A researcher compared the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year. At the end of the year, the researcher found that the children who had used brand X has significantly fewer cavities than the children who had used brand Y. The difference was significant at the .05 level. What is the null hypothesis

Answer:

a A=$47,887.81

b.A=$46,430.80

Step-by-step explanation:

a. Given the initial amount is $40,000 with a 3-year term and a 6% rate compounded daily.

-Take 1 year=365 days

#First we calculate the effective interest rate corresponding to the daily compounding;

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^{365}-1\\\\=0.06183[/tex]

#We use the calculated effective rate, 0.06183, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.06183)^3\\\\=47887.81[/tex]

Hence, the total future value for a daily compounding is $47,887.81

b. For a sinking fund with a 5% compounded quarterly:

#We calculate the annual effective rate:

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.05/4)^4-1\\\\=0.05095[/tex]

#We use the calculated effective rate, 0.05095, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.05095)^3\\\\=46430.80[/tex]

Hence, the future value of the sinking fund is $46,430.80

Answer: f(2x)

Step-by-step explanation:

ed 2020

Answer:

The predicted percentage vote for Al Gore for the county with 44.0954% African Americans is 25.76%.

Step-by-step explanation:

The least square regression line is used to determine the relationship between a response variable (or dependent variable) and an explanatory variable (or independent variable).

The least square regression line can be used to predict the future value or estimate the past value of the dependent variable based on the independent variable.

The general form of a least square regression line is:

[tex]y=\alpha +\beta x[/tex]

Here,

y = response variable

x = explanatory variable

α = intercept

β = slope

The least square regression line for predicting the percentage vote for AI Gore (y) from the percentage of county residents who were African American (x) is given by:

[tex]\hat y=25.4495+0.6956 x[/tex]

Compute the predicted value of y for x = 44.0954% = 0.440954 as follows:

[tex]\hat y=25.4495+0.6956 x[/tex]

  [tex]=25.4495+0.6956 \times 0.440954\\=25.4495+0.3067276024\\=25.7562276024\\\approx 25.76[/tex]

Thus, the predicted percentage vote for Al Gore for the county with 44.0954% African Americans is 25.76%.

Using the equation of the estimated regression line, the predicted percentage vote for Al Gore in Baker County, Georgia is approximately 56.3555% based on a population that was 44.0954% African American.

In this scenario, we have a linear regression line of the form y^ = 25.4495 + 0.6956x, where y^ represents the estimated percentage vote for Al Gore, and x represents the percentage of county residents who are African American. We are given that in Baker County, Georgia, 44.0954% of residents are African American. By substituting this x value into the equation, we can find the predicted y value:

y^ = 25.4495 + 0.6956*(44.0954)

This gives an estimated vote for Al Gore in Baker County as y^ = 56.3555 approximately, to four decimal places. This implies that the model predicts that about 56.3555% of the vote in Baker County went to Al Gore.

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Initial bacteria count is 3, as it doubles every 12 hours; after 2 days, totaling 48 bacteria.

To solve this problem, we can use the formula for exponential growth, which is  

[tex]- \( N \)[/tex]is the final number of bacteria,

[tex]- \( N_0 \)[/tex] is the initial number of bacteria,

[tex]- \( t \)[/tex] is the elapsed time in hours, and

[tex]- \( d \)[/tex] is the doubling time in hours.

Given that the doubling time is 12 hours and after 2 days (which is 48 hours) there are 48 bacteria, we can plug these values into the formula and solve for [tex]\( N_0 \):[/tex]

[tex]\[ 48 = N_0 \times 2^{(48/12)} \][/tex]

Solving this equation:

[tex]\[ 48 = N_0 \times 2^4 \][/tex]

[tex]\[ 48 = N_0 \times 16 \][/tex]

Now, to find [tex]\( N_0 \)[/tex]:

[tex]\[ N_0 = \frac{48}{16} \][/tex]

[tex]\[ N_0 = 3 \][/tex]

So, there were 3 bacteria at the beginning of the first day.

