A local charity has put together 20 care packages for
people. Each package contains $15 worth of goodies
and $2.50 per food satchel added to it. If the charity
spent $800 on the care packages how many food
satchels were in each package? Write and solve an
equation for this scenario.

A radioactive substance will have a decay of A ≈ 31.1936 mg after 32 hours.

Radioactive decay (additionally referred to as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the manner with the aid of using which an volatile atomic nucleus loses electricity with the aid of using radiation. A fabric containing volatile nuclei is taken into consideration radioactive.

Every atom seeks to be as strong as possible. In the case of radioactive decay, instability happens whilst there's an imbalance withinside the quantity of protons and neutrons withinside the atomic nucleus. Basically, there's an excessive amount of electricity withinside the nucleus to preserve all of the nucleons together.

Initial Radioactive substance, A₂ = 110 mg Remains substance, A = 55 mg time, t = 22 hours

Here, radioactive substance decay. exponentially.

[tex]a=a_{0}e^{at} \\\\55=110*e^{22k} \\\\\frac{55}{110} = e^{22k} \\\\ \\e^{22k} =\frac{1}{2}[/tex]

Taking lo both side, we get ln (1/2) = lne²²K

ln (1/2) = k*22

[tex]k=\frac{ln(1/2)}{22}[/tex]

K = -0.03150669

Substance remains after 32 hours,

t=32 hr

[tex]A=110*e^{( (-0.03150669))*32} \\A=110*e^{(-1.2602676)} \\\\[/tex]

A = 110x 0.283578131

A = 31.19359441

A ≈ 31.1936 mg

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Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance.

The null hypothesis is accepted.

There is no significant difference between the attractiveness ratings given by the three groups of girls.

Surveyed two random samples of 390 men and 360 women who were tested.

first sample percentage,

p1 = 360 ÷ 390 = 0.9230

second sample percentage,

p2 = 47 ÷ 52 = 0.9030

There is no change, according to the null hypothesis the percentage of males who have positive tests is significantly from the percentage of women who have positive tests.

Different Hypotheses:

There is a discrepancy in the percentage of schoolgirls who heard about a male with stylish clothes, a great automobile, or a confident demeanor across the three groups that were randomly allocated.

Z = (p1 - p2) ÷ √(PQ((1 ÷ n1) + (1 ÷ n2)))

where

p = (n1p1 + n2p2) ÷ n1 + n2

p = 0.920

Z = (0.9230 - 0.9030) ÷ √(0.9230((1 ÷ 390) + (1 ÷ 52)))

Test statistic Z =  0.13008

Level of significance = 0.10

The critical value Z₀.₁₀ = 1.645

Test statistic Z=0.13008 < 1.645 at 0.1 level of significance

The null hypothesis is accepted.

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The number k is equal to 60 when the top right angle at the intersection of the lines y and x is (2 k + 11) degrees and the bottom left angle is 131 degrees.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical expression is a sentence that includes numbers, variables, or both. The equal sign is never used in expressions. A mathematical statement stating the equality of two expressions is known as an equation.

Here,

Those two angles have the same measure. so you have,

2k+11=131

22k=120

k=60

The value of k where at the intersection of lines y and x, the top right angle is (2 k + 11) degrees and at the intersection of lines z and x, the bottom left angle is 131 degrees is 60.

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A function is a relationship between inputs where each input is related to exactly one output.

The function with a decay rate of 5% is

f(x) = 100(0.95)

This is with a decay rate of 5%

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Decay rate = 5%

5% = 5/100 = 0.05

The total rate = 100%

100% = 100/100 = 1

The rate to multiply with the function.

= 1 - 0.05

= 0.95

A)

f(x) = 100(-5)

This is not a decay rate of 5%

B)

f(x) = 105(0.05)

This is with a decay rate of 95%.

C)

f(x) = 100(0.95)

This is with a decay rate of 5%

D)

f(x) = 100(1.05)

This is not a decay rate function.

E)

f(x) = 100(5) ​

This is not a decay rate function.

Thus,

The function with a decay rate of 5% is

f(x) = 100(0.95)

This is with a decay rate of 5%

Option C is the correct answer.

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The probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.

What is the probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Two dice are rolled.

Then the sample space (n) = 36

Possible outcomes = {(6,1), (6, 2), (6, 3), (6, 4)}

Probability = 4/36

                 = 0.11

Hence, the probability of getting the 6 on the first die given that the minimum of two numbers is 4 would be 0.11.

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The correct option is, there is a main effect for Factor A but there is no interaction.

What is two factor anova?

The mean of a quantitative The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the levels of two categorical variables.

Two-way analysis of variance is an extension of one-way analysis of variance in statistics that looks at the impact of two different categorical independent variables on a single continuous dependent variable.

The parallel lines indicates no interaction effect.

For the above problem option 'a' is correct.

There is a main effect for Factor A but there is no interaction

Hence, the correct option is, there is a main effect for Factor A but there is no interaction.

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Complete question:

A two-factor ANOVA is conducted and the data are plotted. The chart shows two parallel lines separated by a distance of 9 points. The lines represent Factor A and the x axis of the chart represents the levels of Factor B. How should you interpret these results?

Select one:

a. There is a main effect for Factor A but there is no interaction

b. There is a main effect for Factor A and there is also an interaction effect

c. There is a main effect for Factor B and there is an interaction effect

d. There is no interaction effect and no main effects

Answer:

1 3/4 * 3

we turn 1 3/4 to improper fraction:

7/4

so,

7/4 * 3 = 21/4 or 5 1/4

Step-by-step explanation:

There is enough evidence to suggest p>0.5

What is hypothesis in statistics?

A type of statistical analysis called hypothesis testing involves testing your presumptions regarding a population parameter. It is used to estimate the relationship between 2 statistical variables.

Thus, a hypothesis is a set of possible explanations or resolutions applicable to a situation. In other words, the hypotheses pose different scenarios in which the aim is to explain the origin and eventual resolution of the problem.

Let's discuss few examples of statistical hypothesis from real-life -

We are testing :

H0: p <= 0.5

H1: p > 0.5

Test statistic:

Z = [(364/562) - 0.5] / √[0.5(1-0.5)] / 562

= 7.00

P-value = P(Z>7.00) = 0.0000

Hence, there is enough evidence to suggest p>0.5.

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Jerial would be responsible for paying $295 if she used more than the allotted 2 GB in a given month.

Word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

Using linear equations,

Data plans cost $45 per month.

Additional fee equals $15 per GB

Jerial would be responsible for paying the following in a month if she used 2 GB more than allowed: = $45 + $15(5) = $45 + $ 250 = $ 295

The monthly payment that Jerial will be required to make as her usage exceeded x GB is:

= $45 + $15 (x)

= $45 + $15x

Hence, Jeriel will pay $45 + $15x when he used over a GB in a month.

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The statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.

Given,  three different groups of subjects memorized a list of nonsense syllables and were then tested for their memory of those syllables at different delays.

Group 1 was tested for memory after a delay of one hour.

Group 2 was tested after a delay of two hours.

Group 3 was tested after three hours.

we have to find the statistical test that is used to test whether length of delay affects memory.

So, the statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.

Hence, the statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.

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Answer:

The regular price of the suit was $625.

Step-by-step explanation:

First, convert 76% into a decimal by moving the decimal place over twice to get 0.76. Then, set up this equation:

475 ÷ 0.76 = 625

Now, we can check if this is right by setting up this equation:

0.76 x 625 = 475.

Yep! It checks out! Our final answer is $625.

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The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years is -6.54

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

Mean :

Mean = [10+3 + (-7) ] / 3 = 2

sample standard deviation :

subtract the mean from each data element.

10- 2 = 8

3-2 = 1

-7 - 2 = -9

Square those numbers.

8² = 64

1² = 1

(-9)² = 81

Add those

64+1+81 = 146

Divide by (number of elements -1 = 3 -1 = 2)

146/2 = 73

Take square root

8.54

So, the sample standard deviation  = 8.54

The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years

=  2 - 8.54

= -6.54

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Total number of ways in which dinner can be assembled will be 120.

