Help with pre calc question

Answer:

1):  (4d + 1) (3d - 1)

2:  (3x- 4)^2

3:  (6b+ 11w) (6b - 11w)

4.  (3y - 8) (7y + 2)

Step-by-step explanation:

See attached worksheet.

The prοbabilities are,

a) P(X = 5)=0.204 ,  P(X ≤ 5) =0.849 and P(X ≥ 5)= 0.355

b) P(X ≥ 1) = 0.995 ,  P(X ≤ 1)=0.044

c) P(5 ≤ X ≤ 7)= 0.571

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

a) Prοbability οf exactly 5, P(X = 5) then

Using excel binοmial functiοn:

=> BINOM.DIST(5, 9, 0.44, 0)

=> 0.204

Prοbability οf at mοst 5, P(X ≤ 5) then

Using excel binοmial functiοn:

=> BINOM.DIST(5, 9, 0.44, 1

=> 0.849

Prοbability οf at least 5, P(X ≥ 5) = 1 - P(X ≤ 4)

Using excel binοmial functiοn:

=> 1 - BINOM.DIST(4, 9, 0.44, 1)

=> 0.355

b)Prοbability οf at least 1, P(X ≥ 1) = 1 - P(X ≤ 0)

Using excel binοmial functiοn:

=> 1 - BINOM.DIST(0, 9, 0.44, 1)

=>  0.995

Prοbability οf at mοst 1, P(X ≤ 1) =

Using excel binοmial functiοn:

=> BINOM.DIST(1, 9, 0.44, 1)

=> 0.044

c) Prοbability between 5 and 7, P(4 ≤ X ≤ 6) = P(X ≤ 7) - P(X < 5)

=>  P(X ≤ 6) - P(X ≤ 3)

=> BINOM.DIST(6, 9, 0.44, 1) - BINOM.DIST(3, 9, 0.44, 1)

=> 0.571

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Answer:

16 - 25z²

Step-by-step explanation:

(4 - 5z)(4 + 5z)

each term in the second factor is multiplied by each term in the first factor, that is

4(4 + 5z) - 5z(4 + 5z) ← distribute parenthesis

= 16 + 20z - 20z - 25z² ← collect like terms

= 16 - 25z²

Answer:

16-25z

Step-by-step explanation:

you will use the first term 4 to multiply the first which is (4+5z) then after that you will use the second term which is -5z to multiply the same (4+5z) to give you 16+20z-20z-25z then you will also simplify to give you 16-25z

According to the information, the symmetry axis of the 7.3cm bar would be located at 3.65cm. Additionally, the perpendicular bise of the 9.5cm line would be located in 4.75cm

An axis of symmetry is a term that refers to an imaginary reference line that allows any figure to divide in two parts, its opposite points are equidistant to each other, that is, they are symmetrical.

The perpendicular Bise is a term to refer to a straight line perpendicular to a given segment. A characteristic of the perpendicular Bise is that it is located at the midpoint of the segment.

According to the above to find the axis of symmetry and the perpendicular bise we must divide the values into 2 to find its half.

Note: This question is incomplete. Here is the complete information:

Attached image

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Answer:

n ≤ -48

Step-by-step explanation:

The price of each student ticket is $12.50 and the price of each guest ticket is $15.

The substitution method is a technique in algebra for solving systems of equations, which involves solving one equation for one variable, and then substituting that expression into the other equation.

Let's start by assigning variables to represent the unknown prices of the student and guest tickets.

Let:

x be the price of a student ticket

y be the price of a guest ticket

Using this information, we can set up two equations based on the given information:

Equation 1: 10x + 5y = 200 (from the first day's sales)

Equation 2: 6x + 2y = 105 (from the second day's sales)

Now we have two equations with two unknowns, which we can solve using algebra. To do this, we can use a method called substitution, which involves solving one equation for one variable, and then substituting that expression into the other equation. Here's how to do it:

Solve Equation 1 for y:

10x + 5y = 200

5y = 200 - 10x

y = (200 - 10x)/5

y = 40 - 2x

Substitute y into Equation 2:

6x + 2y = 105

6x + 2(40 - 2x) = 105

6x + 80 - 4x = 105

2x = 25

x = 12.50

So the price of a student ticket is $12.50.

To find the price of a guest ticket, we can substitute x = 12.50 into Equation 1:

10x + 5y = 200

10(12.50) + 5y = 200

125 + 5y = 200

5y = 75

y = 15

So the price of a guest ticket is $15.

Therefore, the price of each student ticket is $12.50 and the price of each guest ticket is $15.

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The expressions after factorizing are;

1. (x+4)(x - 6). Option A

2. (x+ 5)(x - 6). Option A

3.  (x - 8)(x - 9). Option A

From the information given, we have the following quadratic equations;

To factorize the expressions, we need to first, multiply the coefficient of x²   by the constant value.

Then, find the pair factors of the product whose sum would give the coefficient of x variable and substitute the values.

For the first expression;

x² - 2x - 24

x² - 6x + 4x - 24

group in pairs

(x² - 6x) + (4x -24)

factorize

x(x - 6) + 4(x - 6): (x+4)(x - 6)

x² - x - 30

x² - 6x + 5x - 30

group in pairs and factorize

x(x - 6) + 5(x - 6): (x+ 5)(x - 6)

x² - 17x + 72

x² - 9x - 8x + 72

Group in pairs and factorize

x(x - 9) - 8(x - 9): (x - 8)(x - 9)

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The answer to this question is that we cannot find qrs without additional information about what q and s represent. We can only make educated guesses based on the context of the problem.

Sure, I'd be happy to help! To find qrs, we need to know what these variables represent. Based on the given information, we know that p=62-5x and r=133, but we don't know what q represents. Therefore, we cannot directly solve for qrs.

However, we can make an educated guess based on the context of the problem. It's possible that q is related to p and r in some way. For example, q could be the sum of p and r, or it could be the product of p and r. Without more information, we can't be sure.

Another possibility is that qrs is actually three separate variables, q, r, and s. In this case, we would need to know what s represents in order to solve for qrs.

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The numeric value of the composite function at x = 1 is given as follows:

(h ∘ k)(1) = 28.

The composite function of f(x) and g(x) is given by the rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, in this example g(x), serves as the input of the outer function, in this case f(x).

Hence the numeric value at x = 1 for the function in this problem is:

h(k(1)).

The numeric value of k at x = 1 is:

k(1) = 3.

Then, as the numeric value of h at x = 3 is of 28, the composite function is:

(h ∘ k)(1) = 28.

The problem is given by the image presented at the end of the answer.

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The volume of the pyramid is found to be approximately 18.046 cubic units.

To find the volume (V) of the pyramid, we need to use the formula for the volume of a pyramid, which is V = (1/3) × Base Area × Height.

In this case, the base is a square, so we can find the area of the base by squaring one of the sides: Base Area = AB² = 4.5² = 20.25.

To find the height of the pyramid, we need to use the Pythagorean theorem to find the slant height, and then use that to find the height. Let h be the height of the pyramid and s be the slant height. We have:

s² = AB² + (1/2) DC² (Pythagorean theorem for triangle ABC)

s² = 4.5² + (1/2) DC²

Since all edges of the pyramid are congruent, we have DC = AB = 4.5. Substituting this into the equation above, we get:

s² = 4.5² + (1/2) × 4.5²

s² = 30.375

s ≈ 5.509

To find the height h, we can use the Pythagorean theorem again for triangle ABD:

h² = AB² - (1/4) s²

h² = 4.5² - (1/4) × 30.375

h² ≈ 7.875

h ≈ 2.807

Now that we have found the base area and the height, we can use the formula for the volume of a pyramid to find V:

V = (1/3) × Base Area × Height

V = (1/3) × 20.25 × 2.807

V ≈ 18.046

Therefore, the volume of the pyramid is approximately 18.046 cubic units.

