A group of friends wants to go to the amusement park. They have no more than $85 to spend on parking and admission. Parking is $9.75, and tickets cost $10.75 per person, including tax. Use the drop-down menu below to write an inequality representing pp, the number of people who can go to the amusement park.

(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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The values of a and b for the exponential function are given as follows:

The standard definition of an exponential is given as follows:

y = ab^x.

In which the meaning of the parameters a and b is given as follows:

The function passes through the points (0,10000), hence the value of the parameter a is given as follows:

a = 10000.

The function also passes through the point (3,3430), hence the value of the parameter b is obtained as follows:

10000b³ = 3430

b = cubic root of (3430/10000)

b = (3430/10000)^1/3

b = 0.1143.

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The amount which Cassie will pay the studio per month will be $115.

The equation by taking data from the question will be

6m - 40 = 650

6m−40=650

On solving this we get ,

6m = 610

m = 115

The regular cost per month is $115.

The above question is an example of multi-step equation.

Multi-step equations are algebraic expressions that must be solved using more than one operation, such as subtraction, addition, multiplication, division, or exponentiation. When solving multi-step equations, it is critical to understand the order of operations.

Solve an equation with a single unknown variable, x, by using algebraic operations on both sides of the equation to isolate x. The goal is to select an algebraic operation sequence that will leave x on one side of the equal sign and put everything else on the other side.

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The probability of not pulling hip hop CDs is equal to 3/5. The correct option is (A).

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

Given that,

The number of country, rock, hip hop, and jazz CDs are 10, 5, 12 and 3 respectively.

Then, the total number of CDs are 10 + 5 + 12 + 3 = 30

Now, the probability of not selecting hip hop is equal to the probability of selecting the remaining types of CDs which is given as,

P(Not hip hop CDs) = (10 + 5 + 3)/30    

                                 = 18/30

                                 = 3/5

Hence, the probability that the first CD that Kyle pulls from the box will not be hip hop is 3/5.

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A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.

A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.

x= -2, x=7

Given,

P(x) = 0

This polynomial function has the roots,

x= -2, x=7

So,

(x+2)(x-7)

We have to multiply both of them we get,

P(x)=(x+2)(x-7)

0=x²-5x-14

x²-5x-14=0

Therefore, P(x)=x²-5x-14 is the polynomial function.

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Answer:

-65

Step-by-step explanation:

Substitute: g (1) =_50-15

Calculate the sum or difference:

Answer=-65

the height of the flag pole should be 108 inches.

Length is 4 ft and  width is is 3ft.

What is width ?

The "size" of a body is measured in geometry by its mean width; for more information on the various body measures, see Hadwiger's theorem. One must take into account -dimensional hyperplanes parallel to a specific direction in where is the n-sphere.

[tex]\begin{aligned}& w^2+(w+1)^2=5^2 \\& \frac{w^2+w^2+2 w+1}{}=25 \\& 2 w^2+2 w-21\end{aligned}[/tex]

[tex]\begin{aligned}& 2 w^2+2 w-24=0 \\& w^2+w-12=0\end{aligned}[/tex]

[tex]\begin{gathered}(w-3)(w+4)=0 \\w=3,-4\end{gathered}[/tex]

The width must be three because we can't have negative widths. Since the length is four feet, we have the dimensions of our poster.

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There will be 66 wolves there will be in 5 years according to given exponential function.

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main body:

given =  y=y₀ e^{0.027 t}

here , y₀ = 58

t = 5 years

y = 58 e^(0.027 * 5)

y = 58 e^(0.135)

y = 58 * 1.144537

y = 66.383133

y = 66

Hence there will be 66 wolves there will be in 5 years.

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Step-by-step explanation:

44r + 43g = 217

45r + 18g = 144

r = a pound of raspeberries

g = a pound of grapes

Answer:

35 cm²

Step-by-step explanation:

Base of triangle = 10 cm

Height of triangle = 7 cm

Area of triangle = 1/2 x (base x height)

= 1/2 x (10 x 7)

= 1/2 x 70

= 35

So, area is 35 cm²

Answer:

7/8

Step-by-step explanation:

First, we need to get 7/8 and 5/6 to the same denominator which is 48. 7/8 becomes 42/48 whilst 5/6 becomes 40/48

we can simply put them both with the same denominator and check, the larger numerator will be it.

so hmmm let's multiply one by the denominator of the other

[tex]\cfrac{7}{8}\hspace{5em}\cfrac{5}{6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}\cdot \cfrac{6}{6}\implies \cfrac{42}{48}\hspace{5em}\cfrac{5}{6}\cdot \cfrac{8}{8}\implies \cfrac{40}{48}\hspace{9em}\boxed{\cfrac{42}{48} ~~ {\Large \begin{array}{llll} > \end{array}}~~ \cfrac{40}{48}}[/tex]

Answer:

Error: 131π

Surface Area = 131π=411.5 yd^2

Step-by-step explanation:

All the other steps were correct but 131π = 411.5486376, so there's no way the person should have gotten 411.3 yd^3.

Finally, if we round 411.5486376 to the nearest tenth, we get 411.5 yd^2.

Using the distance formula, [tex]AP=\sqrt{(-1-2)^2+(-1-7)^2} \approx \boxed{8.54}[/tex]

Answer: The coefficient of the term with the power of 3 is (D. 1)

Step-by-step explanation:

The power of 3 is x^3. When there's no number besides x, we can think of it as an imaginary 1. So, therefore, it's D-1.

The equation of line r, in slope-intercept form, is: y = -1/9x - 9.

The equation that represents a line, in slope-intercept form, is expressed or written as:

y = mx + b, where the slope is m, and the y-intercept is b.

The slope of line q, with the equation y + 7 = 9(x + 4) is 9. The negative reciprocal of 9 is -1/9. This means line r that is perpendicular to line q and passes through (9, -10) has a slope, m = -1/9.

To write the equation of the line in slope-intercept form, first, substitute m = -1/9 and (a, b) = (9, -10) into y - b = m(x - a):

y - (-10) = -1/9(x - 9)

y + 10 = -1/9(x - 9)

Rewrite in slope-intercept form:

y + 10 = -1/9x + 1

y = -1/9x + 1 - 10

y = -1/9x - 9

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The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.

What is power?

The power (or exponent) of a number says how many times to use the number in multiplication. It is written as a small number to the right and above the base number.

The expression 7 raised to the negative second power times 7 raised to the third power is equivalent to 7 raised to the (negative second + third) power, which is 7 raised to the first power. This is equal to 7.

The quantity 7 raised to the first power all raised to the negative third power is equal to 7 raised to the (first + negative third) power, which is 7 raised to the negative second power.

Therefore, the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power all raised to the negative third power is 7 raised to the negative second power, which is 1/7^2 = 1/49.

Hence, The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.

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Answer: 12.5%

Explain:

There are two main ways to express a fraction as a percentage:

-Divide 100 by the numerator, and then multiply both numerator and denominator by the answer.

-Convert the fraction to a decimal first, then multiply the answer by 100.

The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 are (-2.6,5.2).

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.

If a point (x,y) divides the line segment joining the points A(x1,y1) and B (x2,y2) is in the ratio m:n, then

[tex]x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n} \\[/tex]

Here,

m:n = 3:10

The endpoint of line AB are at: A(-4,8) and B(2,-4)

We substitute the given values to obtain:

x= 3*2+10*(-4)/3+10

x= -34/13

x= -2.6

and

y= 3*(-4)+10*(8)/3+10

y= 68/13

y= 5.2

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the initial statement here is

z

∝

x

y

2

to convert to an equation multiply by k the constant

of variation

⇒

z

=

k

x

y

2

to find k use the given condition

z

=

18

when

x

=

6

and

y

=

2

z

=

k

x

y

2

⇒

k

=

y

2

z

x

=

4

×

18

6

=

12

equation is

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

z

=

12

x

y

2

2

2

∣

∣

∣

−−−−−−−−−−−−−

when

x

=

8

and

y

=

9

z

=

12

×

8

81

=

32

27

Answer:

168015

Step-by-step explanation:

b(c) = 2c³5c² - 6c - 13

b(7)=2(7)³5(7)²-6(7)-13

b(7)=2(343)5(7)²-6(7)-13

b(7)=(686) 5(49)-6(7)-13

b(7)=(686) (245)-6(7)-13

b(7)=(686) (245) -42-13

b(7)=168070-42-13

b(7)=168028-13

b(7)=168015

(Usually this is how you would solve it but because there was no sign between the 2c^35c^2 I got sort of confused so I just multiplied, if wrong I'm sorry..)

[tex]b(-7)=-168041[/tex].

