Gina bought lunch at school. She had a sandwich and a dessert that cost her $7. Her dessert cost
$3.75. Solve the equation 7 = 5 +3.75 to find the cost of Gina's sandwich, s.
...
S=
- Gina's sandwich cost $

Option (c) x² + sin x is the correct option.

Given that F(x) = ∫f(t² + sin t) dt

The fundamental theorem of calculus is given as: If f is continuous on [a,b] then F(x) = ∫f(t)dt from a to x is differentiable at x and F'(x) = f(x)Given that F(x) = ∫f(t² + sin t) dt

Differentiating F(x) with respect to x, we get; F¹(x) = f(x² + sin x) * (2x + cos x)Therefore, the value of F¹(z) = f(z² + sin z) * (2z + cos z)

Thus, option (c) x² + sin x is the correct option.

Calculus is a branch of mathematics that deals with the study of change and motion. It is divided into two main branches: differential calculus and integral calculus.

Differential calculus focuses on the concept of derivatives, which measures how a function changes as its input (usually denoted as x) changes. The derivative of a function at a particular point gives the rate at which the function is changing at that point. It helps analyze properties of functions such as their slopes, rates of growth, and optimization.

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1) Point slope form equations are written according to this general formula:

2) Since we've got the slope and one point we can plug them into the formula:

That yields the equation of the line y=4/3x -4 (slope-intercept form). So in Point Slope form, the answer is:

(y-0)=4/3(x-3)

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

The equation y = mx + b, where y is the y-coordinate, denotes a linear function. m represents the line's slope, or how steep it is. The coordinate for x is x.

The equation y = mx + b, where y is the y-coordinate, denotes a linear function.

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The number of ways in which we can selected these 5 officers are 157,872.

This is a question of permutations and combinations.

Given that:-

Number of members in the club = 24

Number of pledges in the club = 13

We have to find the number of ways in which we can selected these 5 officers.

We know that:-

Number of ways of selecting a president, vice-president, and secretary from the members = \(^{24}C_3=2024\)

Number of ways of selecting a pledge chairman and pledge vice chairman from the pledges = \(^{13}C_2=78\)

Hence, number of ways of selecting 5 officers are 2024*78 = 157,872.

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Answer:

n = 0.15037593985

Step-by-step explanation:

−2(−4n + 1)+5(25n − 8)=−62

8n-2+125n-40= -62

133n = -20

133/133 = 20/133

n = 0.15037593985

This equation might be screwed up; I'd talk to your teacher about it.

Answer Using the method of alligation. 40.0= 20/(10/20) qts of 50% solution to add to your 20 qts of 20% solution. 60.0= (20+40.0) qts of the final 40% solution.

Answer:

Step-by-step explanation:

When the question comes with answer choices, please share them.   In this case it sounds like there were four graphs from which to choose.

f(x) = |x^2 − x − 2| is always zero or greater, due to the absolute value function.

x^2 − x − 2 = 0 factors to (x - 2)(x + 1) = 0, so the zeros of f(x) are {-1, 2}.

Plot x-intercepts {-1, 2}.  The axis of symmetry is the vertical line x = 1/2, which is precisely halfway between the x-intercepts.  If we now choose the test number x = 0, we find the value of f(0) to be |-2}, which tells us that the y-intercept is (0, |-2|), or (0, 2), so we have a parabolic curve opening down between x = -1 and x = 2 and touching (but not crossing) the x-axis at those x-values. To the left of x = -1 the curve increases steadily from y = 0 in Quadrant II; to the right of x = 2, the curve increases steadily from y = 0 in Quadrant I.

The graph for the given function is plotted below.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=|x²-x-2|.

Graph the absolute value using the vertex and a few selected points.

Put x= -2, -1, 0 and 1 in the given function, we get

When x=0

y= |0-0-2|

y=0

When x=1

y=|1-1-2|

y=2

When x=-2

y=|4+2-2|

y=2

Now, plot points (-2, 4), (-1, 0), (0, 2) and (1, 2) on graph

Therefore, the graph for the given function is plotted below.

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Answer: 23.25

Step-by-step explanation:

to find mean add all yours values up and than divide by the number of values in the equation, so 5+9+6+73= 93 and than divide it by 4, which gets u 23.25

Answer:

Step-by-step explanation:

In this case total surface area of the prism is the sum of each of the areas of the sides of the triangular prism including the base. In order to find out the exact numerical value of the total surface area we can sum up the areas of each of the sides including the base.

the prism has 5 sides as it is triangular, so we have five values of area.

Let A1 and A2 be area of the triangular sides. A1=A2

A3 be the base area

A4 be the slant side's area

A5 be the area of the side with 6cm height

A1=A2=(8*6)/2=24cm^2

A3=8*4=32cm^2

A4=10*4=40cm^2

A5=6*4=24cm^2

A=A1+A2+A3+A4+A5

A=24+24+32+40+24=144cm^2

Answer:

its C

Step-by-step explanation:

Answer:

16/3 pounds

Step-by-step explanation:

We are give that each friend took 2/3 pound of grapes from the bowl. Therefore, to know the total amount taken by the four friends, we will simply do cross multiplication as follows:

1 friend .................> 2/3 pounds

4 friends ...............> ?? pounds

Amount taken by the 4 friends = [4*(2/3)] / 1 = 8/3 pounds

The bowl originally had 8 pounds and 8/3 pounds were taken, therefore:

remaining amount = 8 - 8/3 = 16/3 pounds                                                                           hope this helps!

Part A: To find the height at which the eagle catches the oyster, we need to set the two functions h(t) and g(t) equal to each other. So we have:

-4.9t^2 + 39 = -4t + 27

Simplifying the equation, we get:

-4.9t^2 + 4t - 12 = 0

Now we can solve this quadratic equation for t using factoring, completing the square, or the quadratic formula. After finding the values of t, we can substitute them back into either h(t) or g(t) to determine the height at which the eagle catches the oyster.

Part B: To find the time it takes for the eagle to catch the oyster, we set the two functions h(t) and g(t) equal to each other and solve for t, similar to Part A. Once we have the values of t, we can determine the time it takes for the eagle to catch the oyster by comparing the values of t with their respective units of time (seconds).

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See below for the vocabularies and their correct definition

Match the following vocabulary

The terms are given as:

To get the inverse of a conditional, the hypothesis and the conclusion are negated, without interchanging them.

So, we have:

Inverse of a conditional ⇒ A new statement formed by negating both the hypothesis and the conclusion.

To get the contrapositive of a conditional, the hypothesis and the conclusion are negated, after interchanging them.

So, we have:

Contrapositive of a conditional ⇒ Formed by exchanging the hypothesis and the conclusion and negating both of them.

To get the converse of a conditional, we simply interchange the hypothesis and the conclusion, without negating them

So, we have:

Converse of a conditional ⇒ A statement formed by interchanging the hypothesis and the conclusion in a conditional statement.

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Answer:

The answer is Convers because it literally takes the hypothesis and the conclusion and interchanges them.

Step-by-step explanation:

Answer:

x > 88/7

Step-by-step explanation:

i hope this helps :)

The 'x' coordinate is negative and 'y' coordinate is positive.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

We know that :

π = 180

Therefore,

3π/4 = (3×180)/4 = 3 × 45

3π/4 = 135

In second quadrant, we have negative value if x coordinate and positive value of y coordinate.

Hence, the angle lies in the second quadrant. Second quadrant is enclosed by the negative x axis and positive y axis.

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Answer:

x is negative, and y is positive.

Step-by-step explanation:

The answer above is correct.

80% = $18

(divide both sides by 80 to find 1%)

1% = 0.225

(multiply both sides by 100 to find 100%)

100% = $22.50

Answer:

f(n) = 2 × \(3^{n-1}\)

Step-by-step explanation:

In order to write an explicit rule for a geometric function, you need to know the common ratio; you can find the common ratio by dividing two consecutive terms:

6 ÷ 2 = 3, 18 ÷ 6 = 3, 54 ÷ 18 = 3, etc..

Now you know the common ratio is 3. At this point you can write your explicit function following the rule f(n) = [1st term] × [common ratio]^(n-1):

f(n) = 2 × 3^(n-1)

Answer:

Step-by-step explanation:

When you have four terms and 3rd degree equation (the highest power is 3) you will want to try to "factor by grouping"

Group together two terms, watch out for the negative signs!

x^3 + 2x^2-5x-10=0

(x^3 + 2x^2) - (5x+10)=0

Find a common factor in each group and factor it out. You're hoping that what is left in the parenthesis is the same in both cases.

x^2(x+2)-5(x+2)=0

Now you can factor out that (x+2) because it is both terms.

x^2(x + 2) - 5(x + 2)=0

~~~~ ~~~~

Pull these out.

What will be left is the x^2 and the - 5 (dont lose that - in front of the 5)

(x + 2)(x^2 - 5) = 0

If all you have to do is factor, then you're done. It is factored. But if you have to "solve" also, then put x+2=0 and x^2-5=0 and solve.

x = -2 and x = +- sqrt5

The box plot that represents the data on the sandwiches sold by Super Sandwiches is Box Plot 1.

The box plot that shows the data of sandwiches is the one that has the correct measure of the value of Q1 or the lower quartile. This is because the box plots are similar except for the lower quartile.

To find the lower quartile, arrange the numbers;

50, 66, 74, 88, 100, 109, 113, 127, 150

The lower quartile would be the median of the lower half of :

50, 66, 74, 88

The lower quartile is:

= ( 66 + 74 ) / 2

= 70

The first box plot has this Q1 value and so is correct.

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The solution of the given function using Laplace transform the required solution is, L{F(s)}= \(\frac{1}{s^{2} } e^{-s}\)

Given data,

F(s): L{(t-1)u(t-1)}

Where L is the Laplace transformation

Laplace transform is the integral transform of the given derivative function with real variable t to convert into a complex function with variable s. For t ≥ 0, let f(t) be given and assume the function satisfies certain conditions to be stated later on.

F(s) = \(\int\limits^\alpha _0 {f(t)} e^{-st} t^{l} \,\)

Where,

s = σ + \(iw\)

F(s) = Laplace transform

s = complex number

t = real number >=0

\(t^{l}\) = first derivative of the function f(t)

The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra.

So,

We can write,

F(s): L{(t-1)u(t-1)}

F(s) = \(\int\limits^\alpha _0 {f(t)} e^{-st} t^{l} \,\)

F(s) = \(\int\limits^\alpha _0 {(t-1)u(t-1)} e^{-st} \, dt\)

F(s) =  \(e^{-s} (\frac{1}{s^{2} } )\)

F(s) = \(\frac{1}{s^{2} } e^{-s}\)

Therefore,

The solution of the given function using Laplace transform the required solution is, L{F(s)}= \(\frac{1}{s^{2} } e^{-s}\)

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In data analytics, a population refers to all possible data values in a certain dataset.

Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.

The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.

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   Sum of an arithmetic sequence is defined by the formula,

\(T_n=\frac{n}{2}[2a+(n-1)d]\)

Total length of the wooden boards will be \(14\frac{1}{6}\) feet.

    It's given in the question,

Since, 1 inch = \(\frac{1}{12}\) feet

Therefore, \(4\) inch = \(\frac{4}{12}\) feet

                             = \(\frac{1}{3}\) feet

So, each stair is \(\frac{1}{3}\) feet shorter than one below.

Now the sequence formed will be,

\(\frac{7}{2},[\frac{7}{2}-\frac{1}{3}],[\frac{7}{2}-\frac{2}{3}],......\frac{13}{6}\)

\(\frac{21}{6},\frac{19}{6},\frac{17}{6}....\frac{13}{6}\)

It's an Arithmetic sequence with common difference 'd' = \(-\frac{1}{3}\) and first term 'a' = \(\frac{7}{2}\) and nth term \(T_n=\frac{13}{6}\)

If there are 'n' stairs, expression for the for the top stair of the arithmetic sequence will be,

\(T_n=a+(n-1)d\)

\(\frac{13}{6}=\frac{21}{6}+(n-1)(-\frac{1}{3})\)

\(\frac{13}{6}-\frac{21}{6}=-(n-1)\frac{1}{3}\)

\(\frac{8}{6}=(n-1)\frac{1}{3}\)

\(\frac{4}{3}=(n-1)\frac{1}{3}\)

\((n-1)=4\)

\(n=5\)

Therefore, there are 5 stairs.

Now total length of the wooden boards = Sum of 5 terms of the sequence

                                                                    = \(\frac{n}{2}[2a+(n-1)(d)]\)

                                                                    = \(\frac{5}{2}[2(\frac{21}{6})+(5-1)(-\frac{1}{3})]\)

                                                                    = \(\frac{5}{2}[\frac{21}{3}-\frac{4}{3}]\)

                                                                    = \(\frac{17}{3}\times \frac{5}{2}\)

                                                                    = \(\frac{85}{6}\)

                                                                    = \(14\frac{1}{6}\) ft

    Therefore, total length of the wooden boards will be \(14\frac{1}{6}\) ft.

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Answer:  

Rectangular pyramid  8 edges

Rectangular prism    12 edges

Triangular Prism   9 edges

Triangular Pyramid  6 edges

Step-by-step explanation: Faces connected at edges

Rectangular pyramid    1 Base  and 4  slanted  triangular sides

Rectangular prism    2 top and bottom bases and 4 sides

Triangular Prism   2 top and bottom triangular bases 3 rectangular sides

Triangular Pyramid    1 triangular base, 3 slanted triangular sides

The matching is as follow:

Rectangular pyramid:  8 edges

Rectangular prism:  12 edges

Triangular Prism: 9 edges

Triangular Pyramid: 6 edges

A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.

Rectangular pyramid have one Base and 4 slanted triangular sides

Rectangular prism have 2 top and bottom bases and 4 sides

Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.

Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.

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In the end, Moe played 51 games, while  Meeny played 17 games and Miny played 35 games.

We can start solving the problem by using algebra. Let x be the number of games Moe played. Then, since Meeny and Miny played 17 and 35 games respectively, the total number of games played is 17 + 35 + x = x + 52.

We know that in the second game and on, the one who sat out the preceding game would replace the loser of that game. Therefore, the number of games played by Moe is one less than the number of games played by Meeny and Miny combined.

x = (17 + 35) - 1 = 51.

So, Moe played 51 games.

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The complete question is -

Meeny, Miny and Moe were playing tennis. From the second game on, the one who sat out the preceding game would replace the loser of that game. In the end, Meeny played 17 games and Miny played 35 games. How many games did Moe play?

Answer:

D m =  \(-\frac{3}{8}\)

Step-by-step explanation:

factor the expressions in the denominator and the numerator to simplify the expression:

=> \(\frac{2(-2m + 1)(2m - 1)}{2(2m - 1)(8m + 3)}\)

=> \(-\frac{2m + 1}{8m + 3}\)

to make a fraction undefined, the numerator should be 0, thus, we substitute the values of m from the options into the denominator to make the denominator equals to 0:

=> \(-\frac{2m + 1}{8(-\frac{3}{8} ) + 3}\) = \(-\frac{2m + 1}{-3 + 3}\) = \(-\frac{2m + 1}{0}\)

in this case, the values of m from option D make the denominator of the fraction equals 0.

Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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The plane which intersect plane GFL and the plane contain A nd C is CAB

Answer: 1) CAB

Answer:

Step-by-step explanation:

The two triangles are similar, so the ratio of their corresponding side lengths is constant. We can find this ratio by dividing any two corresponding side lengths. For example, we can divide the side length of 4 in the first triangle by the side length of 2 in the second triangle. This gives us a ratio of 2:1. We can also divide the side length of 9 in the first triangle by the side length of 22 in the second triangle. This also gives us a ratio of 2:1. Therefore, the ratio of the corresponding side lengths of the two triangles is 2:1.

To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.

Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.

Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.

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There are 20! rational numbers between 0 and 1 for which the product of the resulting numerator and denominator is 20!.

To write a rational number as a fraction in lowest terms, we need to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Let's calculate the product of the resulting numerator and denominator for 20! and determine how many rational numbers between 0 and 1 will have this product.

First, let's calculate 20! (the factorial of 20):

\($20! = 20 \times 19 \times 18 \times \ldots \times 2 \times 1$\)

Next, we'll express 20! as a fraction in lowest terms. Since 20! is an integer, we can write it as a fraction over 1:

\($\frac{20!}{1}$\)

To find the product of the resulting numerator and denominator, we'll simplify the fraction:

\($\frac{20!}{1} = \frac{20 \times 19 \times 18 \times \ldots \times 2 \times 1}{1} = 20 \times 19 \times 18 \times \ldots \times 2 \times 1$\)

Now, to determine how many rational numbers between 0 and 1 will have the product 20!, we need to consider the number of unique fractions that can be formed with 20! as the numerator.

Since the denominator can be any positive integer less than or equal to 20!, the number of rational numbers will be equal to 20!.

Therefore, there are 20! rational numbers between 0 and 1 for which the product of the resulting numerator and denominator is 20!.

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