11. Jessica is buying several bunches
of bananas to make desserts for a
fundraiser. She can buy 10 pounds
of bananas for $14.90 or 8 pounds
of bananas for $12.08. Which is the
better buy? Explain.

The Excel function used when deciding to reject or fail to reject the null hypothesis is the T.TEST function.

This function is used to calculate the probability of obtaining the observed results or more extreme results, assuming that the null hypothesis is true. If the probability, also known as the p-value, is less than the significance level, typically 0.05, the null hypothesis is rejected, and it is concluded that there is sufficient evidence to support the alternative hypothesis.

Otherwise, if the p-value is greater than the significance level, the null hypothesis is not rejected, and it is concluded that there is not enough evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the level of significance (alpha) chosen for the test, typically 0.05 or 0.01, then the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the chosen alpha level, then the null hypothesis is not rejected.

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Answer:

99 ÷ 9 equal 11

Step-by-step explanation:

99 ÷ 9 = 11. yeah

It will take 3 years for the value of the computer of initial value $1000 to reach $512.

Given, Timothy purchased a computer for $1,000.

The value of the computer depreciates by 20% every year.

we have to find the number of years value of computer will take to reach $512.

Let, the function representing this situation be,

V(t) = AB^t

where, A is the initial value of the computer and B is the depreciating rate.

So, V(t) = (1000)(1 - 20/100)^t

V(t) = (1000)(0.8)^t

Now, the value will be, 512

512 = 1000(0.8)^t

0.512 = (0.8)^t

t = 3

So, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

Hence, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

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Answer:

43650 rupees

Step-by-step explanation:

Discount = D

Tax : T

D = 15% of 45000

D = (45000 x 15) ÷ 100

D = 675000 ÷ 100

D = 6750 rupees

The price after the discount :

45000 - 6750 = 38250 rupees

T = 12% of 45000

T = (45000 x 12) ÷ 100

T = 540000 ÷ 100

T = 5400 rupees

Melissa will pay :

 (45000 - 6750) + 5400

= 38250 + 5400

= 43650 rupees

Answer:

\( \sf \: a) \: 27 = 9p \: ; p = 3\)

Step-by-step explanation:

Given information,

→ Simon have 27 pieces of candy.

→ Each person will get 9 pieces.

Now we have to,

→ Find the required equation.

The equation will be,

→ 27 = 9p

→ 9p = 27

=> As each person (p) gets 9 pieces.

Then the value of p will be,

→ 9p = 27

→ p = 27 ÷ 9

→ [ p = 3 ]

Hence, option (a) is correct.

Answer:

The probability of choosing 2 girls from a list of 6 girls and 6 boys can be calculated using combinations.

The number of combinations of choosing 2 girls out of 6 girls is given by the formula: C(6,2) = 6! / (6-2)!2! = 15.

So, the probability of choosing 2 girls is 15 / (C(12,2) = 66) = 15/66 = 5/22.

Therefore, the probability of Mr. Mackinson choosing 2 girls to lead the class field trip is 5/22 or approximately 0.227.

Answer:

c

Step-by-step explanation:

7^5 means that there are 5 7s eg 2^4 would be 2×2×2×2

Answer:

Weathering

Step-by-step explanation:

Weathering is the physical and chemical breakdown of rock at the earth's surface.  The physical breakdown of rock involves breaking rock down into smaller pieces through mechanical weathering processes. These processes include abrasion, frost wedging, pressure release (unloading), and organic activity.

Answer: I would like to say this is the act of weathering

Step-by-step explanation:

I hope this helps

Have a great day :)

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\(( x + 1 ) ^ { 2 } - 5 x ( x + 3 ) ( x - 3 )\)

Use binomial theorem \(\left(a+b\right)^{2}=a^{2}+2ab+b^{2}\) to expand \(\left(x+1\right)^{2}\).

\(x^{2}+2x+1-5x\left(x+3\right)\left(x-3\right) \)

Use the distributive property to multiply -5x by x+3.

\(x^{2}+2x+1 + (-5x^{2}-15x)(x-3)\)

Use the distributive property to multiply \(-5x^{2}-15x\) by x-3 and combine like terms.

\(x^{2}+2x+1-5x^{3}+45x \)

Combine 2x and 45x to get 47x.

\( \boxed{\boxed{\bf\:x^{2}+47x+1-5x^{3} }}\)

Follow the same steps till \(x^{2}+2x+1-5x^{3}+45x \) and then use the algebraic identity ⇨ a + 2ab + b² = (a + b)²

\(\boxed{\boxed{\bf\:-5x^{3}\left(x+1\right)^{2}+45x}}\)

Answer:

24

Step-by-step explanation:

The sum of the three angles in a triangle is always 180 degrees.