What is restaurant?

A restaurant is a place of business where customers can order and receive food and drinks. Meals are typically prepared and consumed on the premises, but many eateries also provide take-out and delivery options.

A commercial space where customers can buy food or drinks.

There are 4 different types of appetizers, so there are 4 ways to choose one of them, which comes out to 4C1 = 4.

Similarly, there are 3 ways to choose desserts and 5 ways to choose an entrees.

2 methods for selecting wines are also included.

As a result, there are

5 x 4 x 3 x 2 = 120 different ways to assemble dinner in total.

Hence, total number of ways in which dinner can be assembled will be 120.

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There are maximum 3 people could go to the park.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Water Park A water park charges $12 for admission and $5 to park your vehicle.

Let x be the number of people

y is the cost

The equation becomes,

y=mx + b,

m will be price for each person and

b will be the fixed price for parking;

x, must be of whole numbers only

Here, m = 12, b = 5, y = 50.

⇒ 12x + 5 = 50

But we want the inequality

⇒ 12x + 5 ≤ 50

Replace x by p

⇒  12p + 5 ≤ 50

where p is the number of peoples.

Solving inequality,

12p ≤ 50 - 5

12p ≤ 45

p ≤ 45/12

p ≤ 3

Hence, there are maximum 3 people could go to the park.

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Answer: 2(x-3)2+13

To find the equivalent expression, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers. This property is given by the following equation:

(a-b)2 = a2-2ab+b2

In this case, the expression we are trying to simplify is 2x2-12x+23, which we can rewrite using the property of square roots as follows:

2x2-12x+23 = 2(x2-6x+11)

Then, we can use the property of square roots that says that the square of the difference of two numbers is the difference of the squares of the numbers to simplify the expression as follows:

2x2-12x+23 = 2(x2-6x+11) = 2(x2-6x+36-25)

Finally, we can use the commutative property of addition and the associative property of addition to simplify the expression even further:

2x2-12x+23 = 2(x2-6x+36-25) = 2((x-3)2+11) = 2(x-3)2+22

Therefore, the equivalent expression to 2x2-12x+23 is 2(x-3)2+13. This means that the correct answer is 2(x-3)2+13.

Answer:  80%

Step-by-step explanation:

If a set of scores does have a standard deviation of 4 and just a mean of 54, the score that is 1 standard deviation well below mean is 50.

For the given values-

Mean = 54

standard deviation = 4

1 value below the standard deviation is;

54 - 4 = 50

Thus, if a group of scores does have a standard deviation of 4 and just a mean of 54, the score that is 1 standard deviation well below mean is 50.

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The time taken to travel upstream will be t = 5/(s - r) and the time taken to travel downstream will be equal to t = 10/(s + r).

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

Speed of boat in still water = s

Distance to travel upstream = 5 km and,

Distance to travel downstream = 10 km

Then, the time taken to travel upstream,

t = d/s

t = 5/(s - r)

And, the time is taken to travel downstream.

t = d/s

t = 10/(s + r)

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Answer:

A: 18/81

Step-by-step explanation:

A: 18/81 = 0.222222222.....

B: 11/88 = 0.125

C: 1/5 = 0.2

D 5/8 = 0.625

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In order to complete the square for the given equation x^2+16x=18, the number added to both sides is 64.

Complete the square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial. To complete the square, add or subtract the same value to both sides. In this case, add the square of half the coefficient of the x -term, (b/2)^2 to both sides of the equation. Hence, the number to add would be (16/2)^2 = 64.

Thus,

x^2+16x + 64 =18 + 64

x^2+16x + 64 =82

x^2+ 2*8x + 64 =82

(x + 8)^2 = 82

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The sample results would be somewhat expected if the null hypothesis were true.

The correct option is (b).

Given,

In the question:

The complete question is this:

Select the most appropriate response.

What does it mean when sample results are not statistically significant?

The question is based on MCQ's

Now, According to the question:

What does it mean when sample results are not statistically significant?

