Truman is buying a teddy bear and flowers for his girIfriend. Flowers Galore charges $13 for the teddy bear and $0. 75 per flower. Famous Florist charges $9 for the teddy bear and $1. 25 per flower. Which inequality represents the number of flowers, f, Truman would need to buy to make Flowers Galore the cheaper option?

Answers

Answer 1

The inequality represents the number of flowers, Truman would buy at Flowers Galore is f < 8.

Price of teddy bear = $13

Price of the flower = $0. 75

Florist charges the price of a teddy bear = $13

The florist charges the price of the flower = $1.25

Assume that number of flowers Truman buys = f

The total cost of purchasing teddy bears and flowers at Flowers Galore =

C1 = 13 + 0.75f

The total cost of purchasing teddy bears and flowers at  Famous Florist is C2 = 9 + 1.25f

The inequality for Flowers Galore can be written as:

C1 < C2

13 + 0.75f < 9 + 1.25f

0.5f < 4

Dividing on both sides by 0.5,

f < 8

Therefore, we can conclude that the inequality represents the number of flowers, Truman would buy is f < 8.

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Related Questions

Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.

Answers

The values of the inverse trigonometric functions are 72°, 76° and 85°.

How to explain the steps

The range of the inverse trigonometric function is limited to a certain interval based on the domain of the original trigonometric function.

Its also important to identify the trigonometric ratio that corresponds to the given value.

The value on degree for inverse of sin (2/3) will be 41.81° which is 42°. Also, inverse of tan(4) is 76° using the calculator.

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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.

inverse of sin (2/3)

inverse of tan(4)

inverse of tan (0.1)

Let f:R → R be a function that satisfies ∫f(t)dt then the value of f(log e 5) is

Answers

Unfortunately, I cannot provide an answer to this question as it is incomplete. The given information ∫f(t)dt is not enough to determine the value of f(log e 5). More information about the function f would be needed, such as its explicit form or additional properties. Please provide more context or information to help me answer your question accurately.
Given that f is a function f:R → R that satisfies ∫f(t)dt, we need to find the value of f(log e 5).

By definition, log e 5 is the natural logarithm of 5, which can be written as ln(5). Therefore, we want to find the value of f(ln(5)).

However, without further information on the function f or the integral bounds, it's not possible to determine the exact value of f(ln(5)). Please provide more details about the function or the integral to get a specific answer.

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How to find the area of this whole figure? Please help me

Answers

The area of the whole figure is 31.5 sq. units.

What is the area of a figure?

The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.

From the given question, the figure given can be likened to a rhombus. So that;

area of a rhombus = (diagonal 1 * diagonal 2)/ 2

Then,

area of the figure = (diagonal 1 * diagonal 2)/ 2

where: diagonal 1 = 7.5, and diagonal 2 = 8.4

So that;

area of the figure = (7.5*8.4)/ 2

                             = 63/ 2

                             = 31.5

The area of the whole figure is 31.5 sq. units.

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The probability that Sam parks in a no-parking zone and gets a parking ticket is 0. 07,and the probability that Sam Connor finr a legal parking space and has to park in the no-parking zone is 0. 50. On Monday,Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket.

Answers

The probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.

We can use Bayes' theorem to solve this problem. Let A be the event that Sam gets a parking ticket and B be the event that Sam parks in a no-parking zone. Then, we want to find P(A|B), which is the conditional probability of A given B.

Bayes' theorem states that P(A|B) = P(B|A)*P(A)/P(B), where P(B|A) is the probability of B given A, P(A) is the prior probability of A, and P(B) is the prior probability of B.

From the problem, we know that P(A) = 0.07, P(B|A) = 1 (since if Sam parks in a no-parking zone, he will definitely get a parking ticket), and P(B|not A) = 0.50 (since if Sam finds a legal parking space, he has a 0.50 probability of parking in a no-parking zone).

To find P(B), we can use the law of total probability, which states that P(B) = P(B|A)*P(A) + P(B|not A)*P(not A), where P(not A) = 1 - P(A).

Therefore, P(B) = 10.07 + 0.50(1-0.07) = 0.5351.

Finally, we can use Bayes' theorem to find P(A|B):

P(A|B) = P(B|A)P(A)/P(B) = 10.07/0.5351 ≈ 0.1308.

Therefore, the probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.

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On Friday, Jacob planted a pinto bean in science class. When he returned to school on Monday, the bean had sprouted a stem that was 3 millimeters long. At the end of the week, Jacob's bean sprout had a stem that was 42 millimeters long. How many centimeters did Jacob's bean sprout grow during the week?

Answers

Jacob's bean sprout grew 3.9 centimeters during the week.

What is measurements?

Measurements in math involve the assignment of numerical values to physical quantities, such as length, area, volume, mass, time, temperature, and so on. Measuring objects or events allows us to compare and quantify them, and is an essential part of mathematical problem-solving, as well as many other fields of study

Jacob's bean sprout grew 42 millimeters - 3 millimeters = 39 millimeters during the week.

To convert millimeters to centimeters, we need to divide by 10 since there are 10 millimeters in 1 centimeter.

So, the growth in centimeters is 39 millimeters ÷ 10 = 3.9 centimeters.

Therefore, Jacob's bean sprout grew 3.9 centimeters during the week.

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A string has a length of 80 cm. It is cut into pieces in the ratio 1: 4: 5. Calculate the length of the longest piece.

Answers

First, we need to find the total number of parts in the ratio 1:4:5:

1 + 4 + 5 = 10

This means that the string is divided into 10 equal parts. To find the length of each part, we divide the total length of the string by the number of parts:

80 cm ÷ 10 = 8 cm

Now, we can find the length of the longest piece, which is 5 times the size of each part:

8 cm x 5 = 40 cm

Therefore, the length of the longest piece is 40 cm.

The function f(x) = 2x + 7x{-1} has one local minimum and one local maximum. This function has a local maximum at x = with value and a local minimum at x = with value

Answers

The function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.

To find the local maximum and minimum of the function f(x) = 2x + 7x⁻¹, we need to find the critical points of the function and then use the second derivative test to determine if they are local maxima or minima.

First, we find the derivative of f(x):

f'(x) = 2 - 7x⁻²

Setting f'(x) = 0, we get:

2 - 7x⁻² = 0

Solving for x, we get:

x = ±√(2/7)

Next, we compute the second derivative of f(x):

f''(x) = 14x⁻³

At x = ±√(2/7), we have:

f''(±√(2/7)) = ±∞

Since f''(±√(2/7)) has opposite signs at the critical points, ±√(2/7), we conclude that f(x) has a local maximum at x = -√(2/7) and a local minimum at x = √(2/7).

To find the values of the local maximum and minimum, we plug them into the original function:

f(-√(2/7)) = 2(-√(2/7)) + 7/(-√(2/7)) = -3√14

f(√(2/7)) = 2(√(2/7)) + 7/(√(2/7)) = 3√14

Therefore, the function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.

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Find the slope of the line

Answers

Answer:

m = -2

Step-by-step explanation:

We Know

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-3,2) (-2,0)

We see the y decrease by 2, and the x increase by 1, so the slope is

m = -2

The slope is -2 that’s the answer

A pyramid has a base that is a regular hexagon with each side measuring 10 units. The base of the pyramid is shown below.If the pyramid has a height of 12 units, what is the approximate volume of the pyramid?

Answers

Answer:

Step-by-step explanation:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * Base Area * Height

To calculate the volume of this pyramid, we need to first find the area of its regular hexagonal base. The formula for the area of a regular hexagon is:

A = (3√3/2) * s^2

where s is the length of one side of the hexagon. Substituting s = 10, we get:

A = (3√3/2) * 10^2 = 259.80 square units (approx)

Now we can use the formula for the volume of a pyramid to find the volume of this pyramid:

V = (1/3) * 259.80 * 12 = 1039.20 cubic units (approx)

Therefore, the approximate volume of the pyramid is 1039.20 cubic units.

Can someone help me please

Answers

Answer:

A

Step-by-step explanation:

Simple interest gains interest only on the principal sum and so each year has the same interest. So, this example is not simple interest. Compound interest is calculated on the principal and the accumulated interest of the previous years. So, this is compound interest.

      Interest is 4%.

      [tex]A = P*(1 + R \%)^n[/tex]

Here A is the amount we receive after n years, P is the principal and R is the rate of interest.

        A = $1300 , R = 4%

            [tex]1300 = P * (1+0.04})\\\\1300 = P * 1.04\\\\\dfrac{1300}{1.04}=P\\\\\\\dfrac{130000}{104}=P[/tex]

            P = $ 1250

Here is a set of data showing the test scores for US History class:


56, 88, 70, 72, 90, 85, 99, 65, 66, 54, 74, 85, 91, 92, 72, 88, 97, 62, 88 Create a stem and leaf plot to show this data. Hint: Decide how many stems you will need.


can somebody help me ?

Answers

Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.

Step 1: Arrange the data in ascending order.


54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99

Step 2: Determine the range of the data.


The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.

Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).

5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9

Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.

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4. Use the data below for the calculations.
Average hours sleeping per weeknight: 4, 5, 8, 12, 10, 6, 7, 9, 8, 8, 6, 6, 4, 3, 9
Mean:

Median:

Mean Absolute Deviation:


Absolute Deviation from Median:

Answers

The mean is 7

The median is the middle value, which is 7.

Mean Absolute Deviation: 2

How to solve for the mean absolute deviation

Step 3: Find the absolute deviation of each value from the mean:

|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|

These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.

Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:

Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2

Step 5: Find the absolute deviation of each value from the median:

|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|

These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.

Therefore, the absolute deviation from the median is 5.

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The cone is formed from 3,200 ft3 of gravel. If the height of the cone is 24 feet, what is the radius, in feet, of the base of the cone? Use the π button on your calculator to determine the answer. Round your answer to the nearest tenth of afoot. The radius of the base of the cone is approximately ____ feet

Answers

The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.

Height of cone =  24 feet

The volume of the cone = [tex]3,200 ft^3[/tex]

To find the volume of the cone, the formula used here is:

V =π* [tex]r^2h[/tex]

Here, the values of V and H are known terms. we need to calculate the radius r of the cone.

π = 3.14 constant value

Substituting the values in the above equation, we get:

[tex]3,200 = (1/3)^2*(24)*[/tex] π

[tex]r^2[/tex]= 3,200 / (8π)

[tex]r^2[/tex] = 400 / π

r = 12.65

Therefore, we can conclude that the radius of the base of the cone is  12.65 feet.

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In the formula


A(t) = Pert for continuously compound interest, the letters P, r, and t stand for ---Select--- percent interest prime rate amount after t years principal number of years , ---Select--- interest rate per year rate of return investment amount investment per year interest rate per day , and ---Select--- number of months number of days number of time periods number of years number of times interest is compounded per year , respectively, and A(t) stands for ---Select--- amount of principal amount after t days amount of interest earned after t years amount of interest earned in year t amount after t years. So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $. (Round your answer to the nearest cent. )

Answers

In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for Principal, rate of interest, and time respectively, and A(t) stands for Amount after t amount of time.  If $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $225.5.

The formula for Compound Interest at a continuous period of time is denoted by [tex]A(t) = Pe^{rt}[/tex]

where the Principal amount is multiplied by the exponential value of the interest rate and time passed.

Hence we are given here

P = $200, r = 4% = 0.04, and the amount to be calculated for t = 3 years

Hence we will find the amount by replacing these values to get

A(3) = 200 × e⁰°⁰⁴ ˣ ³

= $200 × e⁰°¹²

= $225.499

rounding it off to the nearest cent gives us

$225.5

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Correct Question

In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for ______ , _______ , and __________ respectively, and A(t) stands for _______ .

So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $__________. (Round your answer to the nearest cent.)

Find the area of the polygon.
18 m
29 m
36 m
The area of the polygon is 14
14 m
square meters.

Answers

The total area of the composite figure is 576 square meters

Calculating the area of the polygon figure

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Surface area = Rectangle + Trapezoid

Using the area formulas, we have

Surface area = 29 * 16 + 1/2 *(14 + 18) * (36 - 29)

Evaluate

Surface area = 576

Hence. the total area of the figure is 576 square meters

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Complete question

Find the area of the polygon.

See attachment

The area of the polygon is ____ square meters.

Ralph's t-shirt company sells custom t-short for $5. 00 each plus a $20 shipping and design fee. Frank's t-shirt company sells t-shirts for $10 each with no additional fees

Answers

To compare Ralph's and Frank's t-shirt companies, let's calculate the total cost of buying a certain number of t-shirts from each company.

1. Ralph's t-shirt company:

- Price per t-shirt: $5.00

- Shipping and design fee: $20.00

Total cost for Ralph's t-shirts = (number of t-shirts * $5.00) + $20.00

2. Frank's t-shirt company:

- Price per t-shirt: $10.00

- No additional fees

Total cost for Frank's t-shirts = number of t-shirts * $10.00

Now you can compare the total costs for each company depending on the number of t-shirts you want to buy.

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When solving two-step equations, you are using the reverse order of operations to solve the two-step equations.

Select one:
True
False

Answers

Therefore , the solution of the given problem of equation comes out to be False.

What is an equation?

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

False.

The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,

which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:

=> 2x + 5 = 11

To get the following result, we would first subtract 5 from both sides, then divide by 2.

=> x = 3

In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.

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Every time you practice, you gain more skills.



Conditional:


Hypothesis:


Conclusion:


Converse:


Inverse:


Contrapositive:

Answers

Hypothesis: Every time you practice, you gain more skills.

What happens when you practice?

Conclusion: Gain of skills is a result of practice.

Converse: If you gain more skills, then you practice every time.

Inverse: If you don't practice, then you don't gain more skills.

Contrapositive: If you don't gain more skills, then you don't practice every time.

The hypothesis states that practicing leads to an increase in skills. This can be interpreted as a cause and effect relationship between the two variables.

The conclusion reiterates that gaining skills is a result of practice.

The converse of the statement flips the order of the hypothesis and the conclusion. It states that if you gain more skills, then you must have practiced every time.

This may not be entirely true because there can be other factors that contribute to the gain of skills besides practice.

The inverse of the statement negates both the hypothesis and the conclusion. It states that if you don't practice, then you don't gain more skills.

This statement is true because practice is a necessary condition for gaining skills. However, it doesn't mean that practicing alone guarantees the gain of skills.

The contrapositive of the statement flips the order of the negated hypothesis and the negated conclusion. It states that if you don't gain more skills, then you didn't practice every time.

This statement is also true because if one doesn't practice, they cannot expect to gain more skills.

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A three digit number is such that twice the hundreds digit is more than the tens digit by 2. The unit digit is thrice the hundred digit. When the digits are reversed the number is increased by 594. Find the number.(5 marks)

Answers

Answer:

Step-by-step explanation:

Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.

From the problem, we have two equations:

Equation 1: $2a=b+2$

Equation 2: $c=3a$

We can use these equations to solve for $a$, $b$, and $c$.

Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.

Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.

Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.

Thus, the original three-digit number is $abc=824$.

When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.

Therefore, the answer is $\boxed{824}$.

I NEED HELP PLEASE!

1. 3 statements about limiting frictional force between two surfaces are given below.


A - Nature of surfaces in contact affects to limiting frictional force.

B - Normal reaction between them affects to limiting frictional force.

C - Area of surfaces in contact affects to limiting frictional force.


Correct statement / statements from above A, B, C is/ are,

(1) A

(2) B

(3) A and C

(4) A, B and C

Answers

The correct statement is (3) A and C.

The limiting frictional force between two surfaces is dependent on the nature of the surfaces in contact and the area of the surfaces in contact. The normal reaction between them is not a factor affecting the limiting frictional force.
Let's analyse the options:Option 1: Statement A is correct. The nature of surfaces in contact determines the friction between them. Rough and irregular surfaces have higher friction than smooth surfaces.Option 2: Statement B is incorrect. The normal reaction between the surfaces does not affect the limiting frictional force. Only the maximum static friction depends on the normal reaction.Option 3: Statements A and C are correct. Both nature of surfaces and area of contact determine the friction between them.Option 4: All statements A, B and C are incorrect. Nature of surfaces, normal reaction and area of contact affect the limiting frictional force between two surfaces.

The limiting frictional force depends only on:

A. The nature of surfaces in contact: Rough and irregular surfaces have higher friction than smooth surfaces. C. The area of surfaces in contact: Larger the contact area, higher is the friction between the surfaces.(3) A and C is the right option

PLEASE HELP WILL GIVE BRAINLEST !!!!

Answers

The answer is the first one.

AH = Actual Hours SH = Standard Hours AR = Actual Rate SR = Standard Rate Compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable or no variance

Answers

To compute the direct labor rate and efficiency variances, we will use the given terms: Actual Hours (AH), Standard Hours (SH), Actual Rate (AR), and Standard Rate (SR). Here's a step-by-step explanation:

Step 1: Calculate the Actual Labor Cost
Actual Labor Cost = AH * AR

Step 2: Calculate the Standard Labor Cost
Standard Labor Cost = SH * SR

Step 3: Calculate the Labor Rate Variance
Labor Rate Variance = (AR - SR) * AH

Step 4: Classify the Labor Rate Variance
If the Labor Rate Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.

Step 5: Calculate the Standard Labor Cost for Actual Hours
Standard Labor Cost for Actual Hours = AH * SR

Step 6: Calculate the Labor Efficiency Variance
Labor Efficiency Variance = (AH - SH) * SR

Step 7: Classify the Labor Efficiency Variance
If the Labor Efficiency Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.

By following these steps, you can compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable, or no variance.

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Let S be the part of the plane 3+ + 2) + z = 1 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F = 3i+3j + 4k across the surface S.

Answers

The surface integral of the dot product between the vector field F = 3i + 3j + 4k and the unit normal vector of the surface S is equal to zero.

To use Stokes' theorem to find the flux of the vector field F = 3i + 3j + 4k across the surface S, which is the part of the plane 3x + 2y + z = 1 in the first octant and oriented upward.

Stoke's theorem statement is “the surface integral of the curl of a function over the surface bounded by a closed surface will be equal to the line integral of the particular vector function around it.” Stokes theorem gives a relation between line integrals and surface integrals.

First, we need to parametirize the curve C that bounds the surface S. Since S is in the first octant, x, y, and z are all non-negative.

The boundary C consists of three line segments: (i) from (0, 0, 0) to (1/3, 0, 0), (ii) from (1/3, 0, 0) to (0, 1/2, 0), and (iii) from (0, 1/2, 0) to (0, 0, 0). Next, calculate the curl of F, which is the cross product of the del operator and F:
curl(F) = (∂Fz/∂y - ∂Fy/∂z)i - (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k = (0 - 0)i - (0 - 0)j + (0 - 0)k = 0.

Since curl(F) = 0, the line integral of F over C is also 0.

According to Stokes' theorem, the flux of F across S equals the line integral of F over C, which we found to be 0.

Therefore, the flux of the vector field F = 3i + 3j + 4k across the surface S is 0.

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Which of the following is an even function? g(x) = (x – 1)2 1 g(x) = 2x2 1 g(x) = 4x 2 g(x) = 2x

Answers

The only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.

A function is even if it satisfies the property g(-x) = g(x) for all x.

Checking each of the given functions:

g(x) = (x - 1)^2 is not even, because g(-x) = (-x - 1)^2 = x^2 + 2x + 1, which is not equal to g(x) = (x - 1)^2.

g(x) = 2x^2 is even, because g(-x) = 2(-x)^2 = 2x^2 = g(x) for all x.

g(x) = 4x^2 is even, because g(-x) = 4(-x)^2 = 4x^2 = g(x) for all x.

g(x) = 2x is odd, because g(-x) = 2(-x) = -2x = -g(x) for all x.

Therefore, the only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.

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On a baseball diamond, home plate and second base lie on the perpendicular bisector of the line segment that joins first and third base. First base is 90 feet from home plate. How far is it from third base to home plate? Sketch a baseball diamond on a separate sheet of paper, labeling home plate as point A
, first base as B
, second base as C
, and third base as D. Label the intersection of AC⎯⎯⎯⎯⎯
and BD⎯⎯⎯⎯⎯
as E. Using the Perpendicular Bisector Theorem, determine how far it is from third base to home plate. Describe your conclusion in the context of the situation

Answers

Using the Perpendicular Bisector Theorem, the distance from third base to home plate is 90 feet. This means that all the bases are equidistant from home plate, which is a fundamental property of a baseball diamond.

To find the distance from third base to home plate, we need to use the Perpendicular Bisector Theorem, which states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

First, we draw a baseball diamond with points A, B, C, and D labeled as described in the problem.

Next, we draw the line segment that joins first base (B) and third base (D), and we construct the perpendicular bisector of this segment by drawing a line through the midpoint of BD and perpendicular to BD. Let's label the point where the perpendicular bisector intersects the line that connects home plate (A) and second base (C) as E.

Since E lies on the perpendicular bisector of BD, it is equidistant from B and D. We know that first base (B) is 90 feet from home plate (A), so the distance from home plate to E must also be 90 feet. Therefore, the distance from third base (D) to home plate (A) is also 90 feet.

In conclusion, using the Perpendicular Bisector Theorem, we determined that the distance from third base to home plate is 90 feet.

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A cylindrical jar of peanut butter has a height of 4 inches and a diameter of 3 inches. How many cubic inches of peanut butter can the jar hold? Use π = 3.14.

28.26 in3
37.68 in3
113.04 in3
150.72 in3

Answers

The jar can hold 28.26 cubic inches of peanut butter

How to calculate the amount of cubic inches of peanut butter?

The first step is to write out the parameters

A cylindrical jar of peanut has a height of 4 inches

The diameter is 3 inches

The next step is to calculate the radius, this is done by dividing the diameter by 2

radius= 3/2

= 1.5

The formula used to calculate the cubic inches of peanut butter is

V= πr²h

= 3.14 × 1.5² × 4

= 3.14 × 2.25 × 4

= 28.26

Hence the jar can hold 28.26 cubic inches of peanut butter

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Is the triangle similar to PQR? State whether each triangle similar to PQR by answering yes or no

Answers

Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.

Describe Congruency of triangle?

Congruency of triangles refers to the condition in which two or more triangles have the same size and shape. In other words, if two or more triangles have congruent sides and angles, then they are said to be congruent.

The criteria for determining the congruency of triangles are based on the properties of sides and angles. There are various ways to show that two triangles are congruent, including the following:

Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the two triangles are congruent.

Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.

Angle-Angle-Side (AAS) Congruence: If two angles and a side not between them in one triangle are equal to two angles and the corresponding side not between them in another triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) Congruence: If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.

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A magazine listed the number of calories and sodium content​ (in milligrams) for 13 brands of hot dogs. Examine the​ association, assuming that the data satisfy the conditions for inference. Complete parts a and b

Answers

Option B is correct. In this context, the meaning is: Among hot dogs with the same number of calories, the sodium content varies, with a standard deviation of about 75 milligrams

The calculated test statistic is 3.75

How to get the correct option

The test statistics can be gotten from the data that we already have available in this question

The coefficient is given as 2.235

The Standard error of the coefficient is given as 0.596

The formula used is given as

Such that t = coefficient /  Standard error

where the coefficient = 2.235

The standard error = 0.596

We have to apply the values to formula:

= 2.235 / 0.596

= 3.75

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Solve problems 1 and 4 ONLY with the rules given on the paper.

Answers

The solution to the equations obtained using inverse trigonometric function values are;

1. x ≈ 0.65

4. x ≈ 0.95

What are trigonometric functions?

Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.

The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;

The inverse function for sine is arcsine

The inverse function for cosine is arccosine

The inverse function for the tangent of an angle is arctangent

1. sin(x) = 0.6051

Therefore; x = arcsine(0.6051) ≈ 0.65 radians

The value of x in the interval [0·π, 2·π] is x ≈ 0.65

4. tan(x) = 1.3972

Therefore, x = arctan(1.3972) ≈ 0.95

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PLease help 1 and 2 Pythagorean Theorem and if you can explain please

Answers

Answer:

Step-by-step explanation:

The Pythagorean theorem has the formula a squared(leg) + b squared(leg) = c squared(longest leg). This means [tex]12^{2} +16^{2} =20^{2} -- > 144+256=400[/tex] which is true meaning number 1 is a right triangle. [tex]10^{2} +49.5^{2} = 50.5^{2} -- > 100+2450.25=2550.25[/tex] is true meaning number 2 is also a right triangle because the sum of the shortest legs squared are equal to the longest leg (hypotenuse) squared.

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