Answer:

the answer is A.Use the numbers in the table to create ordered pairs. and D.Draw a straight line that starts at the origin and connects all the points.

Step-by-step explanation:

I just did it on edgnuity and got it right.

Answer:

The correct answer is A C and D

Step-by-step explanation:

Answer:

55%

Step-by-step explanation:

Answer:

I'm just going to take a guess and say 36?

Step-by-step explanation:

Answer:

1. 75582

2. 3047466240

Step-by-step explanation:

1.  If order does not matter, this is a combination problem.  You are choosing 8 sticks from a set of 19. (Octagons have 8 sides.)

The formula for combinations of n things chosen r at a time "n choose r" is

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

[tex]_19C_8=\frac{19!}{8!(19-8)!} = \frac{19!}{8!11!}=75582[/tex]

2. If order matters, there are more possibilities. This is a permutation problem.  The number of permutations of 19 things taken 8 at a time, "19 permute 8" is

[tex]_nP_r=\frac{n!}{(n-r)!} \\ _{19}P_8=\frac{19!}{(19-8)!} = 3047466240[/tex]

Answer:

2,5, and 6

Step-by-step explanation:

hope this helps

The solid will be a triangular prism .The solid will have some faces that are rectangles and some faces that are triangles.

The solid will have five faces.

Answer:

5x+20

Step-by-step explanation:

5(x+4)

Distribute

Multiply 5 by each term inside the parentheses

5*x + 5*4

5x+20

(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when [tex]t=0[/tex] and [tex]t=3[/tex], and because the velocity function is continuous, you need only check the sign of [tex]v(t)[/tex] for values on the intervals (0, 3) and (3, 6).

We have, for instance [tex]v(1)\approx-0.91<0[/tex] and [tex]v(4)\approx0.91>0[/tex], which means the particle is moving the positive direction for [tex]3<t<6[/tex], or the interval (3, 6).

(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:

[tex]\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt[/tex]

which follows from the definition of absolute value. In particular, if [tex]x[/tex] is negative, then [tex]|x|=-x[/tex].

The total distance traveled is then 4 ft.

(g) Acceleration is the rate of change of velocity, so [tex]a(t)[/tex] is the derivative of [tex]v(t)[/tex]:

[tex]a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)[/tex]

Compute the acceleration at [tex]t=4[/tex] seconds:

[tex]a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}[/tex]

(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)

Answer:

6

Step-by-step explanation:

A triangular prism, a shape with two identical triangular faces and three identical rectangular faces, has 6 vertices where the edges of these faces meet.

In geometry, a shape's vertices are the points where two or more lines or edges meet. When we consider a triangular prism, we see that it is a figure with two triangular faces and three rectangular faces. Each triangular face has 3 vertices, and since these faces are identical, they share vertices. If you count up all these points, we find that a triangular prism has 6 vertices in total.

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Answer:

$34.20

Step-by-step explanation:

First, find the cost with tax

You are paying 7.2% tax, but you are also paying for 100% of the bill

100%+7.2%=107.2%

So, you are really paying for 107.2% of the bill

Convert 107.2% to a decimal by dividing by 100 or moving the decimal 2 spaces to the right

107.2/100=1.072

Multiply the decimal by the cost of the bill

1.072*45.90=49.2048

But, we also have a coupon for $15 off

Subtract 15 from the cost with tax

49.2048-15=34.2048

Round to the nearest cent/hundreth

$34.20

Hope this helps! :)

Answer: 1 = 57.2

2 = angle S

3 = the triangles are similar (the second choice)

Step-by-step explanation: i got the question right on my work on e d g e n u i t y

Consider the triangles.

Triangle C D E. Angle C is blank, angle D is 87.3 degrees, angle E is 35.5 degrees. Triangle R S T. Angle R is blank, angle S is 57.2 degrees, angle T is 87.3 degrees.

Answer the questions about these triangles.

What is the measure of angle C?

✔ 57.2

Which angle corresponds to angle C?

✔ angle S

What can be concluded about the triangles?

✔ The triangles are similar.

The measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Since the sum of angles in a triangle is always 180 degrees, we can find the measure of angle C in triangle CDE by subtracting the measures of angles D and E from 180 degrees:

Angle C = 180 degrees - Angle D - Angle E

Angle C = 180 degrees - 87.3 degrees - 35.5 degrees

Angle C = 57.2 degrees

Therefore, the measure of angle C in triangle CDE is 57.2 degrees.

Angle C corresponds to angle R in triangle RST, since they are both unknown angles in their respective triangles.

We can conclude that the two triangles are  similar or congruent.

Hence, the measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

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Answer:

The answer is Steps 1 and 2.                                Step 1: -3(x+2) = 5(x-7)

                                                                               Step 2: -3x-6 = 5x-35

Step-by-step explanation:

Answer:

133/1152

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

19+15+14 = 48 marbles

Of which 19 are red, 15 are yellow and 14 are blue.

What is the probability of pulling out a blue marble, followed by a red marble, if you replace the blue marble first

Blue marble

48 marbles, of which 14 are blue.

So [tex]P_{A} = \frac{14}{48} = \frac{7}{24}[/tex]

Red marble

48 marbles, of which 19 are red.

So [tex]P_{B} = \frac{19}{48}[/tex]

Both:

[tex]P = P_{A} \times P_{B} = \frac{7}{24} \times \frac{19}{48} = \frac{133}{1152}[/tex]

So the correct answer is:

133/1152

Answer:

[tex]\hat p = \frac{Lower+Upper}{2}[/tex]

And replacing the info from the problem we have:

[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]

So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %

Step-by-step explanation:

We want to find a confidence interval for a proportion p who represent the parameter of interest.

The confidence interval would be given by this formula:

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For this case the 90% confidence interval is given by (1.8%=0.018, 4.6%=0.046) after apply the last formula

Since the confidence interval is symmetrical we can estimate the point estimator of the true percentage with this formula:

[tex]\hat p = \frac{Lower+Upper}{2}[/tex]

And replacing the info from the problem we have:

[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]

So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %

Given:

Given that Steven purchased a box of chocolate shaped like a square pyramid.

The box is 12 inches tall and the area of the bottom of the box is 35 square inches.

We need to determine the expression that is used to find the number of chocolates that the box holds.

Expression:

The expression that is used to find the number of chocolates that the box holds can be determined using the formula,

[tex]V=\frac{1}{3} Bh[/tex]

where B is the area of the base and h is the height of the pyramid.

Substituting B = 35 and h = 12 in the above formula, we get;

[tex]V=\frac{1}{3}(35 \cdot 12)[/tex]

Thus, the expression that is used to find the number of chocolates that the box holds is [tex]\frac{1}{3}(35 \cdot 12)[/tex]

Hence, Option b is the correct answer.

Answer:

Option 2

Step-by-step explanation:

Volume of a pyramid

⅓ × base area × height

⅓ × 35 × 12

12 × 35 × ⅓

Answer: The answer would be D

Step-by-step explanation:

This is because all of the models on the graph show in the same place having the same middle but at different heights but not the same standard deviation.

Each distribution has the same mean and a different standard deviation is the correct statement about the graph.

Three different normal distributions are given in the graph.

The spread in the given normal curves is due to different standard deviation.

The mean for all the three curves lies at the center of the curve.

Therefore, the graph shows that each distribution has the same mean and a different standard deviation.

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The complete question is given below.

The graph below shows three different normal distributions.

Which statement must be true?

Each distribution has a different mean and the same standard deviation.

Each distribution has a different mean and a different standard deviation.

Each distribution has the same mean and the same standard deviation.

Each distribution has the same mean and a different standard deviation.

Answer:

Prism A

Step-by-step explanation:

Volume of a triangular prism is calculated like this : 1/2 × 7 × 4 × 9 = 126 m^3

Volume of a cuboid is calculated like this : 8 × 8 × 2 = 128 m^3

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The school play ground is.

5ft long rectangle

The designer want to increase the length,

Then, there will be 3 identical rectangle of total length of 17ft

By how much did he increase the of each rectangle

Original, the length of the rectangle is 5ft, now, we want to design three rectangle. This three identical rectangle will have total length of (5+5+5)ft,

The original length of the three rectangle is meant to be 15ft,

Now he increase the length to 17ft,

This shows that he has increase all the three rectangle by 2ft.

So, each rectangle is expected to be increased by ⅔ft

So, he increased each rectangle length by ⅔ft.

Mathematically,

Let the increase be x

Then, he increase each length by x, so the new length is

5+x

Then, there are 3 rectangles, so their total length after increase is 3×(5+x)

And this total length after increase is give as 17ft

Then,

3(5+x) = 17

Solving this

15 + 3x = 17

3x = 17-15

3x = 2

x = ⅔ ft

So, the mathematical model of the increase is 3(5+x) = 17 and the increase is ⅔ft

Answer:

Steve should use:

Step-by-step explanation:

Let Steve cut the wire so that the first piece has length x.

Therefore, the second piece will have a length of (52 - x).

The wire of length x is used to make a circle

Circumference of a Circle,

[tex]c = 2\pi r\\Therefore\\2\pi r=x\\r=\dfrac{x}{2\pi}[/tex]

[tex]\text{Area of a circle, A}=\pi r^2= \pi (\dfrac{x}{2\pi})^2=\pi (\dfrac{x^2}{4\pi^2})\\A=\dfrac{x^2}{4\pi}[/tex]

The wire of length (52-x) is used to make a square.

[tex]\text{Side length of the Square,}[/tex] [tex]s= \dfrac{52-x}{4}[/tex]

[tex]\text{Area of the Square},s^2= \left(\dfrac{52-x}{4}\right)^2=\dfrac{(52-x)^2}{16}=\dfrac{x^2-104x+2704}{16}[/tex]

Total Area = Area of Circle + Area of Square

[tex]Area=\dfrac{x^2}{4\pi}+\dfrac{x^2-104x+2704}{16}[/tex]

Let us simplify the expression

[tex]Area=\dfrac{16x^2+\pi(x^2-104x+2704)}{16\pi}\\=\dfrac{16x^2+\pi x^2-104\pix+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)-104\pi x+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)}{16\pi}-\dfrac{104\pi x}{16\pi}+\dfrac{2704\pi}{16\pi}\\A=\dfrac{x^2(16+\pi)}{16\pi}-6.5x+169[/tex]

This is the function of a parabola which opens up.

To find where A is minimum, find the axis of symmetry.

[tex]$Using \: x=-\frac{b}{2a}[/tex]

[tex]a=\dfrac{16+\pi}{16\pi}, b=-6.5\\ x=-\dfrac{-6.5}{2(\dfrac{16+\pi}{16\pi})}=8.53\:Inches[/tex]

Steve should cut the wire so that the length of wire used to make a circle is 8.53 Inches.

Length of wire used to make the square =52-8.53=43.47 Inches

Answer:

[a]. sample is 25 randomly selected students

    also population is all students

[b]. (20.0, 23.0)

[c]. (8.8, 24.2)

Step-by-step explanation:

here is a step by step process to solving this, i hope you find this helpful.

1). The population is all students who graduated from his school  while the

sample is 25 randomly selected students from the email list

2). given alpha = 1-0.86=0.14

critical z value(two tailed) for 86% confidence level is:

z=normsinv(0.07) or normsinv(0.93)=1.476

Margin of error=1.476*(4.6/SQRT(20))=1.5

86% confidence interval for population mean

=21.5+/-1.5

=(20.0, 23.0)

3). if population standard deviation is not known,we will use t distribution.

df=20-1=19

t*=tinv(0.05,19)=2.093

Margin of error=2.093*(5.7/sqrt(20))=2.7

95% confidence interval for population mean

=21.5+/-2.7

=(18.8, 24.2)

cheers i hope this helps!!!!

Answer:

42,690

Step-by-step explanation:

it is the rule of LONG numbers

The value of the car in 2020 is $5532.53

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

Given that, You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually.

The exponential decay is given by =

[tex]A = P(1-r)^t[/tex]

A = final amount

P = principal amount

r = rate of decrease.

t = 10

Therefore,

A = 25000(1-0.14)¹⁰

A = 25000×0.86¹⁰

A = 5532.53

Hence, the value of the car in 2020 is $5532.53

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Answer:

Adb , cbd, 1

Step-by-step explanation:

Answer:

ADB CBD 1

Step-by-step explanation:

The situation can illustrate the distributive property in math (6*(2+3)=6*2 + 6*3), representing 'a' as six cars, and 'b' and 'c' as the people in each car.

The situation described can be used to illustrate the distributive property in mathematics. The distributive property states a(b + c) = ab + ac. In this scenario, the six cars can be represented as 'a', while the 'b' and 'c' can represent the two people in front and the three in the back. Therefore, the total number of people in all cars is 6*(2+3) which according to the distributive property equals 6*2 + 6*3. That is, 12 people in the front seats and 18 in the back seats, summed up to be 30 people in total.

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Final answer:

The distributive property states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars.

Explanation:

The distributive property in mathematics states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars. Each car has 2 people in front and 3 people in back, so we can write the expression as (2 + 3) * 6. Using the distributive property, we can simplify this expression to 2 * 6 + 3 * 6, which equals 12 + 18, or 30 people in all the cars.

Answer:

The volume is 2144.66

Step-by-step explanation:

The equation i used when solving this question.

V=4/3πr3

The volume of sphere when rounded to nearest 100th will be 2143.574 cubic units

Given: a sphere of radius 8 units

To find: Volume of sphere

The volume of a sphere can be calculated using the formula [tex]V = \frac{4}{3}\pi r^3[/tex], where r is the radius of the sphere. To find the volume, plug in the value of the radius into the formula and calculate the result.

[tex]V = \frac{4}{3}\pi r^3\\[/tex]

[tex]V = \frac{4}{3}\pi (8)^3\\[/tex]

[tex]V = \frac{4}{3}\pi (8)^3 = 682.667 \pi[/tex]

If we insert the value of [tex]\pi = 3.14[/tex] we get:

[tex]V = 682.667 \times 3.14 = 2143.57438[/tex]

When rounded to nearest 100th we will get volume equal to 2143.574 cubic units.

Answer:

r = 4.5m

d = 57 yds

Step-by-step explanation:

The radius is 1/2 of the diameter

d= 9 meter

  r = d/2  =9/2 = 4.5 m

The diameter is twice the radius

r = 28.5 yds

d = 2r = 2*28.5 =57 yds

Answer:

a) r=4.5 m

b) d= 57 yd

Step-by-step explanation:

a)

The diameter is twice the radius, which can be written as:

d=2r

We know the diameter is 9, so we can substitute that in for d.

9=2r

To solve for r, we need to isolate the variable. To do this, divide both sides by 2

9/2=2r/2

4.5=r

So, the radius is 4.5 meters

b)

The diameter is twice the radius, or

d=2r

We know the radius is 28.5, so we can substitute that in for r

d=2*28.5

Multiply

d=57

So, the diameter is 57 yards

Answer:

4 hours

Step-by-step explanation:

We know that there are 24 hours in a day. Therefore, we will subtract from 24.

If mark spends one-third of his day sleeping, then he will be asleep for 8 hours.

[tex]\frac{1}{3}\times24 \\=\frac{24}{3} \\=8[/tex]

We also know that if Mark spends one-sixth of his day at soccer practice, he will have been practicing for 4 hours.

[tex]\frac{1}{6}\times24 \\=\frac{24}{6} \\=4[/tex]

We now simply subtract from 24:

[tex]\text{hours in a day - hours asleep - hours at school - hours practicing} \\24 - 8 - 8 - 4 \\= 4[/tex]

Therefore, Mark will have 4 hours of free time.

Answer:

Communitive property of addition

Step-by-step explanation: