please help!!!
A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $9, and tickets cost $20 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.

All the inequalities that model the given situation are;

x + y ≥ 25

x > 10

y > 0

We are told that;

x represents the number of apples.

y represent the number of oranges.

Now, Mia needs to bring at least 25 pieces of fruit to the school picnic. Thus, the inequality is expressed as;

x + y ≥ 25

She is bringing both apples and oranges, and was told to be sure to bring more than 10 apples. Thus, the inequality is expressed as;

x > 10

Since we are not told the maximum number of oranges, then we can say it must be more than zero and as such we have the third inequality as; y > 0

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The length of AC is equal to 5 units.

Given:

From the figure :

ΔABC is a right angled triangle with sides:

AB = 3 and BC = 4

Right angled triangle:

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

The third side is called the hypotenuse, which is the longest side of all three sides.

we know that,

According to pythagorean theorem:

[tex]AB^2+BC^2 = AC^2[/tex]

3^2 + 4^2 = AC^2

9 + 16 = AC^2

AC^2 = 25

AC = [tex]\sqrt{25}[/tex]

AC = 5 units.

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Full question:

is in the image uploaded

The complete table of values of the linear equation y = -3x - 4 is

x     y

-1     -1

0     -4

1     -7

From the question, we have the following parameters that can be used in our computation:

y = -3x - 4

Also, we have the following table of values

x     y

-1

0

1

The above table of values mean that the x values are

x = -1, 0 and 1

Substitute x = -1, 0 and 1 in the equation y = -3x - 4

So, we have the following representation

When x = -1

y = -3(-1) - 4 = -1

When x = 0

y = -3(0) - 4 = -4

When x = 1

y = -3(1) - 4 = -7

So, we have the following ordered pairs

(-1, -1), (0, -4) and (1, -7)

When represented on the table of values, we have

x     y

-1     -1

0     -4

1     -7

The above represents the complete table of values

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Answer: A

Step-by-step explanation:

18.6 is less than 18.7

so 18.6<18.7

The percentage of the quality cost, that is taken up by the prevention and appraisal costs are:

The prevention cost would be the cost associated with customer service training as this ensures that less mistakes are made.

The appraisal cost would be the cost to verify credit card information.

The percentage of total quality control cost that prevention cost is, would be:

= 379, 600 / 949, 000 total

= 40 %

The percentage for appraisal cost is:

= 189, 800 / 949, 000

= 20 %

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The rest of the question is:

Present the percentage values of prevention and appraisal as a percentage of the quality cost.

Answer:

[tex]\textsf{D.} \quad 5^9=x[/tex]

Step-by-step explanation:

Given logarithmic equation:

[tex]\log_5x-\log_525=7[/tex]

[tex]\textsf{Apply the quotient log law}: \quad log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]

[tex]\implies \log_5\left(\dfrac{x}{25}\right)=7[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 5^7=\dfrac{x}{25}[/tex]

Multiply both sides by 25:

[tex]\implies 25 \cdot 5^7=x[/tex]

Rewrite 5 as 5²:

[tex]\implies 5^2 \cdot 5^7=x[/tex]

[tex]\textsf{Apply exponent rule}: \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 5^{2+7}=x[/tex]

[tex]\implies 5^9=x[/tex]

The number of boats needed for 1491 people are 20.

What is the cross-product?

The cross product, also known as the vector product in mathematics, is a binary operation on two vectors in a Euclidean vector space that is oriented in three dimensions. It is represented by the symbol times.

We have,
134 people decided to go scuba diving,
523 people decided to neither scuba dive nor go on a boat tour,

So, people go to boat tour = 2148 -(134 + 523)
= 2148 - 657
= 1491
now, since each boat holds 78 people.

[tex]\frac{1491}{78} = 19\frac{3}{26}[/tex]

= 20 boats.
Hence, the number of boats needed for 1491 people are 20.

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Complete Question
The 2148 guests at a hotel have the. the choice to either go on a boat tour or go scuba diving.  134 people decided to go scuba diving.  523 people decided to neither scuba dive nor go on a boat tour. Each boat holds 78 people. How many boats are needed? Explain your reasoning.

The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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The year in which Gert will find that she has doubled her money is year 20.

Simple interest is when the interest earned on an investment increases linearly each year.

The formula that can be used to determine simple interest is:

Simple interest = amount invested x duration of the investment x interest rate.

When the amount of money in the account is double what it is now, it means that the interest earned would be $2000 and the value of the account would $4000 (2000 + 2000).

Year when investment would have doubled  = simple interest / (amount invested x interest rate)

Year when investment would have doubled  = $2000 / (0.05 x 2000)

Year when investment would have doubled  = $2000 / 100 = 20 years

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The number of votes that Candidate B received, given the rate and the votes received by Candidate A, is 63 votes

The question shows that for every 5 votes received by Candidate A, Candidate B will receive 7 votes.

This means that if Candidate A has 45 votes, the number of votes that Candidate B would receive can be found to be :

= Number of votes received by Candidate A / Number of votes Candidate A receives per Candidate B x Number of votes  Candidate B receives per Candidate A

= 45 / 5 x 7

= 9 x 7

= 63 votes

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The first part of the question is:

Candidate A receives about 5 votes for every 7 votes received by Candidate B.

[tex] \frac{1}{2} x - 4 < 3 \\ [/tex]

Add both sides 4

[tex] \frac{1}{2} x - 4 + 4 < 3 + 4 \\ [/tex]

[tex] \frac{1}{2} x < 7 \\ [/tex]

Multiply both sides by 2

[tex]2 \times \frac{1}{2} x < 2 \times 7 \\ [/tex]

[tex]x < 14[/tex]

_____________________________________________

[tex]7 \leqslant 3x + 5[/tex]

[tex]3x + 5 \geqslant 7[/tex]

Subtract both sides minus 5

[tex]3x + 5 - 5 \geqslant 7 - 5[/tex]

[tex]3x \geqslant 2[/tex]

Divide both sides by 3

[tex] \frac{3x}{3} \geqslant \frac{2}{3} \\ [/tex]

[tex]x \geqslant \frac{2}{3} \\ [/tex]

Am pula mare!

Da aaaaaaaaaaa????

The difference between their average hiking rates is 0.51 miles/hour.

Given that, it took Lannie 1.9 hours to hike Ranger Cove Trail. It took Ava 4 hours to hike Mohawk Trail.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Using speed =Distance/Time

Here, Ranger Cove distance =4.8 miles and time =1.9 hours

Now, rate =4.2/1.9

= 2.21 miles/hour

Mohawk Trail distance =6.8 miles and time =4 hours

Now, rate =6.8/4

= 1.7 miles/hour

The difference between their average hiking rates

= 2.21-1.7

= 0.51 miles/hour

Hence, the difference between their average hiking rates is 0.51 miles/hour.

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The final amount compounded monthly at a rate of 8% over 6 years on a principal of $5300 is $8551.56

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest as given in the questions is

A = P[(1 + r/n)^nt

Substituting the values into the formula

A = 5300(1 + 0.08/6)^12 * 6

A = 8,551.56

Erica will owe $8551.56

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Exponential decay graph looks like see the given image attached.

The process of diminishing an amount by a constant percentage rate over time is known in mathematics as exponential decay. The quantity drops gradually, followed by a dramatic decline in the rate of change and growth over time.

A linear function reduces the original number by the same amount each time, but exponential decay reduces the original amount by a constant percentage over time. Exponential decay differs from linear decay in this way: the decay factor depends on a percentage of the original quantity.

The exponential decay formula is used to determine this decline in growth.

Formula of exponential decay is given by

Its graph is given by

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The amount of radioactive lead remaining after 4 years, 8 years, and 20 years will be 527.91, 464.48, and 435.69, respectively. And the half-life is 21.66 years.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

An example of 600 g of radioactive lead-210 rots to polonium-210 as per the capability [tex]\rm A(t) = 600 \times e ^{-0.032t}[/tex], where t is time in years.

The amount of radioactive lead remaining after 4 years is given as,

[tex]\rm A(4) = 600 \times e ^{-0.032\times 4}[/tex]

A(4) = 527.91

The amount of radioactive lead remaining after 8 years is given as,

[tex]\rm A(8) = 600 \times e ^{-0.032\times 8}[/tex]

A(8) = 464.48

The amount of radioactive lead remaining after 10 years is given as,

[tex]\rm A(10) = 600 \times e ^{-0.032\times 10}[/tex]

A(10) = 435.69

The half-life is calculated as,

[tex]\rm 300 = 600 \times e ^{-0.032\times t}[/tex]

-0.032t = ln (1/2)

0.032t = -0.693

t = 21.66 years

The amount of radioactive lead remaining after 4 years, 8 years, and 20 years will be 527.91, 464.48, and 435.69, respectively. And the half-life is 21.66 years.

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On solving the given question, we got Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2

A prism is a polyhedron in geometry that has an n-sided polygonal basis, a second base that is a shifted version of the first base, and n additional faces—necessarily all parallelograms. Connect the matching sides of the two bases.

h = 51 cm

a = 2cm

therefore,

volume of a Triangular Prism = (½) abh cubic cm

245.8 = [tex]\frac{1}{2}[/tex] X 2 X b X 51

[tex]= > b = \frac{245.8 X 2}{2 X 51}[/tex]

[tex]= > b = \frac{491.6}{102}[/tex]

[tex]= > b = 4.819[/tex]

Now Area of base of prism

Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2

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The cost of the membership is the initial joining fee plus the cost per month multiplied by the number of months.

If the cost after [tex]m[/tex] months is [tex]c[/tex] dollars, then [tex]c=20m+40[/tex].

How to find a parabola's equation using its Vertex Form

Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)2+k. ...

Step 2: find the value of the coefficient by substituting the coordinates of point P into the equation written in step 1 and solving for a.

Each side of quadrilateral A changed by a factor of 1/4

When quadrilateral A was reduced the size of each angle remain unchanged

The dimensions of quadrilateral A are 16, 10, 6, 20

The dimensions of quadrilateral B are  4, 2.5, 1.5, 5

comparing the two dimensions

Let the factor be r

4r = 16

r = 16/4

r = 4

2.5r = 10

r = 10/2.5

r = 4

1.5r = 6

r = 6/1.5

r = 4

5r = 20

r = 20/5

r = 4

Therefore we can conclude that quadrilateral B was increased by 4, similarly, quadrilateral A was reduced by a factor of 1/4

16 * 1/4 = 4

10 * 1/4 = 2.5

6 * 1/4 = 1.5

20 * 1/4 = 5

since the reduction are similar quadrilateral A is similar to quadrilateral B

and the size of each angle were not affected

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The free fall speed of a parachutist can exceed 216 kilometres per hour. During his 20 seconds of free fall, the parachutist will plunge 1960 metres.

Every time an object is subject to a net force that is greater than zero, acceleration happens. You can experience it when riding down a steep hill on your sled in the snow or when you slightly accelerate or decelerate in an elevator. Furthermore, we know that the universe as a whole is expanding at an even faster rate because to the general theory of relativity. This implies that the distance between two places is always enlarging, yet we are oblivious to this on a daily basis because every scale in the universe also expands.

During free only acceleration due to gravity(g) acts on the parachutist. Assuming acceleration due to gravity is positive i.e. g=9.8m/s² .

For conversion we know that

1 km = 1000 m and

1 hr = 3600 seconds

216 km/hr = 60 m/s

Location of parachutist during 20 seconds

[tex]h = \frac{1}{2} \times g \times t^2[/tex]

[tex]h=\frac{1}{2} \times 9.8 \times 20^2[/tex]

h = 1960 meters

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The ABCD parallelogram turns into a rhombus if all of its sides are equal.

All Sides are equal.

Diagonals bisect at 90°.

In our question,

AB = DC is given for a quadrilateral ABCD (parallelogram).

When a parallelogram's sides are uneven, symmetry is disrupted and its diagonals do not bisect at 90 degrees. However, when all of the sides are equal, the diagonal does bisect at 90 degrees and the parallelogram becomes a rhombus.

Therefore, when all of a parallelogram's sides are equal, it becomes a rhombus.

The complete question is:

You are trying to prove that quadrilateral ABCD is a rhombus. You know that both pairs of opposite sides are parallel (a parallelogram). Which additional fact would prove that ABCD is a rhombus?

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Her son mowed the most lawn

35%of the lawn meeds to be mowed

The fourth term of the polynomial (d - 4b)³ is D. -64d³.

A polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.

Given the expression (d - 4b)³, we need to open the bracket, hence:

(d - 4b)³ = d³ + 3(d²)(-4b) + 3(d)(-4b)²

             = d³ - 12bd² + 48b²d - 64d³

Therefore, the fourth term of (d - 4b)³ is D. -64d³

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Multiply the fraction's bottom numbers with the top numbers in the two fractions.

The two fractions' top numbers should be multiplied, as should the bottom numbers.

Find the fraction of the following two fractions, for instance:

2/3, and 4/5

= 2/3 × 4/5

= (2×4)/(3×5)

= 8/15

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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[tex]72x^{2}+3x+3[/tex]Answer:

Step-by-step explanation:

[tex]1. (4x^{2}+34x^{2} +34x^{2} )+(x+x+x)+3\\ 2. 72x^{2} +3x+3[/tex]

The number that should be multiplied by 2/3 to get a product 1 is 3/2

What is the Reciprocal of two numbers?

One of two numbers that, when multiplied together, equals to 1 is known as a reciprocal or multiplicative inverse.

Transposing the numerator and denominator will allow you to get the reciprocal if you can reduce the number to a fraction.

Let the number that would result in product 1 be "x"

So, According to the question:

=> x × 2/3 = 1

Solving for x,

Dividing by 3/2 both sides

⇒x = 3/2 which is the reciprocal of 2/3

Hence,

The number that should be multiplied is 3/2

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The amount of lavender oil y is proportional to the amount of jojoba oil x

Two quantities are said to be linearly proportionate if change in one quantity produce proportionate amount of change in the other quantity, or the ratio of the two quantities is fixed.

Given,

In the first case, 20 drops of lavender oil and 8 teaspoons of jojoba oil.

In second case, 50 drops of lavender and 20 teaspoons of jojoba oil.

Ratio in first case:

x:y  =  20:8

      = 5:2

Ratio in second case:

x:y  =  50:20

      = 5:2

Since ratio is fixed in both the cases, the amount of lavender oil y is proportional to the amount of jojoba oil x.

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