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The area of the blue region is 28.93 cm²

To find the area of the blue region, we need to subtract the area of the four circle from the area of the rectangle.

Since the diameter of the circle is 3cm. The radius (r) = 3/2 = 1.5 cm.

Length of the rectangle (L) = 4 * diameter of circle (we have 4 circles)

Length of the rectangle = 4 * 3 = 12 cm

Width of the rectangle (W) = diameter of circle = 3 cm

Area of rectangle = L * W

Area of rectangle = 12 * 3 = 36 cm²  

Area of circle = πr²

Area of circle = π * 1.5² = 2.25π cm²  

Area of the blue region = Area of rectangle - Area of circle

Area of the blue region = 36 - 2.25π

Area of the blue region = 36 - (2.25* 22/7)

Area of the blue region = 28.93 cm²

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Complete Question

Check the attached image

If a rectangle door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters, the perimeter of the door in the scale drawing is 70 centimeters.

To find the perimeter of the door in the scale drawing, we first need to determine the dimensions of the door in the scale drawing. To do this, we need to multiply the actual dimensions of the door by the scale factor of 3.5.

The height of the door in the scale drawing would be 7 cm x 3.5 = 24.5 cm, and the width would be 3 cm x 3.5 = 10.5 cm.

The perimeter of the door in the scale drawing can be calculated by adding up the lengths of all four sides. The two vertical sides have a length of 24.5 cm, and the two horizontal sides have a length of 10.5 cm. Therefore, the perimeter of the door in the scale drawing is:

P = 2(24.5 cm) + 2(10.5 cm) = 49 cm + 21 cm = 70 cm

Note that the scale drawing is a proportional representation of the actual door, where all corresponding dimensions are multiplied by the same factor of 3.5.

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Answer:

15

Step-by-step explanation:

The first 15 odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

The formula to find the median of a set of numbers is:

Median = [(n + 1) / 2]th term

where n is the total number of terms in the set.

In this case, we have 15 terms in the set of the first 15 odd numbers. So, substituting n = 15 in the formula, we get:

Median = [(15 + 1) / 2]th term

Median = 8th term

To find the 8th term, we can simply list the first 15 odd numbers in ascending order and count 8 numbers from the beginning of the list. The 8th term is 15.

Therefore, using the formula, we get:

Median = 8th term = 15.

So, the median of the first 15 odd numbers is 15.

Answer:

Step-by-step explanation:

16y-57

Ben should have received $735 in Australian dollars at the given exchange rate.

The value of one currency represented in terms of another is called an exchange rate. It is the cost associated with exchanging one currency for another. The dynamics of supply and demand in the market dictate exchange rates, which are continually changing in response to a variety of political and economic variables including inflation, interest rates, trade balances, and geopolitical events. Currency rates have an impact on the price and profitability of transactions between nations, making them crucial for international commerce and investment. As they govern how much foreign currency can be received for a certain quantity of local currency, they are especially crucial for those who travel or transfer money overseas.

Given that, the exchange rate was £1 = $2.1.

Thus,

£350 * $2.1/£1 = $735

Therefore, Ben should have received $735 in Australian dollars.

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Answer: The acceleration of the bus can be calculated using the formula:

a = (v2 - v1) / t

where:

a = acceleration

v2 = final velocity = 306 m/s

v1 = initial velocity = 126 m/s

t = time = 3 seconds

Substituting the given values into the formula, we get:

a = (306 m/s - 126 m/s) / 3 s

a = 180 m/s / 3 s

a = 60 m/s^2

Therefore, the acceleration of the bus is 60 m/s^2.

Step-by-step explanation:

Answer:

6cm

Step-by-step explanation:

The volume of the cylinder = π · r² · h

r = 4

h = ?

Let's solve

96π = π · 16 · h

96 = 16 · h

h = 6cm

So, the height is 6cm

The missing measures of the pentagon are a = 18.4, c = 61.2, d = 75, and x = 22.08.

Let's label the sides of the first pentagon as a, 20, c, 30, and x, and the sides of the second pentagon as 46, 50, d, 102, and 24.

Since both pentagons have the same shape, we know that the corresponding sides are proportional. This means we can set up the following equations:

a/46 = 20/50 = c/d = 30/102 = x/24

Solving for the missing variables:

a = 46(20)/50 = 18.4

c = 30(102)/50 = 61.2

d = 50(30)/20 = 75

x = 24(46)/50 = 22.08

Therefore, the missing measures are a = 18.4, c = 61.2, d = 75, and x = 22.08.

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The third term of the given sequence is =60.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers

a(1)=20

and

[tex]a_n=a(n-1)*\frac{3}{2}\\\\n=3\\\\a_3=20(2)*\frac{3}{2}\\\\a_3=60[/tex]

The complete question is-

​a(1)=20 a(n)=a(n-1)*3/2 What is the 3rd term in the sequence?

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Answer:

150 isnt a thing but I will gladly take 5 :)

(2x+3)(2x−9)

Step-by-step explanation:

Hope this helps^^

"The multiplier for 0.85% growth is calculated by adding 1 to the percentage as a decimal:

Multiplier for 0.85% growth = 1 + 0.0085 = 1.0085

The multiplier for 300% growth is calculated in the same way:

Multiplier for 300% growth = 1 + 3.00 = 4.00

Therefore, the multipliers for 0.85% and 300% growth are 1.0085 and 4.00, respectively." (ChatGPT, 2023)

The statement that is true regarding the graphed functions is that: B. f(-2) = g(-2).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (2, 0), an equation of the line f(x) can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (-4 - 0)/(-2 - 2)(x - 2)

y = -x + 2

For line g(x), we have:

y - 4 = (-2 - 4)/(0 + 2)(x + 2)

y = -3(x + 2) + 4

y = -3x - 2

When x = 0, we have:

g(0) = 0 + 2 = 2

f(0) = 0 - 2 = -2.

When x = -2, we have:

g(-2) = -(-2) + 2 = 4

f(-2) = -3(-2) - 2 = 4.

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The area of the sector with a central angle of 30 degrees and a radius of 12.5 cm is 40.89 cm².

The area of a sector is expressed as;

A = ( θ/360 ) × π × r²

where θ is the central angle in degrees, r is the radius, and π is approximately 3.14.

Given the data in the question;

Substituting the given values, we get:

Area = ( θ/360 ) × π × r²

Area = (30/360) × 3.14 × 12.5²

Area = 40.885 cm²

Area = 40.89 cm²

Therefore, the measure of the area is 40.89 cm².

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The equation we would use to find the distance between the two points is d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)

To find the distance between two points on a number line or in a coordinate plane, we use the distance formula. The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

None of the options provided represents the distance formula in its entirety. However, we can use option B as the first part of the distance formula, since it represents the absolute value of the difference between the x-coordinates of the two points:

|2 - (-4)|

Simplifying this expression gives:

|2 + 4|

|6|

Therefore, the equation we would use to find the distance between the two points is:

d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)

We still need to determine the y-coordinates of the two points in order to complete the distance formula.

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The given statement "B ∩ C = C ∩ B" is true, since the intersection of two sets is a commutative operation, which means the order in which we list the sets does not matter.

To find the intersection of two sets, we need to identify the elements that are common to both sets. In this case, we can list the elements of each set and identify their common elements:

B = {a, b, c}

C = {a, c, e, g}

B ∩ C = {a, c}

C ∩ B = {a, c}

As we can see, the intersection of B and C is {a, c}, and the intersection of C and B is also {a, c}. The order in which we list the sets does not affect the result of the intersection operation, since the elements of both sets are the same.

Therefore, we can conclude that B ∩ C = C ∩ B is true, and that the intersection of B and C contains the same elements regardless of the order in which we list the sets.

