The pair of points (−6, y) and (4, 8) lie on a line with a slope of 5/2. Set up and solve for the missing y-value using the slope formula. Show all work to receive credit.

The number of student like at least one kind of ice cream is given by (d) 275.

Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.

Now given that, n(C) = 145, n(P) = 150

Also given that, 123 students do not like neither chocolate or pistachio ice cream.

So, n(P' and C') = 123

The required number of student like at least one kind of ice cream is given by,

N = 398 - n(P' and C') = 398-123 = 275

Hence the correct option is (d).

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Answer:

Step-by-step explanation:

1. Divide by -2 and thus flip the inequality

2. (n-5.5)<21/-2

3. Add 5.5 to both sides

4. n<-5

5.Check by plugging in any number less than -5 and see if the inequality is true

6. Example: plug in -10

Is -2(-10-5.5)>21?

Yes

31>21 your solution is n<-5

On solving the linear inequality −2(n − 5.5) > 21 for n, we get n < -5.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'.

Given in the question,

-2(n - 5.5) > 21

Solving the inequality,

-2n + 11 > 21

-2n > 21 - 11

-2n > 10

-n > 5

n < -5

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The number of pairs of the parallel lines after the rotation is 2

The transformation is described by

Rotation by 90° counterclockwise about vertex G

There are four types of transformation, and they are:

As a general rule of rotation:

When a shape, line or an angle is rotated, the size of the properties in the rotated figure remains unchanged

Before rotation, a rhombus has two pairs of parallel sides

This means that the parallel sides would remain parallel after rotation

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Answer:

[tex]y_{min}=-17[/tex]

[tex]y_{max}=15[/tex]

Step-by-step explanation:

Given function:

[tex]y=2x^2-12x+1[/tex]

The critical points are those values of x which make the derivative of the function zero.  

Differentiate the function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2 \cdot 2x^{2-1}-12x^{1-0}+0[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=4x-12[/tex]

Set the derivative to zero and solve for x:

[tex]\implies 4x-12=0[/tex]

[tex]\implies 4x=12[/tex]

[tex]\implies x=3[/tex]

To find the y-value of the critical point, substitute the found value of x into the function:

[tex]\implies 2(3)^2-12(3)+1[/tex]

[tex]\implies 2(9)-12(3)+1[/tex]

[tex]\implies 18-36+1[/tex]

[tex]\implies -18+1[/tex]

[tex]\implies -17[/tex]

Therefore, the critical point is (3, -17).

To find the endpoints of the function in the interval [0, 7], substitute x = 0 and x = 7 into the function:

[tex]\begin{aligned} x=0 \implies 2(0)^2-12(0)+1&=0-0+1\\&=1\end{aligned}[/tex]

[tex]\begin{aligned} x=7 \implies 2(7)^2-12(7)+1&=2(49)-12(7)+1\\&=98-84+1\\&=14+1\\&=15\end{aligned}[/tex]

Therefore:

Therefore the minimum y-value is -17 and the maximum y-value is 15 in the given interval [0, 7]

The minimum and maximum y value of the function is -17 and 15 respectively.

This is a basic problem in calculus.

Given function: [tex]y=2x^{2} -12x+1[/tex]

Step 1: First, let's find the derivative of the function

[tex]\frac{dy}{dx} = 2.2x^{2-1} -12x^{1-0} +0\\\frac{dy}{dx} = 4x-12[/tex]

Step 2: Equate the derivative with zero

4x-12=0

x=3

Therefore, x=3 is the critical value for x

Step 3: Find the critical value for y

[tex]y=2x^{2} -12x+1[/tex]

[tex]y=2\times3^{2} -12\times3+1\\y=-17[/tex]

Thus, the critical points for the function [tex]y=2x^{2} -12x+1[/tex] are (3,-17)

Step 4: Find endpoints using the given interval [0,7]

This can be done by substituting x1=0 and x2=7 simultaneously in the given function and finding y1 and y2.

For x1=0,

[tex]y1=2\times0^{2} -12\times0+1\\y1=0+0+1\\y1=1[/tex]

For x2=7,

[tex]y2=2\times7^{2} -12\times7+1\\y2=98-84+1\\y2=15[/tex]

Now, we have both critical points and endpoints.

Therefore, The minimum and maximum y value of the function is -17 and 15 respectively.

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Answer: D

Step-by-step explanation:

a)The probability of exactly 5 accidents will occur is 0.1008.

b) The probability of fewer than 3 accidents will occur is 0.42318.

It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12. Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.

Given,

Mean = 3

a) By using Poission probability formula,

P( X = 5) = e⁺³ (3)⁵/5!

P(X = 5) = 0.1008

The probability of exactly 5 accidents will occur is 0.1008.

b) fewer than 3 accidents will occur:

P( X <3) = e⁻³ (3)⁰ + e⁻³ (3)¹ + e⁻³(3)²

P( X< 3) = 0.4978 + 0.14936 + 0.22404

P( X < 3) = 0.42318

The probability of fewer than 3 accidents will occur is 0.42318.

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GIVEN :

TO FIND :

OPTIONS :

(A) 20 ducks, 15 buffalo

(B) 15 ducks, 20 buffalo

CASE (i) - 20 ducks, 15 buffalo

= 20·2 + 15·4

= 40 + 60

= 100

CASE (ii) - 15 ducks, 20 buffalo

= 15·2 + 20·4

= 30 + 80

= 110

FINAL ANSWER :

Therefore, the number of ducks are 15 and 20 buffalo.

[tex]{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

Answer:

B.

Step-by-step explanation:

The amount to be paid to the broker is 2167.025. Therefore option b is correct.

Percentage:

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, and none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Here we have to find the amount to pay to the broker.

The given values are:

Market rate = 86.681

The commission charges by broker = 2.5%

The broker has to pay = 86.681 × 2.5% × 1000

                                     = 86.681 × 2.5/100 × 1000

                                    = 86681 × 0.025

                                    = 2167.025

Therefore the amount paid to the broker is 2167.025.

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Answer:

B

I got it right

Step-by-step explanation:

If the remainder is paid in equal monthly payments of $250. the number of month that the payments must be made is 24.

First step is to find the remainder after down payment

Remainder  = 6500-500

Remainder  = 6000

Now let find the number of monthly payment

Number of monthly payment = Remainder  / Monthly payment

Number of monthly payment = 6000 / 250

Number of monthly payment = 24

Therefore the monthly payment is 24.

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The answer is 237.55

Define Percentage

A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

Given expression is,

125.8% of £188.83

Rewrite it as,

⇒ 125.8 / 100 * 188.83

⇒ 1.258 * 188.83

⇒ 237.54814

⇒ 237.55 (rounded to 2 Decimal places)

Hence, the answer is 237.55

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Answer:

DEFG = (1/2)a^2

Step-by-step explanation:

tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!

So DFB- (1/2)(DF)(FB)=(1/2)a2

The new function p(x) =  2x³+3x²-23x-12  is the product of expressions x+4, x-3, and 2x+1

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Given: the expressions x+4, x-3, and 2x+1

The product of the expressions  is:

p(x) = (x+4)(x-3)(2x+1)

      = (x²-3x+4x-12)(2x+1)

     =  (x²+x-12)(2x+1)

    = 2x³+2x²-24x+x²+x-12

   =  2x³+3x²-23x-12

Therefore, the new function is p(x) =  2x³+3x²-23x-12.

Since the new function is a polynomial, it demonstrates the Fundamental Theorem of Algebra which states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers

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The distance from the origin to point P graphed on the complex plane is d = [tex]\sqrt{29}[/tex]

Given,

In the question;

From the figure,

To find the distance from the origin to point P graphed on the complex plane .

Now, According to the question:

To see the graph,

The point P lie on the x- axis and y - axis .

x = 2 and y = -5

We know the formula of distance,

Distance (d) = [tex]\sqrt{x^{2} +y^2}[/tex]

d = [tex]\sqrt{2^2 + (-5)^2}[/tex]

d = [tex]\sqrt{4 + 25}[/tex]

d = [tex]\sqrt{29}[/tex]

Hence, The distance from the origin to point P graphed on the complex plane is d = [tex]\sqrt{29}[/tex]

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To simplify the equations so that there would be no fractions, we

1. Multiply both sides by 8

2. Multiply both sides by 12

3. Multiply both sides by 10

4. Multiply both sides by 30

From the question, we are to determine what we could do first to each side of the equations so that there would be no fraction

1. (4x -4)/8 = (x +2)/4

Multiply both sides by the LCM of the denominators

The denominators are 8 and 4

The LCM of 8 and 4 is 8

Thus,

Multiply both sides by 8

8 × (4x -4)/8 = 8 × (x +2)/4

4x -4 = 2(x +2)

2. 3(4 - r)/6 = (4 + r) /4

Multiply both sides by the LCM of the denominators

The denominators are 6 and 4

The LCM of 6 and 4 is 12

Thus,

Multiply both sides by 12

12 × 3(4 - r)/6 = 12 × (4 + r) /4

2 × 3(4 - r) = 3(4 + r)

6(4 - r) = 3(4 + r)

3. (5q + 3)/10 = (q + 2)/5

Multiply both sides by the LCM of the denominators

The denominators are 10 and 5

The LCM of 10 and 5 is 10

Thus,

Multiply both sides by 10

10 × (5q + 3)/10 = 10 × (q + 2)/5

(5q + 3) = 2(q + 2)

4. 4(b - 7)/15 = (b + 3)/10

Multiply both sides by the LCM of the denominators

The denominators are 15 and 10

The LCM of 15 and 10 is 30

Thus,

Multiply both sides by 30

30 × 4(b - 7)/15 = 30 × (b + 3)/10

2 × 4(b - 7) = 3(b + 3)

8(b - 7) = 3(b + 3)

Hence, we will multiply both sides of the equation by 30

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If the soccer team is going to purchase only warm-up pants, then the greatest number of warm-up pants the team can purchase is 42, but if instead the soccer team is going to purchase only duffel bags, then the greatest number of duffel bags the team can purchase is 54.

Inequality, a relationship between two values/expressions that aren't equal to each other, is involved in solving this problem.

The soccer team's got $1,512 to purchase either all warm-up pants or all duffel bags. The cost of the warm-up pants is $36 each and the cost of the duffel bags is $28 each. Since you're asked to find the greatest numbers of each purchase, you'll need to write inequalities to figure out the answer.

The keyword here is "greatest number", so you can use the symbol ≤ for the inequalities. Therefore, 36x ≤ 1,512 is the inequality for finding the greatest number of warm-up pants and 28x ≤ 1,512 is the inequality for finding the greatest number of duffel bags.

The solutions to the first and second inequalities are, consecutively, x ≤ 42 and x ≤ 54, meaning the team can buy at most 42 warm-up pants or 54 duffel bags.

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After simplification, the value of y is 7 when x=9.

In the given question, if y varies inversely as x and y=3 when x=21, find y when x=9.

From the given question y varies inversely as x i.e.

y ∝ 1/x

When we remove the inversly sign then their is one variable should be added. Let the variable should be k.

Now the expression is

y = k/x

As we know that y=3 when x=21.

Now putting the value.

3 = k/21

Multiply by 21 on both side, we get

k = 3*21

k = 63

Now the value of k is 63.

Now finding the value of y when x=9

y = 63/9

y = 7

Hence, the value of y is 7 when x=9.

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Main Answer:

The constant term of h(x) is 4x^3 - 16x^2 - 75x - 63\

Supportive Question and Answer:

What is an Algebraic Expression?

An expression that includes variables, constants, and algebraic operations is an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions.

Solution Explained:
Given,
h(x) = f(x).g(x)

h(x) = (x-7)(2x+3)^2

now, simplify,

(x-7)(2x +3)                                                    Expand the expression
           

(x-7)((2x)^2+2 X 2x X 3+3^2)                        Simplify the expression

(x-7)(2^2 X x^2 +2 X 2x X 3+3^2)                Calculate

(x-7)(4x^2+2 X 2x X 3 + 9)                            Mutiply

(x-7)(4x^2 + 12x + 9)                                       Expand the expression

x X 4x^2 + x X 12x + x X 9 - 7 X 4x^2 - 7 X 12x -7 X 9       Mutiply

4x^3 + 12x^2 + 9x - 28x^2 84x - 7 X 9           Calculate

4x^3 + 12x^2 + 9x - 28x^2 - 84x - 63                    Combine like terms

Hence, the constant term for h(x) is 4x-16x-75x 63.

