A 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. A preliminary sample standard deviation is 3.8. The smallest sample size n that provides the desired accuracy is

Answer:

Step-by-step explanation:

Let x represent the amount invested at 6.25%. Then the total interest earned is ...

  0.0625x + 0.0600(150,000 -x) = 9212.50

  0.0025x = 212.50 . . . . . . subtract 9000, collect terms

  x = 212.50/0.0025 = 85,000

  150,000 - 85,000 = 65,000 . . . . amount invested at the lower rate

$85,000 is invested at 6.25%; $65,000 is invested at 6%.

Answer:

y = 2X-48

Step-by-step explanation:

Cost to the owner for day's supply of hot dogs,buns and mustard = $48

Profit = $2 profit for each hot dog sold

Let X be the number of hot dogs sold

The profit earned by hot dog stand for X number of hot dogs

y = 2X-48

Answer:

Answer is

=950

Answer:

d) 4(s + 4.5) and (s + 4.5) + (s + 4.5) + (s + 4.5) + (s + 4.5)

Step-by-step explanation:

since  you know that one side is (s+4.5) and a square has 4 congruent sides the answer would be 4(s + 4.5) and (s + 4.5) + (s + 4.5) + (s + 4.5) + (s + 4.5)

Answer:

The correct answer is D

Step-by-step explanation:

Step one :

The perimeter of a square is the sum of all four sides given a side as

(s+4.5)+(s+4.5)+(s+4.5)+(s+4.5)

Or

Step 2:

(s+4.5)+(s+4.5)+(s+4.5)+(s+4.5)

Opening bracket we have

s+4.5+s+4.5+s+4.5+s+4.5

Summing all "s'" terms

(4s+18)

4(s+4.5)

Standard deviation = √(n * p * q)

You are given n and p

q = 1 - p

q = 1 -0.2 = 0.8

Standard deviation = √(21 * 0.2 * 0.8)

=√3.36 = 1.83

The answer is A.

The standard deviation for a given binomial distribution [tex]n[/tex] and [tex]p[/tex] would be the following:

[tex]\sigma=\sqrt{n \times p \times q}[/tex]

The variable [tex]q[/tex] is equivalent to [tex](p-1)[/tex]

[tex]=\sqrt{n\times p\times(p-1)}[/tex]

Substitute the values of [tex]p[/tex] and [tex]n[/tex] into the equation

[tex]=\sqrt{21\times0.2\times(1-0.2)}[/tex]

[tex]=\sqrt{21\times0.2\times0.8}[/tex]

Use a calculator to solve for this square root since it would be too hard and complicated to do by hand

[tex]=1.83303027798...[/tex]

Round this to the nearest hundredths place since all answer choices are rounded like that

[tex]=1.83[/tex]

Thus, the answer is choice A. Let me know if you need any clarifications, thanks!

~ Padoru

Answer: 63 student tickets and 38 adult tickets were sold

Step-by-step explanation:

Mike sold raffle tickets for adults and students for the school football game.

Let x= number of student tickets sold

Let y= number of adult tickets sold

The raffle tickets were $3 for students and $7 for adults. This means x student tickets cost $3x and y adult tickets cost $7y

When Mike looked at how much he collected, he counted $455 and 101 ticket stubs. This means

3x + 7y = 455 - - - - - -1

x + y = 101

Substituting x = 101 - y into equation 1, it becomes

3(101 - y) + 7y = 455

303 -3y + 7y = 455

-3y +7y = 455 - 303

4y = 152

y = 152/4 = 38 tickets

x = 101 - y

x = 101 - 38

x = 63 tickets

Answer:

Step-by-step explanation:

63 students and 38 adults tickets

Answer:

$21,000

Step-by-step explanation:

Given,

Net income = $20,000

Depreciation = $2,000

Current assets (increase) = $2,000

Current liabilities (increase) = $1,000

Note: An increase in current assets is a reduction in cash balance while an increase in current liabilities is an increase in cash

Considering the note above,

Cash is provided by operating activities = 20000 + 2000 - 2000 + 1000

                                                                   = $21,000

Answer:

-1.2

Step-by-step explanation:

Given that the designer also programs a bird with a path that can be modeled by a quadratic function.

The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8).

If we treat this curve as line joining these two points then we can find the slope by the formula

Slope = change in y coordinate/change in x coordinate

Here the points given are

(0,20) and (10,8)

[tex]Change in y coordinate = 8-20 = -12\\Change in x coordinate = 10-0 = 10\\Slope = -1.2[/tex]

Slope of the line that represents the turtle's path

=-1.2

Answer: 0.8

Step-by-step explanation: i got it right on edg

second part to the question is

h= 0

k= 20

a= -0.12

third part is letter B

Answer:

5y = -× + c

Step-by-step explanation:

If two lines are perpendicular, the product of their gradient equals -1.

We should note that the general equation of a line is y = mx + c, where m is the gradient.

For the line y = 5x - 2 , the slope is 5. The line that will be perpendicular to this line will have a slope of -1/5.

A line like 5y = -x + c fits the description

Price of one adult ticket is $9 and price of one student ticket is also $9.

Step-by-step explanation:

Let,

Adult ticket = x

Student ticket = y

According to given statement;

x+2y=27   Eqn 1

2x+2y=36   Eqn 2

Subtracting Eqn 1 from Eqn 2;

[tex](2x+2y)-(x+2y)=36-27\\2x+2y-x-2y=9\\x=9[/tex]

Putting x=9 in Eqn 1;

[tex]9+2y=27\\2y=27-9\\2y=18[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{18}{2}\\y=9[/tex]

Price of one adult ticket is $9 and price of one student ticket is also $9.

Keywords: linear equations, subtraction

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Answer:

f(c) = 3c + 5

Step-by-step explanation:

c is independent variable, p is dependent variable, so p = f(c)

6c = 2p -10

3c = p - 5

p = 3c + 5

f(c) = 3c + 5

Answer:

F(c) = 3c +5  

Step-by-step explanation:

6c=2p-10

If c is considered to be as the independent variable, then p is the dependent variable

So we will clear and solve for variable p

6c = 2p-10

Dividing both sides by 2. We will have  

6c/2 = 2(p-5)/2

3c= p-5  

Adding 5 on both sides

3c+5= p

So p =3c+5

By writing the above equation in the functional notation form  

F(c) = 3c +5  

Answer:

Explanation is given in the following attachments

Step-by-step explanation:

Answer:95.44

Step-by-step explanation:

The rate of change between 1990 and 1999 is 15.22

Step-by-step explanation:

The rate of change in this case is given by change in quantity divided by change in time

So,

[tex]Rate\ of\ change = \frac{Increase\ in\ money}{Increase\ in\ time}\\=\frac{549-412}{1999-1990}\\=\frac{137}{9}\\=15.22[/tex]

Hence,

The rate of change between 1990 and 1999 is 15.22

Keywords: Rate of change, median

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Answer:

x-intercepts: -2; 1; 5

Average rate of change: 1.8

Step-by-step explanation:

x- intercepts as per graph are:

Average rate of change over the interval (-1, 4) is:

Answer:

  5 mph

Step-by-step explanation:

The relation between speed, distance, and time is ...

  speed = distance/time

Filling in the given values, we find the speed to be ...

  speed = (1/4 mi)/(1/20 h) = (1/4)(20/1) mi/h = 5 mi/h

Elena's speed is 5 miles per hour.

Answer:

Pounds of apple to be used for a pie = 3 lb

Step-by-step explanation:

Given the bag contains apples weighting  = 5 lb

To make a pie [tex]\frac{3}{5}[/tex] of the apples in the bag is used.

To find the pounds of apples to be used to make a pie we will have to find the  [tex]\frac{3}{5}[/tex]th part of 5 lb of apples.

In order to do that we multiply the fraction to the total weight of apples.

Pounds of apple to be used to make a pie

⇒ [tex]\frac{3}{5}\ of\ total\ pounds\ of\ apple[/tex]

⇒ [tex]\frac{3}{5}\times 5[/tex]

⇒ [tex]3[/tex]

∴ Pounds of apple to be used for a pie = 3 lb

Answer:

Coefficient of determination = 0.149769  

Step-by-step explanation:

We are given the following in the question:

Coefficient of correlation, r = -0.387

We have to find the coefficient of determination.

Coefficient of determination =

[tex]r^2 = (-0.387)^2 = 0.149769 = 14.98\%[/tex]

Coefficient of determination:

Answer:2097

Step-by-step explanation: it is that it the answer plz trust me

ADD me on fortnite @RaZrtNZT

The value of x in the given triangle is equal to 2097 ft by calculating through trigonometric ratios.

These are ratios which are expressed as the ratio of sides of a right angled triangle.

In the given triangle the hypotenuse is 3750 and x is the perpendicular of the triangle.

We have to use sin to calculate because it expresses the ratio of perpendicular and hypotenuse.

sin34°=x/3750

0.5591=x/3750

x=  2096.625

x=2097 approx.

Hence the value of x in the given right angled triangle is 2097 ft.

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Answer: 20%

Step-by-step explanation:

The total amount of water that Leilani drinks throughout is 70 ounces each day. This means that before and after the ride, she drinks a total of 70 ounces daily

in order to stay hydrated before her morning ride she drinks 14 ounces of water.

To determine what percent of her daily amount of water she has before her ride, we would divide the amount she takes before ride by the total daily amount of water and multiply by 100. It becomes

14/70 × 100 = 20%

Answer:

20

Step-by-step explanation:

The researcher's prediction of an interaction between training and gender is true. An interaction occurs when the effect of one variable on an outcome depends on the level of another variable.

The researcher's prediction of an interaction between training and gender is True.

An interaction occurs when the effect of one variable on an outcome depends on the level of another variable. In this case, the researcher predicts that the training course will have a different effect on females compared to males.

For example, if the researcher conducts a study where both males and females participate in the training course, and finds that females benefit significantly from the course while males do not, this would support the researcher's prediction of an interaction between training and gender.

Answer:

4.5%, 0.44%, 0.33%

Step-by-step explanation:

I'm not really good at math,but I do believe this is the answer

Answer:

Orange rose = 3/9

Pink rose = 4/9

Yellow rose = 2/9

Step-by-step explanation:

In order to find probability of picking one item, you add all the possible things you could choose. So, 3+2+4 equals a total of 9 outcomes, and that would be your denominator for your fraction of probability. From there it's really easy. Just put the amount of things your trying to find the probability for in the numerator spot.

Ex.

There are 9 total roses so that would be the denominator (?/9)

To find out the probability for picking an orange rose, you'd put the 2 in as the numerator because that is the total number of orange roses you have (2/?)

Then just put the two together (2/9).

Answer:

First  quartile  list of number median is 23

Step-by-step explanation:

List of numbers = 42,24, 30 , 22 , 26, 19, 33, 35

Arrange them in a sequence:

List of numbers = 19, 22, 24, 26, 30, 33, 35, 42

The median of {19, 22, 24, 26, 30, 33, 35, 42} is= 26+30/2 = 28

Numbers that are less than the median are { 19 , 22 , 24 , 26}

then

median of the list = 22+24/2 = 23

So the first  quartile  list of number median is 23.

The median of the first quartile list is 23.

The given set of numbers {42, 24, 30, 22, 26, 19, 33, 35} can be arranged in ascending order as follows:

{19, 22, 24, 26, 30, 33, 35, 42}.

The median of this sequence is calculated as (26 + 30) / 2, resulting in 28.

The numbers less than the median are {19, 22, 24, 26}.

Next, the median of this subset is found by taking (22 + 24) / 2, yielding 23. Therefore, the median of the first quartile list is 23.

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Answer:

Assuming that this is a normal distribution, probably what is need is to compute the value of the P-value result to judge a system of hypothesis. So, first of all, we have to determine the null and alternative hypothesis.

In this problem, we don't have an exact demand about a hypothesis. We can assume that the purpose is to demonstrate is there's enough evidence to say that second-graders students have greater math skills than others.

So, assuming that others students have a mean score of 50, the system of hypothesis could be:

Null hypothesis: [tex]H_{o} : u=50[/tex]; that is, that the sample students have an mean score of 50.

Alternative hypothesis: [tex]H_{a}: u>50[/tex]; that is, that the sample students have a mean score more than 50.

So, to know if there's enough evidence to stay that second-graders have a higher score than other students, we must to work around the null hypothesis, accepted or rejected.

First, we have to calculate the Z-value with this formula: [tex]Z=\frac{x-u}{\frac{o}{\sqrt{n} } }[/tex]; where x = 55; o = 9; n = 60 and u = 50.

Replacing all values we have: [tex]Z=\frac{55-50}{\frac{9}{\sqrt{60} } } =\frac{5}{\frac{9}{7.7} } =\frac{5}{1.2} = 4.2[/tex]

So, the Z-value is 4.2, approximately 4. Then, we use the Z-table attached to know the P-value, using a 0.01 level of significance (we can use other, but this is the usual level), then we look for the value which is in the column 0.01 with -4 (it doesn't matter the negative sign, because it's the same result). We see that the P-value is 0.00003.

According with the theory, if the P-value is higher than the level of significance, the null hypothesis should be accepted, because it means that there is no enough evidence to accept it. Therefore, based on this test, the second-graders students have a better mathematics skills core than the other students, because the P-values is lower than the level of significance. (0.00003 < 0.01)

To pay off a $8500 credit card balance with a 15.99% APR in 3 years, you would need to make monthly payments of approximately $293.12.

To determine the monthly payment needed to pay off a credit card balance of $8500 with an APR of 15.99% in 3 years, you can use the formula for calculating monthly payments on a fixed-rate loan. The formula is:

[tex]\[ M = P \times \frac{r(1+r)^n}{(1+r)^n-1} \][/tex]

where:

- [tex]\( M \)[/tex] is the monthly payment,

- [tex]\( P \)[/tex] is the principal balance (credit card balance),

- [tex]\( r \)[/tex] is the monthly interest rate (annual interest rate divided by 12 and converted to decimal),

- [tex]\( n \)[/tex] is the total number of payments (number of months).

First, convert the annual interest rate to a decimal: [tex]\( 15.99\% = 0.1599 \).[/tex]

Next, calculate the monthly interest rate: [tex]\( r = 0.1599 / 12 = 0.013325 \).[/tex]

Now, plug in the values into the formula:

[tex]\[ M = 8500 \times \frac{0.013325(1+0.013325)^{3 \times 12}}{(1+0.013325)^{3 \times 12}-1} \][/tex]

After performing the calculations, the monthly payment [tex](\( M \))[/tex] is approximately $293.12.

Answer:

Step-by-step explanation:

25 gallons of milk for $56

We would need to determine the unit rate for a gallon of milk in this particular store.

If 25 gallons of milk for $56

Then 1 gallon of milk would cost

56/25 = 2.24

Target sells 15 gallons of milk for 32.05 dollars

We would also to determine the unit rate for a gallon of milk in this particular store.

If 15 gallons of milk for $32.05

Then 1 gallon of milk would cost

32.05/15 = 2.137

The unit cost of a gallon of milk at target provides a better deal because it has a lower unit cost than the other

Answer:

Explanation:

The question is: given that the first term is    [tex]t_1=5[/tex]    and the recursive definition is    [tex]t_{n+1}=3\cdot t_n[/tex]    , what would be the second term (i.e.    [tex]t_2[/tex]    )

A recursive defintion or recursive formula is an equation (a rule) that you apply over a term to find the next term, and so you can use it repeatedly to find the successive terms of a series.

In this case, your rule is that you multiply each term by 3, starting from 5.

Thus:

Hence, your answer is 15 (the fourth choice).

Answer:

x = 8

Step-by-step explanation:

When cutting the wire we will get two pieces

x             and          12 - x

If we build a circle whith x , the lenght of the circle will be x, and if we look at the equation for a lenght of a cicle  2*π*r = x

then r  = x/2π

and consequentely   A₁  = area of a circle  =  πr²       A₁  = π*x/2π  

A₁  = x/2

With the other piece  12  -  x     we have to make an square so wehave to divide that piece in four equal length

side of the square   =    s

s   = 1/4 ( 12 - x )    and the area is      A₂  = [1/4 ( 12 - x)]²

A₂  = ( 12 - x )²/16

Then     A₁  +  A₂  =  A(t)   and this area as fuction of x

A (x)  = x/2  +  1/16 ( 144 + x² -24x)          A (x)  =[ (8x + 144 + x² -24x)]/16

Taken derivatives in both sides

A´(x)  =  8  +  2x  - 24   = 0

   2x  -16  =  0         x  =  8    and   s =  12 - 8       s  =  4

To minimize the sum of the areas, we need to find the value of x that minimizes the sum of the area of a circle and a square.

To minimize the sum of the areas, we need to find the value of x that minimizes the sum of the area of a circle and a square. The area of a circle is given by the formula A = πr^2, and the area of a square is given by the formula A = s^2. We can set up an equation to represent the sum of the areas: πr^2 + s^2. Since we are given that the wire is cut into two pieces of length x and 12-x, we can substitute the values of r and s in terms of x into the equation. Then we can differentiate the equation with respect to x and set the derivative equal to zero to find the critical points. From there, we can determine which critical point corresponds to the minimum value.

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Answer:

  no

Step-by-step explanation:

The second package costs $2 for each pair of socks. If the first package cost that much, it would be 8×$2 = $16 for 8 pairs of socks. That is not the same as $12 for 8 pairs.

__

Another way to look at it is the first package costs twice as much as the second, but has more than twice as many pairs of socks. That means the rates are not equivalent.

Answer: her mum drove for 12.67 hours and her dad drove for 12.67 hours

Step-by-step explanation:

Her mom drove 75 miles an hour and her dad drove 60 miles an hour.

The ratio of her mum's speed to her dad's speed is 75 : 60

Total ratio = 75 + 60 = 135

Since the speed of her mum and her dad will determine the distance that each of them covered,

Distance covered by mum will be

Speed of mum/ total ratio × total distance covered. It becomes

75/135 × 1710 = 950 miles

Distance covered by dad would be total distance - distance covered by mum. It becomes

1710 - 950 = 760 miles

Time spent by her mum = distance covered by her mum / speed of her mum. This becomes

950/75 = 12.67 hours

Time spent by her dad = distance covered by her dad / speed of her dad. This becomes

760/60 = 12.67 hours