The cost per guest of catering an event of no more than 100 people is modeled by the
function fx=30+4x.The number of guests is modeled by the function g x = 100-x,
where x represents the number of guests fewer than 100 that attend.
Evaluate (f•g) (12) and interpret what it means in the context of the problem.

Answer:

2x-3x=-45

-x=-45

x=45

by simple method

Using the Pythagorean theorem, we get,

Jules will need the fencing length of 30√2 yards to build the square fence. Hence, option (c) is correct.

It can be defined as a rectangle whose two adjacent sides are equal. Single regular polygon with equal interior angles, central and exterior angles (90°), and equal diagonal lengths

Given data:

The length of each side of the yard is AB = BC = CD = AD = 30 yards.

As shown by the dotted line, the fencing should be done along the diagonal BD of the given square plot. Then, applying Pythagoras' theorem to find the fencing length BD as,

BD² = BC²+ CD²

Substitute the values as

   BD² = 30² + 30²

⇒ BD² = 900+ 900

⇒ BD² = 1800

⇒ BD = √1800

⇒ BD = 30√2 yards.

Thus, we can conclude that Jules will need the fencing length to build the fence along the square plot. Therefore, option (c) is correct.

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Answer:

If you spent $56 on candy, she'd buy 8 pounds.

Step-by-step explanation:

Center - radius equation for circle of radius r ,centered at (h,k) is :

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

you have r = √21

[tex]r^{2} =[/tex] (√21)^2 = 21

centre (h,k) = (0,0) so h =0 and k =0

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

[tex](x-0)^{2} + (y -0)^2 = 21[/tex]

[tex]x^{2} + y^{2} = 21[/tex]

Answer:

price of the juice increased by 15%, then the new price of the juice is: New price = Old price + (Percent increase * Old price) Percent increase = 15% Old price = $9.40 New price = $9.40 + (0.15 * $9.40) New price = $9.40 + $1.41 New price = $10.81 Therefore, the new price of the juice after the increase is $10.81.

==================================================

Proof:

We'll break the proof into two cases which I'll label A and B

-----------

Case A: 'a' is even

k = some integer

a = 2k = some even integer

a+1 = 2k+1

a(a+1) = 2k(2k+1) = 2(2k^2+k) = 2*(some integer)

Since 2 is a factor of that last expression, this shows that a(a+1) is even when 'a' is even.

-----------

Case B: 'a' is odd

k = some integer

a = 2k+1 = some odd integer

a+1 = (2k+1)+1 = 2k+2

a(a+1) = (2k+1)(2k+2) = 2(2k+1)(k+1) = 2(some integer)

This shows that a(a+1) is even when 'a' is odd.

-----------

Therefore, for any integer 'a', the expression a(a+1) is always even.

Some examples:

-----------

Here's a slightly different way to interpret why the proof works.

a(a+1) consists of factors 'a' and 'a+1'

Either way, we'll have 2 as a factor somewhere in a(a+1).

Answer:

y = 2x + 10

Step-by-step explanation:

What we know:

10 dollar entrance fee

2 dollars PER ride

"per" is an important word since it tells us that the x will be there.

That means that, if its a 10 dollar entrance fee and 2 dollars per ride, it will be 2x + 10.

[tex]y=2x+10[/tex]

Answer:

hope it will help you ( ꈍᴗꈍ)(✿^‿^)(✿^‿^)!!!

(a) The transformation that maps ΔSTU to ΔLMN is a translation of three units to the right and one unit up, followed by a counterclockwise rotation of 90° around the origin

What is transformation?

A dilation with respect to the origin by a scale factor of 1/3.

To map ΔSTU to ΔLMN, we need to perform a combination of transformations: a translation, a rotation, and a dilation.

First, we translate triangle STU three units to the right and one unit up to get triangle S'T'U', where S'(1,3), T'(-2,5), and U'(0,-2).

Next, we rotate triangle S'T'U' 90 degrees counterclockwise around the origin to get triangle S''T''U'', where S''(3,1), T''(-5,2), and U''(2,0).

Finally, we dilate ΔS''T''U'' by a scale factor of 1/3 with respect to the origin to get ΔLMN, where L(1/3,1/3), M(-5/3,2/3), and N(2/3,0).

Therefore, the transformation that maps ΔSTU to ΔLMN is a translation of three units to the right and one unit up, followed by a counterclockwise rotation of 90° around the origin, and finally a dilation with respect to the origin by a scale factor of 1/3.

(b) The side overline SU corresponds to the side overline LN.

(c) Yes, corresponding sides are congruent. the triangles are congruent by the Side-Side-Side (SSS) congruence criterion.

What is congruent?

We can see this by calculating the length of each side of the two triangles:

Length of ST = distance between points S and T = √(((-5) - (-2))² + ((4) - (2))²) = √(10)

Length of LM = distance between points L and M = √(((-5/3) - (1/3))² + ((2/3) - (1/3))²) = √(10)/3

Length of TU = distance between points T and U = √(((-5) - (-3))² + ((4) - (-3))²) = √(74)

Length of MN = distance between points M and N = √(((-5/3) - (2/3))² + ((2/3) - 0)²) = √(10)/3

Length of US = distance between points U and S = √(((-3) - (-2))² + ((-3) - (2))²) = √(26)

Length of NL = distance between points N and L = √(((2/3) - (1/3))² + ((0) - (1/3))²) = √(2)/3

All corresponding sides have the same length, so the triangles are congruent by the Side-Side-Side (SSS) congruence criterion.

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Step-by-step explanation:

If you are using a fair six - sided cube , there are two numbers out of six that are greater than 4  ( 5 and 6 )

 sooo:    2 out of 6   or  1/3 should be greater than 4

1/3 * 20 = 6 2/3 = ~ 7

Answer:

a. already done

b. x=3, x=4, and x=5

c. x=2, x=3, x=4, and x=6

Step-by-step explanation:

The < symbol means less than, so all values of x less than what is stated are correct

The ≤ symbol means less than or equal to, so all values of x less than, and what is stated are correct

The answer is in the screenshot.
Let me know if it helps

Answer:

a = 1, b = 1, c = 0

Step-by-step explanation:

First, we need to find the vertex coordinates:

x (vertex) =

[tex]x(vertex) = \frac{ - b}{2a} = \frac{ - 1}{2 \times 1} = \frac{ - 1}{2} = - 0.5[/tex]

[tex]y(vertex) = { (- 0.5})^{2} + ( - 0.5) = 0.25 - 0.5 = - 0.25[/tex]

Now, that we have the vertex coordinates, we need to pick three x values to either side of the vertex (as I did in the photo)

The expression equivalent is 9+2x/6x

A fraction is a part of a whole. It is 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

1/4x +1 3/4x - 2/3-1/2x

1/4x + (4x + 3/4x) - 2/3 - 1/2x

(1 + 4x + 3)/4x - (4x - 3)/6x

4 + 4x/4x - 4x - 3/6x

(3(4 + 4x) - 2(4x - 3))/12x

(12 + 12x - 8x + 6)/12x

(18 + 4x)/12x

(9 + 2x)/6x

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We can conclude that the difference between p1 and p2 is statistically significant at the 5% level of significance.

The confidence interval and significance test in part A both provide similar information. The significance test in part A tests if the difference between p1 and p2 is statistically significant, while the confidence interval provides an estimated range of values for the true difference between p1 and p2 with a certain degree of confidence (95% in this case).A confidence interval is a range of values that we believe will include a population parameter with a specified level of confidence.

It can be computed to estimate the population mean or the difference between two population means, such as p1 and p2.In contrast, a significance test assesses whether the difference between two population proportions is statistically significant.

The test calculates a p-value, which is the likelihood of obtaining the observed difference between two proportions, assuming the null hypothesis (that there is no difference between the two proportions) is true. A p-value less than the level of significance (usually 0.05) indicates that the difference between the two proportions is statistically significant, while a p-value greater than the level of significance indicates that the difference is not statistically significant.

Both the confidence interval and the significance test inform us about the difference between two population proportions. The confidence interval provides a range of plausible values for the difference, while the significance test tells us whether the difference is statistically significant or not. In this particular case, since the confidence interval does not contain zero,

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The frequency distribution table for the question is :

Grade 7 | 0.67 | 0.33 | 1.00

Grade 8 | 0.42 | 0.58 | 1.00

Total      | 1.09 | 0.91 | 2.00.

Frequencies refer to the number of times an event or a value occurs in a dataset. It is a count of the occurrences of a particular value or event. Frequencies are commonly used in statistics to summarize data and to help understand patterns in a dataset. The frequency of a value can be expressed as an absolute frequency (the number of times a value occurs) or a relative frequency.

The given table shows the results of a survey conducted among students in Grade 7 and Grade 8 about their preference for joining a movie club or a music club. The students want to make a two-way relative frequency table using row totals. In the table, the row totals represent the total number of students in each grade, and the column totals represent the total number of students who want to join each club.

To complete the table, we need to find the missing values. For example, in the row for Grade 7, the total number of students is 33. We know that 20 of these students want to join the movie club, so the relative frequency of Grade 7 students who want to join the movie club is 20/33, which is approximately 0.61. Similarly, we know that 13 Grade 7 students want to join the music club, so the relative frequency of Grade 7 students who want to join the music club is 13/33, which is approximately 0.39.

Likewise, we can find the missing values in the other rows and complete the table. The completed table shows the relative frequency of students in each grade who want to join each club. For example, 0.61 or approximately 61% of Grade 7 students want to join the movie club, while 0.25 or approximately 25% of Grade 8 students want to join the movie club.

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A combination of two or more simple statements is a compound statement. The connectives generally used in mathematics are ‘and’, ‘or’, ‘if ’, ‘if and only if’.

In mathematics, like in any language, compound statements are created by combining simpler ones using connectives. The truth value of a compound statement is determined by the truth value of its smaller components.

There are four compound statements:

1. ¬p , Not p (i.e. the negation of p)  : Negation

2. p ∧ q, p and q                                : Conjunction

3. p ∨ q, p or q                                   : Disjunction

4. p → q, If p then q                            : Conditional

Beginning with the premise that P (the hypothesis) is true, we create a chain of implications, each of which has previously been proven to be true, ultimately leading to Q. (the conclusion). Imagine the chain has six consequences. As a result, the direct proof technique may be expressed combination as follows:

        P, P ⇒ P1, P1 ⇒ P2, P2 ⇒ P3, P3 ⇒ Q1, Q1 ⇒ Q2, Q2 ⇒ Q.

If P and the implications in the previous chain are all true, we must derive that Q is likewise true logically. But, according to the truth table for          P ⇒ Q, knowing that P ⇒ Q is a true statement does not indicate that P or Q are true, just that the inference is true. Recall that P can be false, Q can be true or false, and the inference might be true or false.

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Question: What are Compound Statements? Write proof and logic for the statements.

The inverse of the function y = 16x² + 17 is y = ±√(x - 17)/16

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

y = 16x² + 17

So, we have

x = 16y² + 17

Make y the subject

This gives

y = ±√(x - 17)/16

Hence, the inverse of the function is y = ±√(x - 17)/16

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the disposal under the following assumptions are:  To Equipment   $78,200

   Being equipment is scrapped at a gain  

a)

Particulars Debit Credit

Loss on disposal $28,300  

Accumulate depreciation of $49,900  

   To Equipment   $78,200

   Being equipment scrapped with no value

b)

Particulars Debit Credit

Loss on disposal $8,800  

Accumulate depreciation of $49,900  

Cash $19,500  

   To Equipment   $78,200

   Being equipment disposed of at a loss

c)

Particulars Debit Credit

Accumulate depreciation of $49,900  

Cash $30,800  

   To Gain on disposal    $2,500

   To Equipment   $78,200

   Being equipment is scrapped at a gain  

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the statement is true.the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.

Simple random sampling is a type of probability sampling technique wherein every member of the population has an equal and independent chance of being selected. Independence means that the selection of one unit does not affect the selection of any other unit. The success-failure condition is an important condition of simple random sampling, which states that the size of each of the two groups (i.e., success and failure) should be at least 10. In this case, the two groups are 289 and 111, which are both greater than 10. Therefore, the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.

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Answer:

x = 21

Step-by-step explanation:

Given exponential equation:

[tex]7^{3-5x}=\left(\dfrac{1}{49}\right)^{2x+9}[/tex]

Rewrite 49 as 7²:

[tex]7^{3-5x}=\left(\dfrac{1}{7^2}\right)^{2x+9}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]7^{3-5x}=\left(7^{-2}\right)^{2x+9}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad (a^b)^c=a^{bc}[/tex]

[tex]7^{3-5x}=7^{-2(2x+9)}[/tex]

Simplify the exponent:

[tex]7^{3-5x}=7^{-4x-18}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]3-5x=-4x-18[/tex]

Add 4x to both sides:

[tex]3-5x+4x=-4x-18+4x[/tex]

[tex]3-x=-18[/tex]

Subtract 3 from both sides:

[tex]3-x-3=-18-3[/tex]

[tex]-x=-21[/tex]

Divide both sides by -1:

[tex]x=21[/tex]

Therefore, the value of x is 21.

Answer:

Will mark Brainliest

Solve the exponential equation for x:

7^3-5x=(1/49)^2x+9

The relation between x and y is defined by the equation: y = 5x, where % is constant of the equation and X and Y are variable.

It is given that y varies directly as x. It means y is proportional to x.

y ∝ x

y = kx

{Where k is constant of proportionality.}

It is given that y=30 when x=6. Put x=5 and y=25 in the above equation to find the value of k.

30 = k(6)

Divide both sides by 6.

The value of k is 5.

Hence The relation between x and y is defined by the equation: y = 5x.

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So, you need to deposit $628.86 monthly to accumulate $100,000 in 15 years with an APR of 7%.

To create a college fund for your child, you must determine the amount you need to deposit every month. The fund that offers an APR of 7% will help you accumulate the amount in the future. Here are the steps to find out how much you need to deposit monthly.
Step 1: Determine the total amount required for college funds.
The first step is to determine the total amount you need to pay for college funds. Suppose you want to create a college fund for your child that requires $100,000 in 15 years. Use a present value calculator or online present value calculator to determine the future value of the college fund.
Step 2: Determine the interest rate
The second step is to determine the interest rate you will receive on your savings. Suppose the fund offers an APR of 7%.
Step 3: Determine the number of years
The third step is to determine the number of years you have until you need the money. Suppose you have 15 years.
Step 4: Use the annuity formula
The fourth step is to use the annuity formula to determine how much you need to deposit every month. The formula is:
PMT = FV × i / ((1 + i)n - 1)
Where PMT is the monthly payment, FV is the future value, i is the interest rate, and n is the number of payments.
Using the given values:
PMT = 100,000 × 0.07 / ((1 + 0.07)^15 - 1)
PMT = 100,000 × 0.07 / 11.283
PMT = $628.86

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6 dogs are the bare minimum that might weigh more than 24 kg.

What do minimum and maximum value mean?

Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.

For example, if we have a set of numbers {2, 4, 6, 8, 10}, the minimum value is 2 because it is the smallest number in the set, while the maximum value is 10 because it is the largest number in the set.

The minimum of the values present in the interval 20 to 40 is 6

The maximum of the values present in the interval 20 to 40 is (12+6) = 18

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The value of each variable include the following:

x = 10.

y = 80.

z = 5.

In Mathematics and Geometry, a rhombus refers to a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).

Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees). This ultimately implies that, all of the three angles are 90 degrees;

m∠1 = 9x = 90

9x = 90

x = 90/9

x = 10

m∠2 = y + x = 90

y + x = 90

y + 10 = 90

y = 90 - 10

y = 80

m∠3 = 18z = 90

18z = 90

z = 90/18

z = 5

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The no of colas that have sold 36 cans.

the translation of the question is :

A merchant obtains €70.50 by selling 57 cans of lemon, 48 of orange and the rest glue. If he sells each can for €0.50, how many colas have you sold?

Total selling price is €70.50

the price of each can is €0.50

So,

the number of cans which is sold is

n = €70.50/€0.50

n = 141 cans

again

the total number of cans = no of lemon + no of orange + no of glue

141 = 57 + 48 + m

m = 36

So the colas have sold 36 cans

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The new variance is 0.0625 / n

We can use the following formula to calculate the variance of a data set

variance = (sum of (x - mean)^2) / (number of data points)

where x is a data point and mean is the mean of the data set.

If the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35, we can find the standard deviation as follows

standard deviation = square root of variance = sqrt(0.35) = 0.59

Now, if the price increases by 25 cents a box, the new mean cost will be

new mean = $4.00 + $0.25 = $4.25

To find the new variance, we need to calculate the sum of (x - mean)^2 for the new data set and divide by the number of data points. Let's assume we are still considering the same number of boxes.

sum of (x - mean)^2 = [(4.25 - 4)^2 × n] = 0.0625 × n

where n is the number of data points.

Therefore, the new variance can be calculated as

new variance = (sum of (x - mean)^2) / (number of data points) = 0.0625 / n

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The function given in graph is an odd function.

What is the definition of a function?

In mathematics, a function is a rule that assigns a unique output to each input in a given set. In other words, a function is a relationship between two sets, called the domain (set of possible inputs) and the range (set of possible outputs), such that each input is paired with exactly one output.

Now,

In mathematics, an even function is a function f(x) that satisfies the following property: f(-x) = f(x) for all values of x in the domain of the function. The graph of an even function is symmetric about the y-axis, meaning that if you fold the graph along the y-axis, the two halves will be identical.

On the other hand, an odd function is a function f(x) that satisfies the following property: f(-x) = -f(x) for all values of x in the domain of the function. In other words, an odd function is symmetric with respect to the origin. The graph of an odd function is symmetric about the origin, meaning that if you rotate the graph 180 degrees about the origin, the graph will look the same.

As we can see the graph will be same when we will rotate it 180°.

Hence,

            Given function is odd function.

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Thus, the volume of sphere of the diameter of  m is found as:  523.33 cu. m.

A sphere is a 3D object that is perfectly round, has a single continuous curving surface, and every point upon that surface is equidistant from the centre.

volume of a sphere V = ⁴⁄₃πr³.

Demeter = 10 m

Radius r = 10/2 = 5 m

V =  ⁴⁄₃ *3.14*(5)³.

V = 523.33

Thus, the volume of a sphere of the diameter of  m is found as:  523.33 cu. m.

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