[tex]b(c)=2c^{3} 5c^{2} -6c-13[/tex]

[tex]b(-7)=2(-7)^{3} 5(-7)^{2} -6(-7)-13[/tex]

[tex]b(-7)=2(-343) 5(49) -(-42)-13\\ \\b(-7)=-168070 +42-13\\ \\b(-7)=-168041[/tex]

The Mann-Whitney U test is not appropriate for a comparison of two means in a causal comparative study.

To determine if two samples are likely to come from the same population, researchers employ the Mann Whitney U test, also known as the Mann Whitney Wilcoxon Test or the Wilcoxon Rank Sum Test (i.e., that the two populations have the same shape). When a continuous level variable is measured across all observations in two groups and we wish to test if the distribution of this variable differs between the two groups but we are unable to assume normality in both groups, we use the Mann-Whitney test.

Here,

Mann-Whitney test In a causal comparative investigation, comparing two means is not acceptable using the U test.

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Answer:

b!vch I am up b!vch I am up b!vch I am up

[tex]2x^4 - 5x^3 + 6x^2 - 15x \\ \\ =x(2x^3 - 5x^2 + 6x-15) \\ \\ =x(x^2(2x-5)+3(2x-5)) \\ \\ =\boxed{x(2x-5)(x^2+3)}[/tex]

The work that gravity does;

W = F.S = mgΔh

In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.

W = mgΔh

g = 9.8 m/s²

Δh  = 4.6 m

m = 0.60 kg

W = 0.60 x 9.80 x 4.6

W = 2.7 J

The source of gravitational potential energy in relation to the ground is;

U = mgh

The release point therefore

Ug = mgh(0)

U0 = 0.60 x 9.8 x 6.1

U0 = 35.87 J

At the point of release

U(gf) = mgh(f)

U(gf) = 0.60 x 9.80 x 1.5

U(gf) = 8.820 J

Gravitational potential energy changes are;

ΔU(g) = U(gf) - U0

ΔU(g) =  8.820 J - 35.87 J

ΔU(g) = -27.05 J

Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.

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The solution to the equation is x = -1.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

To solve this equation, we need to use the order of operations to simplify the expression on the left side of the equal sign.

The order of operations tells us that we should perform operations within parentheses first, then perform any exponents or radicals, then perform any multiplications or divisions (working from left to right), and finally perform any additions or subtractions (also working from left to right).

Using the order of operations, we can simplify the left side of the equation as follows:

-1 - 7x - 6(-7 - x) = 36

(-1 - 7x) - 6(-7 - x) = 36

-1 - 7x - (-42 - 6x) = 36

-1 - 7x + 42 + 6x = 36

5x + 41 = 36

5x = -5

x = -1

Therefore, the solution to the equation is x = -1.

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Answer: The correct answer would be 71.

step-by-step explanation:

9^2 - 10 =

Calculate the exponents: 9^2 : 81

Then subtract 81 by 10

81 - 10 = 71

Answer:Answer to Solved In how many ways can the digits in the number 7, ... Question: In how many ways can the digits in the number 7, 600,000 be arranged?

1 answer

·

Top answer:

Concept used : The number of permutations (arrang...

Step-by-step explanation:

The series appears to be     166, 199, 232, 265, 298, 331

With examples, define sequence?

A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.

                                      In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.

The last number of the common difference must end in 3

And this must be a 2 digit number

So....the first number must end in 6

The the 4th number must be 265

So..... the 5th number  must end in 8

And the last digit  of the last term must end in  1  [ and begin with 3 ]

Putting all this together  we have that

265  + 2d  =  331

2d  = 66   ⇒  d = 33

So  the first term must be  265 - 3 (66)  =  166

the series appears to be     166, 199, 232, 265, 298, 331

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Since the data in the table represent the height of an object over time, a model which best represents the data is: B. quadratic, because the height increases and then decreases.

In Mathematics, a quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

Additionally, the standard form of a quadratic equation in mathematics is given by the following mathematical expression:

ax² + bx + c = 0

In Mathematics, the graph of all quadratic equations (functions) is either an upward or downward parabola, which is typically a u-shaped curve.

In conclusion, we can logically deduce that the graph of a quadratic equation (function) would always form a parabolic curve with the data value increasing on one end and decreasing on the other end as shown in the image attached below.

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Complete Question:

The data in the table represent the height of an object over time.

Which model best represents the data?

quadratic, because the height of the object increases or decreases with a multiplicative rate of change

quadratic, because the height increases and then decreases

exponential, because the height of the object increases or decreases with a multiplicative rate of change

exponential, because the height increases and then decreases