In summary, the intersection of two sets is a commutative operation, which means that the order in which we list the sets does not affect the result. Therefore, B ∩ C = C ∩ B is true, and the intersection of B and C contains the same elements regardless of the order in which we list the sets.

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Complete question is:

If A=(a, e, i, o, u),B=(a, b, c) and C=(a, c, e, g)

Is B ∩ C= C ∩ B true?

It should be noted that the value on the blank on the equation will be -2.

The equation given is:

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

Simplifying the left-hand side:

8x + 2 + 8 = 8x + 4 + 8 - x

Simplifying the right-hand side:

8x + 4 + 8 - _ = 8x + 12 - x

Combining like terms on both sides:

8x + 10 = 8x + 12 - x

Subtracting 8x from both sides:

10 = 12 - x

x = 10 - 12

x = -2

The value will be -2 to make the equations equal.

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According to the means, the average typical daily sales for Farmer's equation Market A are higher than the average typical daily sales for Farmer's Market B.

A mathematical statement which thus proves the equality of two factors linked by an equal sign '=' is known as an equation. For example, 2x - 5 = 13. Two examples of phrases are 2x-5 and 13. The character '=' is used to connect the two expressions. A mathematical formula with two algebraic expressions on either side of a =) (=) is called an equation. It depicts the relationship of equivalence between left and right equations. In any formula, L.H.S. = R.H.S. (left side = right side).

[tex]$30 + $31 + $32 + $33 + $35 + 36 + $38 + $40 + $41 + $42 + $43 + $45 + $47 + $49 + $50 = $575 for Farmer's Market A[/tex]

Because there are 15 days, we divide the total sales by 15 to find the mean:

Farmer's Market A Mean [tex]= $575/15 = $38.33[/tex]

Farmers' Market B:

[tex]$20 + $22 + $24 + $26 + $28 + $31 + $32 + $34 + $36 + $39 + $40 + $42 + $44 + $46 + $49 = $524[/tex]

Farmer's Market A has a mean of $38.33, while Farmer's Market B has a mean of $34.93. According to the means, the average typical daily sales for Farmer's Market A are higher than the average typical daily sales for Farmer's Market B.

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B has a savings account, into which he must deposit $40 each month.

Interest is frequently calculated as an annual percentage of the amount borrowed. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in a high-yield savings account.

From the time he was 11 to the time he was 18, Luke's parents saved for him for 8 years, or 8 years x 12 months every year, or 96 months.

Since they were saving $125 per month throughout this time, Luke had amassed the following sum:

$125/month x 96 months = $12,000

Luke must still pay the following expenses because he needs $12,480 for his first year of technological school:

$12,480 - $12,000 = $480

If he has one year left to save this amount, he will need to save:

$480÷12months = $40per month

Therefore, the answer is B. $40.

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Answer:

c= 3.5 x 20

Step-by-step explanation:

rent $20 hr

Time 3.5 hr

Cost $70

Answer: B

Rate of change is the slope which is the [tex]\frac{rise}{run}[/tex]= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

In the first equation, we will substitute x with any two random numbers to get the y value, which gives us two points. The number you take doesn't matter.

y=2, taking x as 2 so the point is (2,2)

y=1, taking x as 1 so the point is (1,1)

m=[tex]\frac{2-1}{2-1}=1[/tex] SO THE SLOPE FOR A IS 1

In the second equation, we can just pick 2 points on the graph that the line runs through. I picked (2,-1) and (0,-4) to make calculations easy

[tex]m=\frac{-4-(-1)}{0-2}\\ =\frac{-3}{2}\\[/tex]OR THE SLOPE IS -1.5

In the thrid equation, we can again just pick points to find the ROC.

[tex]m=\frac{9-6}{5-4} \\ =3[/tex]THE SLOPE IS 3

Now that we have found this out, we can now find out which one has a bigger ROC.

-1.5<1<3=B<A<C

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