Mark is a salesman. He earns $12 for every item sold.

Let x = number of items

a. Fill in the inequality symbol for: 12x __________ 2400

b. Solve the inequality to find the number of items he needs to sell if he wants to earn $2400 or more this month. (remember inequality sign must be part of your solution)

Answer:

126x9

Step-by-step explanation:

To find the values of k for which the quadratic expression 5x^2 + kx - 8 factors into two binomials, we can use the factoring method or the quadratic formula. Let's use the factoring method.

Step 1: Write the quadratic expression in the form of (ax^2 + bx + c).

The given quadratic expression is already in the correct form: 5x^2 + kx - 8.

Step 2: Find two numbers that multiply to give ac (product of the coefficient of x^2 and the constant term) and add up to give b (the coefficient of x).

In this case, ac = 5 * -8 = -40.

We need to find two numbers that multiply to -40 and add up to k.

Step 3: List all the possible pairs of numbers that multiply to -40.

The pairs of numbers are (-1, 40), (1, -40), (-2, 20), (2, -20), (-4, 10), (4, -10), (-5, 8), and (5, -8).

Step 4: Determine which pair of numbers adds up to k.

Since the coefficient of x is k, we need to find the pair of numbers that adds up to k.

For example, if k = -4, the pair (-5, 8) adds up to -4.

Step 5: Write the factored form of the quadratic expression.

The factored form of the quadratic expression is obtained by writing the binomials with x and the two numbers found in step 4.

For example, if k = -4, the factored form would be (5x - 8)(x + 1).

To find all the values of k, repeat steps 4 and 5 for each pair of numbers. The values of k will be the sums of the pairs of numbers.

For example, if the pairs are (-5, 8) and (5, -8), the values of k would be -4 and 4.

In summary, the values of k that make the quadratic expression 5x^2 + kx - 8 factor into two binomials are -4 and 4.

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Answer:48

Step-by-step explanation:

The cost of each bolt according to the task content is; 35c.

Since, there were 2500 bolts, it follows that there were 12500 nails.

The total cost of nail is therefore; 12500 × 5c. = 62500c = 625$.

Hence, the total cost of bolts is; 1500$ -625$ = $875 = 87,500c.

Consequently, the cost of each bolt is; 87,500c/2500 = 35c.

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The sum of Peter, Richard, and John's ages is 191.

We know that the ratio of Peter's age to Richard's age is = 5/8 --(i)

The ratio of John's age to Peter's age is = 7/12 --(ii)

Similarly, the ratio of John's age to Richard's age is = (5*7)/(8*12)= 35/96 -(iii)

Using the value of (i),(ii),(iii), we get -

Age of Peter = (5*12)/(8*12) = 60/96

= 60 years of age

Age of John = (7*5)/(12*5) = 35/60

=35 years of age

From the value of (iii), since no one is over 100 years of age, the age of Richard= 96 years of age

Hence the sum of their ages is = 96+35+60

= 191

Therefore, we know that the sum of their ages is 191.

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The number of  subscribers they must  sample to obtain this interval is: b) 385.

How to find the sample?

95% confidence interval for z-score is  1.96

Using this formula to find the number of  subscribers  they must sample to obtain this interval

n≥ (zσ/2 ÷ 2ME)²

Where:

n= Sample

zσ = Z-score

ME = margin of error

Let plug in the formula

n≥ [1.96 / 2(0.05)]²

n≥ [1.96 / 0.1]²

= (19.6)²

= 384.16

=385 (Rounded)

Therefore the correct option is B.

The complete question is:

Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of .05. How many subscribers must they sample to obtain this interval?

a) 1537

b) 385

c) 192

d) 10

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Answer:

5/3 is the slope. slope is the same thing as rate of change

Step-by-step explanation:

Answer:

A = -2

B = -8

Step-by-step explanation:

A system of equations has infinitely many solutions when both equations are exactly the same equation, then both graphs intersect in infinitely many points, meaning that the system has infinitely many solutions.

Then if we have the equations:

A*x- y = 8

2*x + y = B

We want to find A and B such that both equations are exactly the same thing.

Notice that in the first one we have negative y, while in the second we have positive y.

Then A needs to be minus the coefficient that multiplies x in the other equation, this means that:

A = -2

And B needs to be minus the corresponding therm in the other equation, then B = -8.

Then the system becomes:

-2*x - y = 8

2*x + y = -8

We can see that one equation is -1 times the other, so if we write both of them as linear equations in the slope-intercept form, we get:

y = -8 - 2*x

y = -8 - 2*x

So both equations are exactly the same thing, meaning that we have infinitely many solutions.

By using the concept of Permutation and Combination, Counting Principle  Phyllis can make 168 ways to select students.

Permutation and Combination are about making arrangements and making selections on the basis of certain formulas

The re-arranging of any given sorted/ordered set is called a permutation. The “permutation” word actually tells us that change the linear order of the ordered set.

Selecting items from a large collection without taking any care about their order is called combinations.

We need to select one freshman out of 12 freshmen. So selecting r things from n things we can do selection in nr ways, so we can do a selection of freshmen in 12c1 ways

Similarly, we need to select one sophomore out of 14 sophomores, so we can do a selection of sophomores in 14c1 ways

We know that ncr is equivalent to \(\frac{n!}{r!(n-r)!}\)

So, using this concept total number of ways to select a student

= ((12c1)×(14c1))

=12×14

=168 ways

Hence Phyllis can select students in 168 ways

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based on the options given, it looks like -2x+5y would be correct although i am not certain

Answer:

Step-by-step explanation:

so in group 1 out of 12 rolls u landed on 4 four times

in group 2 out of 3 rolls u landed on it 1 time

in group 3 u landed on it 1 time

and in group 4 (i assume) u landed on it 1 time

add the denominators

so  7/35 which simplified is 1/5

An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.

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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.

If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.

Let cost token be x and golf games be y, i.e.

16x + 3y = 30

22x + 5y = 43

Lets Solve by using Elimination method both the expression in equal terms

 80x + 15y = 150

- 66x + 15y = 129

14x = 21

x = 21/14

x = 1.5

Then, for y

16(1.5) + 3y = 30

y = 2

Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

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(a) The number of ways that the event can occur is 6.

(b) Probabilities are :

1) 1/2, 2) 1/6 and 3) 1/3.

(a) Given a bag of different shapes.

Total number of shapes = 6

So, if we select one shape from random,

total number of ways that the event can occur = 6

(b) Number of squares in the bag = 3

Probability of choosing a square = 3/6 = 1/2

Number of circles in the bag = 1

Probability of choosing a circle = 1/6

Number of stars in the bag = 2

Probability of choosing a star = 2/6 = 1/3

Hence the required probabilities are found.

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The probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

given that

In a class of 80 students, the professor calls on 1 at random for a recitation in each class period

there are 32 class periods in a term

the probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

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Perimeter = 2(3 mi + 1 mi) = 8 miles.

A coefficient is a numerical factor that is multiplied by a variable or a term in an algebraic expression. In mathematics, coefficients are commonly used in polynomial functions, where they determine the degree of the polynomial and the specific values of the function.

For example, in the polynomial function \(f(x) = 3x^2 + 2x - 1\), the coefficients are 3, 2, and -1. The coefficient 3 is multiplied by the variable \(x^2\), the coefficient 2 is multiplied by the variable x, and the coefficient -1 is the constant term.

by the question.

If you are referring to a rectangle, then the perimeter would be:

Perimeter = 2(length + width)

Assuming the 3 mi and 1 mi are the length and width respectively, then the perimeter would be:

Perimeter = 1 mile + 1 mile + unknown length of the third side

Perimeter = 2(3 mi + 1 mi) = 8 miles

perimeter = 8 mi.

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Complete question -

Find the perimeter of following -

3 mi. 1l mi.​

Answer:

See explanation

Step-by-step explanation:

Depends on what you round the numbers to, but let's say you round 102.3 to the nearest hundred (100) and 4.7 to the nearest one (5). We can easily solve 100/5 and get the answer 20.

the standard deviation of a sample mean, can be calculated by dividing the population standard deviation, σ, by the square root of the sample size, n.

In statistics, the standard deviation measures the dispersion or variability of a set of data. When calculating the sample mean, from a sample of data, the standard deviation of the sample mean, is a measure of how much the sample means vary from the true population mean.The standard deviation of the sample mean is determined by dividing the population standard deviation, σ, by the square root of the sample size, n. Mathematically, it can be expressed as:

sample mean = σ / √n,Where σ is the population standard deviation and n is the sample size.

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The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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Answer:

1

Step-by-step explanation:

1. First, let's take any two points from the graph. For this case, I'm going to take (3,0) and (0,-3).

2. To find the slope given two points, we have to apply the formula \(\frac{y_2-y_1}{x_2-x_1}\) and plug in the corresponding values:

Therefore, the slope is 1!

Answer:

the slope is 1

Step-by-step explanation:

use the formula m= y2-y1/x2-x1

Answer:

Yes, it will still be 27? So, like 27 + 27 = DBC.

Answer:

54

Step-by-step explanation:

Bisecting means to divide in half

<1  = <2

If <2 = 27 , then <1 = 27

The sum of the angle = 27+27 = 54

If DBC is the original angle, then DBC = 54

a) If you choose to climb in the direction of steepest ascent, the initial rate of ascent relative to the horizontal distance is √(29) units per unit distance.

b) This dot product is positive, you are ascending at a rate of (3√(2)/2) units per unit distance.

c) The vector that is perpendicular to the gradient vector and points in a direction that maintains your altitude.

Now,

a)  You are correct that the initial rate of ascent relative to the horizontal distance is the magnitude of the gradient vector of z at the point (1, 1, 3), which is given by:

grad z = (-2i + 5j)

The magnitude of the gradient vector is the square root of the sum of the squares of its components, which in this case is:

|grad z| = √((-2)^2 + 5^2) = √(29)

b) You are correct that going straight northwest means moving in the direction of the unit vector u = (1/√(2))(-i + j).

To determine whether you are ascending or descending, you need to calculate the dot product of the gradient vector of z and the unit vector u:

grad z · u = (-2i + 5j) · (1/√(2))(-i + j)

               = (-2/√(2)) + (5/√(2))

                = (3√(2)/2)

c) if you want to maintain your altitude, you need to move in a direction that is perpendicular to the gradient vector of z at the point (1, 1, 3). One way to do this is to find the cross product of the gradient vector and a vector that is perpendicular to it.

For example, the vector (-5i - j) is perpendicular to the gradient vector (-2i + 5j), so the cross product of these vectors is:

(-2i + 5j) × (-5i - j) = -27k

You can also find other vectors that are perpendicular to the gradient vector by taking cross products with other vectors that are perpendicular to it.

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Complete question is,

You are standing at the point (1,1,3) on the hill whose equation is given by z = 5y - x^2 - y^2.

(a) If you choose to climb in the direction of steepest ascent, what is your initial rate of ascent relative to the horizontal distance?

The answer for (a) I think is the gradient vector of z. Is this right? If I'm right the answer is grad z = -2i + 3j. Please let me know if I'm wrong.

(b) If you decide to go straight northwest, will you be ascending or descending? At what rate?

So what I think is that north is + x direction and west is - y direction, So I think it is ascending.

The rate is the dot product of grad Z and unit vector of NW, so i think it is \(5/\sqrt{2}\) . Please let me know if I'm wrong.

(c) If you decide to maintain your altitude, in what directions can you go?

Answer:

no

Step-by-step explanation:

5:4=5/4

10:6=10/6

10/6 and 5/4 aren't equivalent

Answer:

Given triangles are similar

Step-by-step explanation:

We can tell that given triangles are similar by comparing their side lengths.

HG is proportional to KJ

GI is proportional to JL

IH is proportional to LK

we can see the proportion better if we write it like this:

25/75 = 1/3

30/90 = 1/3

19/57 = 1/3

Answer:

H0 : The mean difference in strikes between pre and post strike is equal to 0

H1 : The mean difference in strikes between pre and post strike is not equal to 0

Step-by-step explanation:

The scenario described abibe meets the condition for a paired (dependent) sample t test as the same subject is involved in both the pre and post strike data. Therefore measurement from the strike(pre) must be paired with measurement from the strike(post) data.

For a paired test involving a single subject ; The mean difference in the two sample is 0 ; that is both are the same while the alternative negates the null by claiming that the mean difference is not equal to zero.

Answer:

1.00

Step-by-step explanation:

Answer:

Approximately 14.65 kilometers.

Step-by-step explanation:

Please refer to the drawing.

So, to find our distance, we essentially just need to find the value of x.

To do so, we can use the Law of Sines.

Note that ∠a corresponds to the 12km, and ∠c corresponds to x.

So, let's find each of the angles first.

Note that from our ending point, the bearing to the lighthouse is 125°.

This means, if you refer to the drawing:

\(a+b=90\)

This is because they are complementary.

We also know that:

\(90+b=125\)

From our bearing.

So, let's solve for b. Subtract 90 from both sides:

\(b=35\)

Substitute this back into our first equation to acquire:

\(a+35=90\)

Subtract 35 from both sides:

\(a=55\textdegree\)

Now, we can use the fact that the interior angles of a triangle sum to 180 to find c. We already know that one angle is 36 and the other is 55. So:

\(36+55+c=180\)

Add:

\(91+c=180\)

Subtract 91 from both sides:

\(c=89\textdegree\)

Now, we can use the Law of Sines, which states:

\(\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\)

It doesn't really matter which ratio we use as long as we align the sides and angles correctly.

Recall that ∠a correspond to 12km while ∠c corresponds to x.

So, let's substitute 12 for a, 55 for A, x for b, and 89 for B. This yields:

\(\displaystyle \frac{\sin(55)}{12}=\frac{\sin(89)}{x}\)

So, to find the distance traveled, we just have to find x.

Cross-multiply:

\(12\sin(89)=x\sin(55)\)

Divide both sides by sin(55). This yields:

\(\displaystyle x=\frac{12\sin(89)}{\sin(55)}\)

Divide. Use a calculator. Make sure you're in Degrees mode. This gives us:

\(x\approx14.65\)

So, the ship approximately traveled 14.65 kilometers from Point A to Point B.

And we're done!

When the two segments have the equal lengths then they are called congruent segments.

As given in the question,

Let us consider two different segments named AB and CD.

Length of the segment AB is equal to 5 cm __(1)

Length of the segment CD is equal to ( 6 - 1 ) cm.

⇒Length of CD = 5cm __ (2)

Length of segment AB is equal to the length of segment CD.

⇒ measure of (AB ) = measure of (CD)

This implies that the two segment with the same length are called congruent to each other.

Therefore, the segment having equal length are called congruent segments.

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Answer:

x = 3 for the point of intersection of these two lines

Step-by-step explanation:

Please, label these functions:  y = 2x + 3 and y = 4x - 3.

Solve this system by equating the left function to the right one:

2x + 3 = 4x - 3

Combining like terms results in:

6 = 2x

Therefore, x = 3 for the point of intersection of these two lines.