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The number of different sequences of stops that the driver can make is 24.

Permutation is simply used it illustrate the number of ways for a given information. The formula is illustrated as:

n! / (n – r)!

N is the number of things you are choosing from,

r is the number of items.

“!” is a factorial of a number

Since the delivery truck has 4 stops to make in a neighborhood, the sequences of stops will be:

= n! / (n – r)!

= 4!

= 4 × 3 × 2

= 24 stops.

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The measure of θ from the given trigonometric equation is 31°.

Given that, sin47°=cosθ and sinθ=cos(θ+16).

We know from geometry if the sum of two angles is 90°, then one angle is called the complement of the other.

The complementary angles are:

sinθ=cos(90-θ)

secθ=cosec(90-θ)

tanθ=cot(90-θ)

A) So, sin47°=cos(90°-47°)

⇒ sin47°=cos43°

Thus, θ=43°

B) sinθ=cos(θ+16)

⇒ sinθ=cos(43+16)

⇒ sinθ=cos 59°

⇒ sin(90-31)=cos 59°

Thus, θ=31°

Therefore, the measure of θ from the given trigonometric equation is 31°.

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The initial amount of the deposit is $7234.23

Compound interest is calculated on a deposit's or a loan's initial principal as well as the accrued interest from earlier periods. Compound interest's impact is frequency-dependent. The most frequent compounding occurs with continuously compounded rewards. The mathematical maximum that compound interest can achieve is continuous compounding. Since most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.

For compound continuous problems, we use the formula [tex]A = Pe^{rt}[/tex]

where A = final amount

P = principal amount invested

e = exponent

r = rate of interest

t = time period in years

[tex]12680 = Pe^{.08(7)} \\12680 = Pe^{0.56}\\ 12680 = P*1.7506\\[/tex]

P = $7243.23

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The triangles are congruent by ASA(angle side angle) theorem

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In other words, triangles are congruent when they have exactly the same three sides and exactly the same three angles.

There are different ways to find that out that triangles are congruent.

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Therefore, the triangles are congruent by ASA(angle side angle) theorem.

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Answer:

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

First, compare the negative numbers as they are smaller than positives since negatives are to the left from zero on the number line and positives are to the right.

Since - 15 is smaller than - 6, the least number is - 3:

Now compare the positives.

Therefore:

The complete order is:

Answer:

-3 < -6/5 < 1/6 < √7 < 45

Step-by-step explanation:

Now the values will be,

→ 1/6 = 0.17

→ -3 = -3

→ √7 = 2.65

→ -6/5 = -1.2

→ 45 = 45

Let's arrange in ascending order,

→ -3, -1.2, 0.17, 2.65, 45

→ -3, -6/5, 1/6, √7, 45

Hence, number -3 comes first.

The post-split market capitalization of Walnut Creek Inc. is $12995089.

Given that, Walnut Creek Inc. is going to do a revers stock split with a 3:4 ratio. The current price per share is $234.75 and the current number of outstanding shares is 38,750,000.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, 3+4 = 7

Now, 1/7 × 38,750,000

= 5535714 .29 shares

So, capitalization is 5535714 × 234.75

= $12995089

Therefore, The post-split market capitalization of Walnut Creek Inc. is $12995089.

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Answer: 0.8

Step-by-step explanation:

a. The system of inequalities that best represent how much of the agricultural products of soybeans and corn the river barge can carry is

b. option A

c. The river barge can safely ship the agricultural products

information gotten from the question include

Corn weighs about 60 pounds per bushel

soybeans weigh about 90 pounds per bushel

A river barge can safely carry up to 4,500,000 pounds of cargo.

Let x = bushels of corn and y = bushels of soybeans.

a. From the statement, it can be deduced that the equation is

A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0

b. some interpretation on inequality

from the interpretation

the correct option is A (graph attached)

c. 60 * 24000 + 90 * 24000

= 3,600,000

The value is ≤ 4,500,000 hence the river barge can carry it

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