It means  The sample results would be somewhat expected if the null hypothesis were true.

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Answer:

yes

Step-by-step explanation:

They are both equal to 2:1 if you simplify.

Answer:

x >= -3 (third choice)

Step-by-step explanation:

The line is bold and not dotted, meaning that it includes the solution. (or equal to...) This way, we can cross out y>-3 and x>-3.

The line stays on x= -3, and goes right. Meaning that all of the solutions include or are larger than -3.

The answer is x >= -3

An exponential decay function is one that has a constant time of halving.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.

Here,

The function which has a constant halving time is in the following form,

A(t)=A₀(¹/²)^(t/h)

Where:  A₀ is the initial amount

             h   is the half life time or the halving time.

             t    is the time

             A(t) the amount that remains at time t

The previous function represents an Exponential decay function.

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The greatest possible area of the triangle be

Area = 1/2 sq. units.

Given, a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle.

we have to find the greatest possible area of the given triangular region.

Let the height of the triangle be, h and the base of the triangle be b.

using Pythagoras theorem, we get

1² = h² + (b/2)²

1 = h² + b²/4

h² = 1 - b²/4

Now, the area of the triangle be,

A = 1/2×b×h

squaring both the sides,

A² = 1/4×b²×h²

A² = 1/4×b²×(1 - b²/4)

A² = 1/4×b²×(4 - b²)/4

A² = 1/16×b²(4 - b²)

On differentiating, we get

2AA' = 1/16×[2b(4 - b²) -2b³]

2AA' = 1/8×[b(4 - b²) -b³]

2AA' = 1/8×(4b - 2b³)

2AA' = 1/4×(2b - b³)

On equating with zero, we get

b(2 - b²) = 0

b = √2

so, h = 1/√2

Therefore, the greatest possible area of the triangle be

A = 1/2 sq. units.

Hence, the greatest possible area of the triangle be

A = 1/2 sq. units.

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The equation that can be used to find the sum of the three numbers in the given situation is (C) (x) + (x + 1) + (x + 2) = - 21.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

So, allow x to be the first number.

Number two: x + 1

Number three: x + 2

Three numbers are added together to provide the sum x + x + 1 + x + 2.

Given that the sum of three consecutive numbers is -21.

So, (x) + (x + 1) + (x + 2) = - 21.

Therefore, the equation that can be used to find the sum of the three numbers in the given situation is (C) (x) + (x + 1) + (x + 2) = - 21.

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Correct question:
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers?

a. x + x + x = - 21

b.  x + 2 x + 3 x = - 21

c.  x + (x + 1) + (x + 2) = - 21

d.  x + (x + 2) + (x + 4) = - 21

Answer:

[tex]\tt \left(3x+5\right)\left(x-1\right)-3[/tex]

Distribute:-

[tex]\tt 3x^2+2x-5-3[/tex]

[tex]\tt -5-3=-8[/tex]

[tex]\tt 3x^2+2x-8[/tex]

Hope this help you!

The statements 1,2,3 are false, true and true respectively.

Given that,

Based on the policyholder's age in years (x1) and the insured car's worth in dollars, IHI Insurance performed a multiple linear regression analysis to forecast the value of the number of yearly claims made by a policyholder for motor insurance (y) (X2). 500 policyholders were chosen at random for the analysis. The sample included people ranging in age from 16 to 70, and the cars ranged in price from $1,100 to $52,000. I = 13 + (-0.5)X1i + (0.1)X2i is the multiple linear regression equation that corresponds to IHI's study.

a) y^i = 13 + (-0.5)x1i + (0.1)x2i

Here X 1i = 26 , X zi = 20

y^i = 13 + (-0.5)x1i + (0.1)x2i

y^i = 13 + (-0.5)(26) + (0.1)(20)

y^i = 2 it doesnt make 28 so it is false.

b) As the coefficient of X 1i  is negative, it will decrease by 0.5

So, it is true.

c) As the coefficient of X 2i  is positive, it will increase by 0.1

So, it is true.

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