estimate the value of 102.3 ÷ 4.7

Answer:

325 x 7.00 = 2275.

2495 - 2275 = 220.

The possible data in the question does not provide sufficient evidence available to support the alternative hypothesis that there is a difference between Mr. Starnes and Ms. McGrail's AP Statistics classes and Mr. Starnes did not stack the class.

In statistics, a hypothesis test is the performance of a test on an assumption made about a population parameter.

The possible data in the question, obtained from a similar online question, using MS Excel, indicates;

The mean of the Starnes GPA ≈ 3.212867

The standard deviation of Starnes GPA ≈ 0.364249

Mean of McGrail GPA ≈ 3.134722

The standard deviation of McGrail's GPA ≈ 0.357995

The null hypothesis is H₀: μ₁ - μ₂ = 0

The alternative hypothesis is Hₐ: μ₁ - μ₂ ≠ 0

The test statistic is found using the following formula;

\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } }\)

The decision rule is obtained with α = 0.05 and the null hypothesis is rejected t₀ ≤ -1.96 or t₀ ≥ 1.96

Therefore, we get;

\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{\dfrac{0.364249^2}{15}+\dfrac{0.357995^2}{18} } } \approx 0.618\)

The parameter for the degrees of freedom is 15 - 1 = 14

The critical value obtained from the t-table, at t.₉₅ is 1.761 which is larger than 0.618, therefore, we fail to reject the null hypothesis, and the evidence is insufficient to suggest that there is a difference in the average score of the two AP Statistics classes.

Taking the variance to be the same, we get;

\(S_p^2= \dfrac{(n_1-1)\cdot s_1^2+(n_2-1)\cdot s_2^2}{n_1+n_2-2}\)

Therefore;

\(S_p^2= \dfrac{(15-1)\times 0.364249^2+(18-1)\times 0.357995^2}{15+18-2}\approx 0.1302\)

\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{s_p^2 \times\left(\dfrac{1}{n_1}+\dfrac{1}{n_2} }\right) }\)

\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{0.1302\times \left(\dfrac{1}{15}+\dfrac{1}{18} }\right) } \approx 0.6195\)

df = 15 + 18 - 2 = 31

From the t-table, the critical value is about 1.697, which is larger than 0.6195, therefore, the null hypothesis cannot be rejected and the evidence available is not enough to suggest that there is a difference between the grade point averages of Mr. Starnes and Ms. McGrail AP Statistics classes and Mr. Starnes did not stack the class

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A) The new box with dimensions 10cm by 10cm by 3cm holds more cereal.

B) The new box with dimensions 10cm by 10cm by 3cm requires more material to make.

To determine which box holds more cereal, we need to calculate the volume of each box.

The volume of a rectangular box is given by the formula:

Volume = Length × Width × Height

Let's calculate the volumes for both boxes:

Original Box:

Length = 8 cm

Width = 3 cm

Height = 11 cm

Volume = 8 cm × 3 cm × 11 cm = 264 cm³

New Box:

Length = 10 cm

Width = 10 cm

Height = 3 cm

Volume = 10 cm × 10 cm × 3 cm = 300 cm³

A) The new box with dimensions 10cm by 10cm by 3cm holds more cereal because it has a larger volume of 300 cm³ compared to the original box with a volume of 264 cm³.

To determine which box requires more material to make, we need to calculate the surface area of each box.

The surface area of a rectangular box is given by the formula:

Surface Area = 2 × (Length × Width + Length × Height + Width × Height)

Let's calculate the surface areas for both boxes:

Original Box:

Length = 8 cm

Width = 3 cm

Height = 11 cm

Surface Area = 2 × (8 cm × 3 cm + 8 cm × 11 cm + 3 cm × 11 cm) = 374 cm²

New Box:

Length = 10 cm

Width = 10 cm

Height = 3 cm

Surface Area = 2 × (10 cm × 10 cm + 10 cm × 3 cm + 10 cm × 3 cm) = 380 cm²

B) The new box with dimensions 10cm by 10cm by 3cm requires more material to make because it has a larger surface area of 380 cm² compared to the original box with a surface area of 374 cm².

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Answer:

Step-by-step explanation:

a)     No of outcomes= 7

       total no of outcomes= 10

       probability = no of outcomes/total no of outcomes

       =7/10

b)     4/10 ( since the outcomes could be 1,2,3,4)

c)     no 1 to 10 has 5 odd numbers

       so, probability = 5/10 = 1/2

d)    multiples of 3 from 1 to 10 are :-

      3,6,9= 3 no's

      so probability = 3/10

Step-by-step explanation:

let the number be x

\(1 \div 3 \: of \: x \\ x \div 3 = 1 \div 2 \: of \: x - 6 \\ x \div 3 = x \div 2 - 6 \\ multiply \: both \: sides \: by \: the \: lcm \: 6 \\ x \div 3 \times 6 = x \div 2 \times 6 - 6 \times 6 \\ x \times 2 = x \times 3 - 36 \\ 2x = 3x - 36 \\ 2x - 3x = - 36 \\ - x = - 36 \\ divide \: both \: sides \: by \: - 1 \\ - x \div - 1 = - 36 \div - 1 \\ x = 36\)

The cost to rent each chair and table is $7.2 and $6.6 respectively.

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables that satisfies all such equations. This implies that the simultaneous equations have a common solution.

Let chairs = c

Let tables = t

5c + 3t = 36 --- 1

2c + 6t = 54 --- 2

From equation 2

2c + 6t = 54

c = 27 - 3t

Substitute c in equation 1

5(27 - 3t) = 36

135 - 15t = 36

135 - 36 = 15t

t = 99/15

t = $6.6

c = 27 - 3(6.6)

c = 27 - 19.8

c = $7.2

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B.) (-1, 3) , (3, 2)

Step-by-step explanation:

Not sure how to explan...

Answer: B: 3,2 A: -1,3

Step-by-step explanation:

To find the third side of an inequality of a triangle, you must first use the Triangle Inequality Theorem.

This theorem states that for any triangle, the sum of any two sides of the triangle must be greater than the third side. This means that in order to find the length of the third side, you must subtract the sum of the two known sides from the smaller of the two sides, then the length of the third side will be equal to the difference between these two numbers. For example, if two sides of a triangle have lengths of 4 and 3, the third side must be greater than 1 (4 + 3 = 7 and 4 - 3 = 1). Therefore, the length of the third side must be greater than 1.

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Answer:

x=5.59cm

Step-by-step explanation:

\(\frac{x}{12} =cos62\\x=12cos62\\\)

cos62°≈0.4695

x=12*0.4659

x=5.5908

x=5.59cm

Answer:

6.053

Step-by-step explanation:

Just try

Answer:

Wassup Fer :p

Answer:

Jenny drove for about 4.93 hours

Step-by-step explanation:

Jenny uses 7/9 gallons of gas per hour.

She used a total of 3 5/6 gallons.

If x is the number of hours she drove, then she used 7x/9 gallons.

X* 7/9 = 3 5/6

3 5/6 can be converted to an improper fraction.

((3*6)+5) / 6 = 23/6 gallons

=> x * 7/9 = 23/6

=> x = (23/6) / (7/9)

=> x = (23/6) * (9/7)

=> x = 69/14

=> x = 4.928571429 hours.

Answer:

x = -51/4

Step-by-step explanation:

3(x+4) = 7(x+9)

3x + 12 = 7x + 63

-4x = 51

x = -51/4

The mean of the distribution of the mean weight per fish based on the sampling is 1.50 pounds, and the standard deviation is 0.06 pounds.

These formulas can be used to calculate the mean and standard deviation of the sampling distribution of mean fish weight:

Mean of the mean weight per fish sampled across the distribution:

μ = μ = 1.50 pounds (mean weight of a single fish)

The sampling distribution's standard deviation for the mean fish weight is:

σ/√n = 0.3/√40 = 0.06 pounds (where n is the sample size and is the standard deviation of the weight of a single fish.)

So, The mean of the distribution of the mean weight per fish based on the sampling is 1.50 pounds, and the standard deviation is 0.06 pounds.

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Answer: x = 1 and y = 5

We already know that x=y-4 so place the value of, "x" in the first equation, -10x+3y=5. So solve the steps like this:

-10(y-4) + 3y = 5

-10y + 40 + 3y = 5

-7y= 5-40

-7y= -35

y= -35/-7

y= 5

Now place the value of y in the first equation.

-10x + 3(5) = 5

-10x + 15 = 5

-10x= 5-15

x= -10/-10

x= 1

So x is 1 and y is 5

Brainliest pls if i am correct!

The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.

In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.

To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.

In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.

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Answer:

the second option

yes, because they are similar triangles

Step-by-step explanation:

the scaling factor is 3

3×3 = 9

3×7 = 21

so, the ratios of the sides remain the same, and the 90 degree angle remains the same. therefore, just one triangle is larger than the other, but the relative attributes and even the orientation are the same, so yes, since we don't know the absolute coordinates of the corners, indeed, the Hypotenuse of both triangles could be on the same line.

Answer:

A'(5, 8)

B'(2, -1)

C'(-1, 2)

Explanation:

We need to rotate each point A, B, and C 90 degrees clockwise around point (1, 1). So, the angles formed in the following diagram are 90 degrees.

Therefore, the coordinates of points A', B' and C' are:

A'(5, 8)

B'(2, -1)

C'(-1, 2)

You should buy ingredients for 2400 cookies and you will end up eating 192 cookies while making 2400 cookies. This is how the problem can be solved by making use of given data and mathematical concepts.

(a) How many cookies should you buy ingredients for?Let's see how to solve the first part of the problem below:Given that, you have promised to bake 200 dozens of cookies.

Therefore,

Total cookies that you have to bake = 200 dozen x 12 = 2400 cookies

Now, you break and eat 8.0% of your cookies while making them.

So,Total cookies you will end up with = (100 - 8)% of 2400

= 92% of 2400

= 0.92 × 2400

= 2208

Therefore, you should buy ingredients for 2400 cookies.

(b) How many cookies will you be eating?

Now, you need to find out how many cookies will you be eating while making 2400 cookies. The number of cookies you will be eating

= 8% of 2400

= 0.08 × 2400

= 192 cookies

Therefore, you will end up eating 192 cookies while making 2400 cookies. To sum up the solution, you should buy ingredients for 2400 cookies and you will end up eating 192 cookies while making 2400 cookies. This is how the problem can be solved by making use of given data and mathematical concepts.

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The volume of ball is 32.49 cubic centimeter.

What is volume ?

 Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here ,

The volume of a ball = 32490 cubic millimeters

To convert into cubic millimeter into cubic centimeter by dividing by 1000, Then,

=>  32490/1000

=> 32.49 cubic centimeter.

Hence the volume of ball in cubic centimeter is 32.49 .

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The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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The floor area of the engineer's model of the sugar factory is 10.825 square feet.

To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.

The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.

To find the floor area, we multiply the length by the width:

Area = Length × Width

= 2.5 feet × 4.33 feet

= 10.825 square feet

It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.

In actuality, a sugar factory would have much larger dimensions.

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Answer:

41.8°, 138.2° and 401.8°

Step-by-step explanation:

Given the expression;

\(3sin^2x + 4sinx - 4 = 0\)

Let P = sinx

The expression becomes;

3P²+4P - 4 = 0

Factorize

3P²+6P-2P - 4 = 0

3P(P+2)-2(P+2) = 0

3P-2 = 0 and P+2 = 0

P = 2/3 and -2

When P = 2/3

sinx = 2/3

x = arcsin 2/3

x = arcsin 0.6667

x = 41.8 degrees

Also if P = -2

sinx = -2

x = arcsin (-2)

x will not exist in this case

To get other values of x

sin is positive in the second quadrant

x = 180 - 41.8

x = 138.2°

x = 360+41.8

x = 401.8°

Hence the values of x within the interval are 41.8°, 138.2° and 401.8°

a. The random variable represents the time which takes to completely tune an automobile engine.

b. The probability of tuning an engine is qual to 0.593, or 59.3%.

a. The random variable here is the time it takes to completely tune an engine of an automobile.

b. To find the probability of tuning an engine in 45 minutes or less,

Use the exponential distribution formula.

The exponential distribution is characterized by a rate parameter, which is the reciprocal of the mean.

The mean is 50 minutes,

The rate parameter (λ) can be calculated as λ

= 1/mean

= 1/50.

Using this rate parameter,

The probability of tuning an engine in 45 minutes or less by integrating the exponential probability density function (PDF) from 0 to 45 minutes,

P(X ≤ 45) = \(\int_{0}^{45}\)λ × \(e^{(-\lambda x)\) dx

Substituting the value of λ = 1/50 into the equation,

P(X ≤ 45) = \(\int_{0}^{45}\) (1/50) × \(e^{(-x/50)\) dx

Rewrite the integral:

P(X ≤ 45) = (1/50) ×  \(\int_{0}^{45}\)  \(e^{(-x/50)\) dx

Apply the integral,

P(X ≤ 45) = (1/50) × [-50 × \(e^{(-x/50)\)] evaluated from 0 to 45

Plug in the limits of integration,

P(X ≤ 45) = (1/50) × [-50 ×\(e^{(-45/50)\) - (-50 × \(e^{(-0/50)\))]

Simplify the expression,

P(X ≤ 45) = (1/50) × [-50 × \(e^{(-45/50)\)+ 50 × \(e^0\)]

Simplify further,

P(X ≤ 45) = -\(e^{(-45/50)\) + 1

Evaluate the expression,

⇒P(X ≤ 45) ≈ -\(e^{(-0.9)\) + 1

⇒P(X ≤ 45) ≈ -0.407 + 1

⇒P(X ≤ 45) ≈ 0.593

Therefore, the probability of tuning an engine in 45 minutes or less is approximately 0.593, or 59.3%.

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The inverse of log X is bˣ , where b is the logarithm's base.

Inverse Function[f][y] provides the value of x for which f[x] equals y. Inverse Function[f][y] represents the inverse of the function f. To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

Let us take,

n = log₁₀ X

Then, 10ⁿ = X

(assuming that the logarithm's base is 10)

If the logarithm's base is b, then it is bˣ.

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Answer:

2.6 minutes

Step-by-step explanation:

Speed of Bob = 8 km/hr

Speed of Shannon = 10 km/hr

Distance of practice course = 1.7 km

As time = (distance)/(speed), so

Time taken by Bob to cover the distance, t1 = 1.7/8=0.2125 hours

Time taken by Shannon to cover the distance, t2 = 1.7/10= 0.17 hours

As t1 > t2, so, Bob takes more time than Shannon to complete the course.

t1-t2= 0.2125-0.17 = 0.0425 hours = 0.0425 x 60 minutes= 2.55 minutes.

On rounding up to tenth digit, t1-t2 = 2.6 minutes.

Hence, It takes 2.6 minutes more time for Bob to complete one trip around the course than Shannon

Answer:

x=5

Step-by-step explanation:

x^2+25-10x = x^2-25

-x^2               -x^2

25-10x = -25

-25        -25

-10x = -50

x=5

lets check

(5-5)^2 = 5^2-25

0^2 = 25-25

0 = 0

Answer:

x = 5

Step-by-step explanation:

(x - 5)^2 = (x - 5) (x - 5) =

x^2 -10x + 25 = x^2 - 25

x^2 - x^2 - 10x + 25 = - 25 (x^2 - x^2 = 0)

- 10x + 25 = - 25

- 10x = - 25 - 25

x = - 50/- 10

x = 5

Answer:

\(y = -x +2\)

Step-by-step explanation:

\(\text{Given that,}\\\\~~~~~~~~~~x^3 +y^3 = 2xy\\\\\implies \dfrac{d}{dx}(x^3 +y^3) = 2\dfrac{d}{dx}(xy)\\\\\implies 3x^2 +3y^2 \dfrac{dy}{dx} = 2 \left( y + x\dfrac{dy}{dx}\right)\\\\\implies 3x^2 + 3y^2 \dfrac{dy}{dx} = 2y + 2x\dfrac{dy}{dx}\\\\\implies 3y^2 \dfrac{dy}{dx}-2x \dfrac{dy}{dx} = 2y - 3x^2\\\\\implies (3y^2 -2x) \dfrac{dy}{dx} = 2y-3x^2\\\\\implies \dfrac{dy}{dx} = \dfrac{2y-3x^2}{3y^2 -2x}\\\)

\(\text{At (1,1),}\\\\\text{Slope,}~ m = \dfrac{dy}{dx}\\\\~~~~~~~~~~~~~=\dfrac{2(1) -3(1^2)}{3(1^2) -2(1)}\\\\~~~~~~~~~~~~~=\dfrac{2-3}{3-2}\\\\~~~~~~~~~~~~~=\dfrac{-1}{1}\\\\~~~~~~~~~~~~~=-1\)

\(\text{Equation of tangent line,}\\\\~~~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -1 = -1(x-1)\\\\\implies y -1 = -x+1\\\\\implies y = -x +1+1\\\\\implies y = -x +2\)