Let x be the measure of the third angle.

Then we have:

102 + 54 + x = 180

Simplifying the left side:

156 + x = 180

Subtracting 156 from both sides:

x = 180 - 156

x = 24

Therefore, the measure of the third angle is 24 degrees.

The probability that a randomly selected point within the circle falls in the white area is frac{1}{4} + frac{1}{{2pi }.

The diameter of the circle is 12 units, and the radius is 6 units.

The area of the circle can be calculated by using the formula of the area of a circle: [A = pi {r^2}]

So, the area of the circle will be:\([A = pi {(6)^2} = 36pi ]\)

The white area can be divided into two parts: a sector and a triangle.

The sector has a central angle of 90° and the radius is 6 units.

So, the area of the sector will be: \([{A{sector}} = frac{90}{360} times pi {(6)^2} = 9pi ]\)

The triangle has a base of 6 units and a height of 6 units.

So, the area of the triangle will be:\([{A{triangle}} = frac{1}{2} times 6 times 6 = 18]\)

Therefore, the area of the white region will be: [{A{white}} = {A{sector}} + {A{triangle}} = 9pi + 18]

Now, we can find the probability that a randomly selected point within the circle falls in the white area by dividing the area of the white region by the area of the circle.

So, we have: \([begin{aligned} P(text{White Area}) = frac{{{text{Area of white region}}}}\)

                     {Area of the circle} =\(frac{9pi + 18}{36pi }\)

                                                     =\(frac{pi  + 2}{4pi }\)

                                                     =\(frac{pi }{4pi} + frac{2}{4pi}\)

                                                     =\(frac{1}{4} +frac{1}{{2pi}\)

Therefore, the probability that a randomly selected point within the circle falls in the white area is \(frac{1}{4} + frac{1}{2pi }.\)

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Find the probability that a randomly selected point within the circle falls in the white area. Ir = 4 cm a = 3.2 cm S = 4.7 cm [?]% Round to the nearest tenth of a percent.

The probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, is 52/217.

To find the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, we can use conditional probability.

Let's define the following events:

A: Applicant has a graduate degree

B: Applicant has over 5 years of experience

We are given:

P(B) = 217/493 (probability of having over 5 years of experience)

P(A ∩ B) = 52/493 (probability of having over 5 years of experience and a graduate degree)

The probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience can be calculated using the formula for conditional probability:

P(A | B) = P(A ∩ B) / P(B)

Plugging in the values:

P(A | B) = (52/493) / (217/493)

P(A | B) = 52/217

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, is 52/217.

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the original equation is:

So we know that a parallel line will have the same slope, so we can calculate the intercept with the slope and the coordinate (35,30)

Answer:

(c) The equation, y = -3x + 100, represents the Model S tank.

(f) The Model T tank drains the fastest at 3.5 gallons per minute.

Step-by-step explanation:

Given

See attachment for models S and T

First, we calculate the equation of both models

Model S

\((x_1,y_1) = (0,100)\\\\(x_2,y_2) = (6,82)\)

Calculate drainage rate (m)

\(m = \frac{y_2 - y_1}{x_2 -x_1}\)

\(m = \frac{82-100}{6-0}\)

\(m = \frac{-18}{6}\)

\(m = -3\) -- This implies that model S drains at 3 gallons per minutes

The equation is:

\(y = m(x - x_1) + y_1\)

\(y = -3(x - 0)+100\)

\(y = -3(x)+100\)

\(y = -3x+100\)

Model T

\((x_1,y_1) = (0,100)\\\\(x_2,y_2) = (4,86)\)

Calculate drainage rate (m)

\(m = \frac{y_2 - y_1}{x_2 -x_1}\)

\(m = \frac{86-100}{4-0}\)

\(m = \frac{-14}{4}\)

\(m = -3.5\) -- This implies that model T drains at 3.5 gallons per minutes

The equation is:

\(y = m(x - x_1) + y_1\)

\(y = -3.5(x - 0)+100\)

\(y = -3.5(x)+100\)

\(y = -3.5x+100\)

From the calculations above, the following options are true:

(c) and (f)

It is required to find which statements are true.

The statements that are true are

The equation, y = -3x + 100, represents the Model S tank.

The Model T tank drains the fastest at 3.5 gallons per minute.

Equation of a line is

\(y=mx+c\)

where,

\(y=\text{Gallons of water left}\)

\(x=\text{Minutes passed}\)

\(m=\text{Slope}=\dfrac{\Delta y}{\Delta x}\)

\(c=\text{Y intercept}\)

The equation of the line for model S is

\(y-100=\dfrac{82-100}{6-0}(x-0)\\\Rightarrow y-100=-3x\\\Rightarrow y=-3x+100\)

The option C is true.

The equation of the line for model T is

\(y-100=\dfrac{86-100}{4-0}(x-0)\\\Rightarrow y-100=-3.5x\\\Rightarrow y=-3.5x+100\)

The slope or rate of drain is 3.5 gallons per minute.

So, option F is true.

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The expected value of probability gain when a person buys one ticket is $-7.64.

The expected value of gain when a person buys one ticket is $-0.50.

Explanation:

Given that, A lottery offers one $1000 prize, one $500 prize, and four $200 prizes. One thousand tickets are sold at $3.00 each. We need to find the expected value of gain if a person buys one ticket.

The probability of winning a $1000 prize = 1/1000

The probability of winning a $500 prize = 1/1000

The probability of winning a $200 prize = 4/1000

The probability of winning nothing = 994/1000

We need to find the expected value of gain when a person buys one ticket.

The expected value of gain = (probability of winning a $1000 prize) × (gain of $1000) + (probability of winning a $500 prize) × (gain of $500) + (probability of winning a $200 prize) × (gain of $200) + (probability of winning nothing) × (gain of nothing)

The gain of nothing is equal to the cost of the ticket = $3The expected value of gain = (1/1000) × $1000 + (1/1000) × $500 + (4/1000) × $200 + (994/1000) × (-$3)=$1+$0.50+$0.80+(-$9.94)=$-7.64

The expected value of gain when a person buys one ticket is $-7.64.

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Answer:

(2,-3) changes to (3,2)

A is correct.

Step-by-step explanation:

Given: The point (2, −3) after a counterclockwise rotation of 90° about the origin.

Rotation is counterclockwise about origin.

We are given coordinate

We can see in diagram also. Please see the attachment for rotation.

Hence, (2,-3) changes to (3,2

Answer: It is equidistant from the segment's endpoints

Step-by-step explanation:  This can also be called "a locus of point" and this is now the perpendicular bisector theorem.

The option that best describes the value 1.5 in the linear equation; u = 0.75·t + 1.5 is option D

D. y-intercept and the initial amount of rain, in inches at midnight

A linear equation is an equation of the form; y = m·x + c, where, m is the slope, and c is the y-intercept of the graph of the equation.

The time at which the analysis of the rainstorm by the meteorologist starts = 10 p. m.

The linear model for the accumulation of rain is; u = 0.75·t + 1.5

The number of hours, t after midnight where; t > 0

The model for the accumulation of rain, indicates that the coefficient of t, which is 0.75 is the rate at which the rain accumulates in inches per hour, therefore, the rain accumulates at a rate of 0.75 inches per hour

The constant term in the linear equation, u = 0.75·t + 1.5, which is the constant, 1.5, is the y-intercept of the graph of the equation.

The y-intercept is the value of the equation, when the input value, the time, t = 0, which is the time at midnight

The 1.5 therefore, indicates that the y-intercept, and the level of the accumulated rain at midnight, when the time, t = 0, which is the initial amount of rain at midnight is 1.5 inches.

The correct option is therefore;

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Answer:  the total cost of the meal is $19.35.

Step-by-step explanation

To fully answer this question, I would need the information presented in Figure 3.14 that provides the computer solution. Unfortunately, I cannot access or view specific figures or external sources. However, I can explain the general approach to solving such a problem and provide a LaTeX code snippet to format the question.

To solve the given problem, it appears to be a linear programming problem where the goal is to optimize the total annual return subject to certain constraints. The decision variables are the number of shares of US Oil (U) and Huber Steel (H) to be purchased.

a. The optimal solution would provide the values of U and H that maximize the total annual return while satisfying the given constraints. The value of the total annual return would be the objective function value at the optimal solution.

b. The binding constraints are those that are active and determine the solution. These constraints limit the risk index, the total investment amount, and the maximum number of shares of US Oil. Interpretation of these constraints would depend on the specific problem and its context.

c. The dual values for the constraints represent the marginal values or shadow prices associated with each constraint. They indicate the rate of change in the objective function value for a small change in the right-hand side of the constraint. Interpretation of dual values would also depend on the specific problem and its context.

d. The impact of increasing the maximum amount invested in US Oil would depend on the objective function and the constraints. It could lead to a higher total annual return if US Oil has a higher return rate and the constraint on the risk index or total investment amount allows for it. However, if the maximum number of shares of US Oil is already binding, increasing the maximum investment amount would not be beneficial.

Please provide any additional information or specific values from Figure \(3.14\) if you have access to it, and I can assist further.

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we know that

Supplementary angles sum 180 degrees

so in this problem

120 and 60and 60

Answer:

you need a dotted point starting at 3 and going to to the right

Step-by-step explanation:

the dotted point means x < , x > and since it is greater you always go to the right

Answer:

5.52 inch

Step-by-step explanation:

Recall :

Area of Sector : θ/ 360 * πr²

Sectors that do not allow movement : (8-3-2) = 3

Total sectors = 8

θ/ 360 = 3/8 ; Area = 35.9

Radius = r

35.9 = 3/8 * π * r²

35.9 / (3/8 * π) = r²

30.472866 = r²

r = √30.472866

r = 5.52 inch

The radius of the spinner is 5.520 inch whose  \(\frac{3}{8}\)  sector area is 35.9 inches square.

It is given that the spinner used in a board game is divided into 8 equally sized sectors. three sectors indicate that the player should move his token forward on the board, two sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board and its area of the sector is 35.9 inches square.

It is required to find the radius of the spinner.

The region enclosed by the two radii of a circle and the arc is known as a sector's area. In other words sector area is a portion of the circle's area.

We know the formula of sector area (A):

\(\rm A= \frac{\theta}{360 \°} \pi r^2\)    Where 'r' is the radius of the circle and \(\rm \theta\) is in degree

The remaining sectors = ( Total sectors - Three sectors - Two sectors)

= ( 8 - 3 - 2) ⇒ 3 sectors indicate the player do not move his token

Total sector = 8

\(\rm \frac{\theta }{360 \° } = \frac{3}{8} \ when \ A = 35.9 \ inches^2\)

Putting these values in the above formula, we get:

\(\rm 35.9 = \frac{3}{8} \pi r^2\\\rm 35.9\times 8 = 3\pi r^2\\\rm 287.2 = 3\pi r^2\\\\\rm \frac{287.2}{3} = \pi r^2\\\\\rm 95.733= \pi r^2\\\rm 30.4728 = r^2\)Where \(\rm \pi\) = 3.14159

\(\sqrt{30.4728} = r\\\rm 5.520= r \\\rm or = 5.520 \ inch\)

Thus, the radius of the spinner is 5.520 inch.

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The system of equation that can be used to represent the number of meals sold is

x + y = 1000

5x + 10y = 3,500

Given:

Number of $5 meals sold = x

Number of $10 meals sold = y

Total number of meals = 1000

Total amount of meals = $3,500

The equations:

Quantity

x + y = 1000

Price

5x + 10y = 3,500

Therefore, the system of equation that can be used to represent the number of meals sold is

x + y = 1000

x + y = 10005x + 10y = 3,500

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Answer:

(c) n = 76

Step-by-step explanation:

a straight line is 180

the angle given is 104

180 - 104 = 76!!

your answer would be c!!

The total number of laps Sarah should run today is given by the equation A = 16 laps

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of laps be represented as A

Now , the equation will be

The total distance ran by Sarah yesterday = 3,682 m

The distance of one lap = 263 m

So , the number of laps ran by Sarah yesterday = total distance ran by Sarah yesterday / distance of one lap

Substituting the values in the equation , we get

The number of laps ran by Sarah yesterday = 3682 / 263

The number of laps ran by Sarah yesterday = 14 laps

Now ,

The distance Sarah wants to run today = 4,222 m

So , the number of laps Sarah should run today A = distance Sarah wants to run today / distance of one lap

Substituting the values in the equation , we get

The number of laps Sarah should run today A = 4,222 / 263

The number of laps Sarah should run today A = 16.05 laps

The number of laps Sarah should run today A = 16 laps

Therefore , the value of A is 16 laps

Hence , the number of laps is 16 laps

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Answer:

15.1

Step-by-step explanation:

The Pythagorean theorem is

a^2 +b^2 = c^2

23^2 + b^2 = 27.5^2

529 +b^2 =756.25

Subtract 529 from each side

529-529+b^2 =756.25-529

b^2 =227.25

Take the square root of each side

b =sqrt(227.25)

b =15.07481343

To the nearest tenth

b = 15.1

Answer:

15.1

Step-by-step explanation:

Answer:

Answer is D hope this helps :)

Step-by-step explanation: