frac{1}{4}\)

= 2 - 5/4

= (8 - 5)/4

= 3/4 kg

Answer:

3

Step-by-step explanation:

Answer:

-1 + 8 + (-3) = 4

Step-by-step explanation: