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Answer:

x = 4

Step-by-step explanation:

3x = 12, x = 4. I took algebra 1 and 2

Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

Given,

In the question:

A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.

To find the how many possible 3-course meals are there?

Now, According to the question:

Let's know:

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N=n_1\) × \(n_2\) × \(n_3\)... ×\(n_n\)

In this problem, considering the number of salads, main courses and desserts, we have that:

\(n_1=4 , n_2=5,n_3=3\)

The total number of options is given by:

N = 4 × 5 × 3

N = 60

Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

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The indefinite integral gives (f(x-1) (x-1)⁵) / 5 + 2f(x-1) (x-1)⁴/4 + 10f(x-1) (x-1)³/3 + 9f(x-1) (x-1)² + 18f(x-1) (x-1) + C.

Given, f(x-1)(x²+9) dx  We need to evaluate the indefinite integral of the given function

To evaluate the given indefinite integral, we use substitution u = x - 1

On substituting, u = x - 1, we get x = u + 1

Differentiating both sides with respect to u, we get dx = du

We substitute the value of x and dx in the given integral as follows,

∫f(x-1)(x²+9) dx = ∫f(u)(u+1)²(u² + 9) du

On expanding the above expression, we get

∫f(u)(u⁴ + 2u³ + 10u² + 18u + 9) du

Now, we integrate each term separately,

∫f(u)u⁴ du + ∫f(u)2u³ du + ∫f(u)10u² du + ∫f(u)18u du + ∫f(u)9 du

We use the power rule to integrate each term

∫f(u)u⁴ du = f(u) u⁵/5 + C1

∫f(u)2u³ du = f(u) u⁴/2 + C2

∫f(u)10u² du = f(u) 10u³/3 + C3

∫f(u)18u du = f(u) 9u² + C4

∫f(u)9 du = f(u) 9u + C5

On substituting back the value of u = x - 1, we get the final answer.

∫f(x-1)(x²+9) dx = (f(x-1) (x-1)⁵) / 5 + 2f(x-1) (x-1)⁴/4 + 10f(x-1) (x-1)³/3 + 9f(x-1) (x-1)² + 18f(x-1) (x-1) + C

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Hello,

All the numbers must begin with  6.

There are still 2,3,4,5 digits :  4 possibilities.

4!=4*3*2*1=24

The first is 62345 and the last 65432.

According to the given statement The final row of numbers represents the coefficients of the quotient. In this case, the quotient is y² + 4y - 16

To divide using synthetic division, follow these steps:

1. Set up the synthetic division table by writing down the coefficients of the dividend in descending order. In this case, the dividend is y³ - 64, so the coefficients are 1, 0, 0, and -64.

2. Write down the divisor, which is y+4, and change the sign, making it -4.
4 | 1   0   0  -64

3. Bring down the first coefficient, which is 1, into the leftmost column.
4 | 1   0   0  -64
           1

4. Multiply the divisor (-4) by the number you just brought down (1), and write the result beneath the next coefficient. Add this new number to the next coefficient.

4 | 1   0   0  -64
        1
 ------------
        -4

5. Repeat steps 3 and 4 until you have gone through all the coefficients.

 -4 | 1   0   0  -64
       1   4
    ------------
      -4   16

6. The final row of numbers represents the coefficients of the quotient. In this case, the quotient is y² + 4y - 16.

So, (y³ - 64) ÷ (y+4) = y² + 4y - 16.

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Answer:

  1.99 radians or 114.02°

Step-by-step explanation:

You want the measure of a circular arc of length 23.88 inches and radius 12 inches.

The equation relating angle, radius, and arc length is ...

  s = rθ . . . . . . s = arc length, r = radius, θ = central angle in radians

Solving for θ gives ...

  θ = s/r = (23.88 in)/(12 in) = 1.99 radians

The corresponding arc measure in degrees is ...

  1.99 radians × 180°/π ≈ 114.02°

The measure of arc AB is 1.99 radians, about 114.02°.

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Answer:

The answer is C.

Step-by-step explanation:

I took the test and got it right

Manuel's argument is correct. Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A thick or empty device with an approximately round or elliptical base that tapers to a notch is known as a cone.

Cone W has a radius of 6 cm and a height of 5 cm.

The base area of the cone will be

A = πr²

A = π (6)²

A = 113.04 square cm

Then the volume of the cone will be

V = (1/3) x base area x height

V = (1/3) x 113.04 x 5

V = 188.4 cubic cm

Square pyramid X has the same base area and height as cone W.

Then the volume of the square pyramid will be

V = (1/3) x base area x height

V = (1/3) x 113.04 x 5

V = 188.4 cubic cm

Manuel's argument is correct. Paul used the incorrect base area to find the volume of square pyramid X.

Then the correct option is C.

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The value of standard deviation of the sample is 11.29 grams.

To calculate the standard deviation of a sample, we need to use the following formula:

s = sqrt [ Σ(xi - x)^2 / (n-1) ]

where s is the standard deviation of the sample, Σ(xi - x)^2 is the sum of the squared deviations of each data point from the sample mean, n is the sample size and x is the sample mean

To calculate the standard deviation for the weights of the 5 mice, we first need to find the sample mean:

x = (56 + 59 + 78 + 56 + 77) / 5 = 65.2

Next, we can calculate the sum of the squared deviations:

Σ(xi - x)^2 = (56 - 65.2)^2 + (59 - 65.2)^2 + (78 - 65.2)^2 + (56 - 65.2)^2 + (77 - 65.2)^2

= 82.36 + 41.64 + 156.64 + 82.36 + 147.56

= 510.56

Finally, we can calculate the standard deviation:

s = sqrt [ Σ(xi - x)^2 / (n-1) ] = sqrt [ 510.56 / (5-1) ] = sqrt [ 127.64 ] = 11.29

Therefore, the standard deviation is 11.29 grams.

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The chemical need to be added to the tank is  16000 cubic cm

The volume is the total capacity of a container.

Total volume of tank = 80,000 cubic centimeters of water

Chemical volume =  5 cubic centimeters

Chemical needed = = 80,000 /5 = 16000 cubic cm is needed.

Thus,  16000 cubic cm chemical is needed.

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Answer:

least common multiple is 180

Answer:

1.9 feet = 19/10 feet = 1-9-10 feet

(I provided the answer as a regular number, as a mixed number, and as an improper fraction.  Feel free to use whichever feels best to you).

Step-by-step explanation:

We can find the remaining amount of string by subtracting the amount of string used from the total amount of string.

Since Jason used 2 2/5 feet of string and started with 4 3/10 feet of string, we subtract 2 2/5 from 4 3/10.

Step 1:  We can subtract improper fractions by subtracting the whole numbers and the fractions themselves.  Then, we can combine the result at the end:

(4 - 2) + (3/10 - 2/5)

2 - (5/50)

2 - 1/10

1.9

Step 2:  When we convert 1.9 into a mixed number, we get 1 9/10 (in the form you used, it's 1-9-10).

As a mixed number, it's 19/10

Answer:

Step-by-step explanation:

Four times a certain number “a”:

Ten more than thrice the number:

The statement is:

The zero of a linear function is the point where the function crosses the x-axis, which means that the y-value is equal to 0.

The best estimate for the zero of the linear function represented in the table can be determined by examining the x and y values.

Considering the given options:
A) Between 0 and 10
B) Between 2 and 33
C) Between 1 and 23
D) Between 3 and 44

You can find the best estimate for the zero by analyzing the table and locating the interval where the y-value changes from positive to negative or vice versa. This means that somewhere within that interval, the y-value would equal 0, making that interval the best estimate for the zero of the linear function.

Remember to always look for the interval in which the y-value crosses the x-axis, and that will help you determine the best estimate for the zero of the linear function.

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Answer:

1/2 of the class

give brainliest if it helps

The area of △XYZ according to the figure is 363ft²

The formula for calculating the area of a triangle is expressed as:

A = 0.5bh

For the triangle  △NMO

Area of  △NMO = 0.5bh

147 = 0.5b(14/12)

147 = 7b/12

7b = 12 * 147

b = 252

b = 252ft

b = 3024in

Get the base of △XYZ

14/3024 = 22/XZ

XZ = 4,752in

Area of △XYZ = 0.5 (4,752)(22)

Area of △XYZ= 52,272in²

Area of △XYZ = 363ft²

Hence the area of △XYZ is 363ft²

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Answer:

\(araea = base \times height \\ area = 19cm \times 17cm \\ area = 323cm {}^{2} \)

The inequality of the amount is x > 5

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

He could now afford the squishy ball for $5 at the school store.

This means that he must have more than $5 in savings

Represent the amount with x

So, we have the following representation

x > 5

Hence, the inequality is x > 5

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The number line shows the value of 5 - (-8) = 13.

Addition:

Subtraction:

Here the given operation is subtraction. Where a subtrahend is a negative number i.e., -8.

Step1: Start from '5' on the number line.

Step2: Since the subtrahend is a negative number, move to the right side on the number line from '5'.

Step3: Thus, the number obtained on the line is 13.

Step4: Algebraically the result is 5 - (-8) = 5 + 8 = 13.

The number line for this operation is shown below.

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The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. For example: is congruent to: (See Solving SSS Triangles to find out more) If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. ... Corresponding means they're in the same position in the 2 triangles.

The value n(A) in the probaility set is 33

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

n(B)=35, n(A n B)=19 and n(A u B)=49

Using the above as a guide, we have the following:

n(A n B) = n(A) + n(B) - n(A u B)

Substitute the known values in the above equation, so, we have the following representation

49 = n(A) + 35 - 19

So, we have

n(A) = 49 - 35 + 19

Evaluate

n(A) = 33

Hence, the solution is 33

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The exact probability cannot be determined without additional information such as the average daily sales rate.

To find the probability of selling more than 250 gallons, we need to find the cumulative distribution function (CDF) of the number of gallons sold, which is the probability of selling a certain amount or less. Since the amount sold follows a Poisson distribution with an average of 200 gallons, the CDF can be calculated using the Poisson cumulative distribution function formula:

P(X <= x) = e^(-μ) * (μ^x) / x!

Where μ is the average number of gallons sold and x is the amount sold. To find the probability of selling more than 250 gallons, we subtract the CDF for 250 gallons or less from 1. This gives us the probability of selling more than 250 gallons.

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The expressions based on the information given are illustrated below

3/4 ÷ 1/2 = 1.5 = quotient is grater than 1

1/2 ÷ 3/4 = 2/3 = quotient is less than 1

2/9 ÷ 1/27 = 6 = quotient is grater than 1

5/3 ÷ 20/6 = 1/2 = quotient is less than 1

4/3 ÷ 3/5 = 20/9 = quotient is grater than 1

19/8 ÷ 2 3/8 = 1 = quotient is equal to 1.

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Answer:

intersection of the lines drawn perpendicular to each side of the triangle through its midpoint

Step-by-step explanation:

The statement ". the intersection of the lines drawn perpendicular to each side of the triangle through its midpoint" option is (D) is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have a statement:

What types of concurrent constructions are needed to find the circumcenter of a triangle?

As we know, the junction of the lines passing through the triangle's middle and perpendicular to each of its sides

The type of concurrent construction is the intersection of the lines drawn perpendicular to each side of the triangle through its midpoint

Thus, the statement ". the intersection of the lines drawn perpendicular to each side of the triangle through its midpoint" option is (D) is correct.

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The correcting answer is - Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.

Fractions represent the parts of a whole or collection of objects.

A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.

Now the given mixed fraction is,

-0.6(5/6)

Now since 5/6 is a repeating decimal,

Therefore converting 0.6 into fraction, we get

0.6 = 6/10

Therefore, -0.6(5/6) = -(6/10)*(5/6)

Rearranging we get,

-0.6(5/6) = -(6/6)*(5/10)

⇒ -0.6(5/6) = -1*(5/10)

or, -0.6(5/6) = -(5/10)

simplifying 5/10 we get,

-0.6(5/6) = -(1/2)

Thus, the correcting answer is - Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.

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The largest product we can get is: 26244,

What is integers?

Integers are whole numbers that are either positive, negative, or zero. They are the building blocks of the number system and are used to represent quantities or perform calculations. Integers are represented in the form of digits and can either be written in the form of standard numbers, Roman numerals, or in the form of exponential notation. Integers are used in many areas of mathematics and are a fundamental concept in the study of algebra, geometry, and calculus. Integers are also used in everyday life, such as in accounting and finance, where they represent monetary values.

We know that for 28,
(k-2)*2 <= k
2k-4 <= k
k <= 4

So, we should only consider numbers less than or equal to 4.

Now, 4 can be replaced by 2*2 and there is no point in taking 1 since it will not increase product result.

So, we are left with 2 and 3. Some possible solutions are:

{3,3,3,3,3,3,3,3,2,2} or {3,3,3,3,3,3,2,2,2,2,2} etc.

Out of all these, the maximum product we can get is from {3,3,3,3,3,3,3,3,2,2} which is: 26244

So, The largest product we can get is: 26244

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The triangles AEB and DEC describes AA similarity .

What is AA Similarity ?

Two triangles are said to be congruent by AA Similarity when two angles in one triangle are congruent to two angles in another triangle .

In the question ,

a figure is given .

in triangle AEB and triangle DEC ,

we can see that ,

∠AEB ≅ ∠DEC    ,   because they are vertically opposite angles .

On rotating triangle CED by  180° around the point E, then the translate point D to point A confirms  ∠EAB ≅ ∠EDC.

Since two angles are Congruent

So , By AA Similarity , triangles AEB and DEC are Congruent .

Therefore , the triangles AEB and DEC are Congruent .

The given question is incomplete , the complete question is

Which of the following triangles in the given figure describes AA similarity ?

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You would gain = (40-30)N =10/100 =10℅

We will simply subtract 3 3/8 from 6 1/2

That is;

6 1/2 - 3 3/8

= 3 4-3/8

=3 1/8

The amount of berry left is more than 3 cups, hence Ryan have enough very stuff to also make a pie

Answer: (8)(-4.5)

Step-by-step explanation: If you were to multiply -4.5 • -8 it would be a positive number but if you multiply (8)(-4.5) that would equal a negative number