Carlson Middle School has a total of 500 students in sixth, seventh, and eighth grades. The table below shows the number of students in each grade.

Grade Number of Students
Sixth 203
Seventh 126
Eighth 171

The principal randomly selects 25 students to receive a free school lunch today. What is the most likely number of sixth graders in the group of 25 selected by the principal?

There is also a picture down below

The value of x is approximately 5.4 when x^3 -10x = 100

How to solve the equation?

The equation is given as:

x^3 -10x = 100

Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100

After several attempts, we have:

x = 5.4 (approximately)

Substitute 5.4 for x in x^3 -10x = 100

5.4^3 -10 * 5.4 = 100

Evaluate

103.5 = 100

Approximate

100 = 100This means that x is approximately 5.4 when x^3 -10x = 100

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Answer:

7

Step-by-step explanation:

slope = rise/run = (difference in y)/(difference in x)

First, we find a difference in y.

Subtract any two values of y.

For example: 35 - 14 = 21

Now we find the corresponding difference in x.

Now subtract the x values corresponding to those y values in the same order.

-1 in x corresponds to 35 in y.

-4 in x corresponds to 14 in y.

That means your difference in x is the subtraction -1 - (-4) = -1 + 4 = 3

The difference in y is 21.

The difference in x is 3.

slope = (difference in y)/(difference in x) = 21/3 = 7

Answer: 7

Answer:

f(x) = -3x + 4

Step-by-step explanation:

Plug domain into each function and see if it matches any values in the range.

1) Let the value of yellow circles = x

Let the value of green butterflies = y

Consider the left string,

3x + y = 15  ----(1)

Consider the right string,

x + 2y = 15 ----(2)

Let us solve the linear equations

(1) *2  => 6x+ 2y = 30 ---(3)

(3) - (2) => 6x+ 2y = 30 - ( x + 2y = 15)

            =>  5x  = 15

            =>   x =  3

Substituting x in (1)

3(3) + y = 15

y = 15- 9

y = 6

The value of yellow circles = 3

The value of green butterflies = 6        

2)  Let the yellow circles = c

Let the green butterflies = b

The linear equations that could be formed are:

a) Left string equation:

3c+b = 15

b) Right string equation:

2b +c = 15

c) Equation of both strings:

4c +3b = 30

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Eugene will save $901.8 on the car overall if he chooses payment plan A.

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Answer:

f'(x) = [tex]\frac{1}{x+2}[/tex]

Step-by-step explanation:

using the chain rule to differentiate

f(x) = g(h(x)) , then

f'(x) = g'(x) × h'(x)

f(x) = ln(2x + 4) , then

f'(x) = [tex]\frac{1}{2x+4}[/tex] × [tex]\frac{d}{dx}[/tex] (2x + 4)

      = [tex]\frac{1}{2x+4}[/tex] × 2

      = [tex]\frac{2}{2x+4}[/tex]

      = [tex]\frac{1}{x+2}[/tex]

The equation that represents the given situation is required.The cost of the ticket after L losses is a. Initial cost of the ticket = $49.64Price decrease per game lost = $0.41Number of games lost = LMoney lost after L losses is So, the cost of the ticket after L losses would be the initial cost of the ticket minus the money lost after L losses.The cost of the ticket after L losses is a. 

The y-intercept of f(x) is equal to the y-intercept of g(x).

the y-coordinate of a point on a surface, curve, or line where they cross the y-axis.

Finding the value of y at x=0 will help you locate the y-intercept on a graph. The graph's intersection with the y-axis occurs here.

When the slope of the line being studied is known, and the provided point is also the y - intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B is used in the equation to indicate the y value of the y intercept point.

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Answer:

  25 kg

Step-by-step explanation:

The sum of the weights of the small and large sacks is 65 kg. The larger sack weighs 15 kg more. You want the weight of the smaller sack.

Let w represent the weight of the sand in the small sack. Then (w+15) is the weight of the sand in the larger sack. The total weight is 65 kg, so we have ...

  w +(w+15) = 65

Subtracting 15 from both sides gives ...

  2w = 50

  w = 25

The weight of the sand in the small sack is 25 kg.

Answer:

1st one: 50%, 0.5, 1/2

2nd one: 25%, 0.25, 1/4

3rd one: 18%, 0.18, 9/50

4th one: 10%, 0.1, 1/10

5th one: 20%, 0.2, 1/5

Step-by-step explanation:

Hope this helps!

The proportional relationship that models this situation is given by:

y = 16.99x, 0 ≤ x ≤ 12.

In a direct proportional relationship, the output variable y is found as the multiplication as the multiplication of the constant k by the input variable x, according to the following rule:

y = kx

In the context of this problem, the input variable and the output variable are given as follows:

The monthly cost for the first 12 months is of $16.99, hence the constant is given as follows:

k = 16.99.

Considering the given domain, the relationship is modeled by the following equation:

y = 16.99x, 0 ≤ x ≤ 12.

The missing information is that for the first 12 months, the monthly cost of the plan is of $16.99.

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By ASA or SAS the triangles can be proves congruent.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.

As, from the given figure we can find some equal parts.

First we have two triangles named KOE and LOB

Now, in both triangles

EO = OB  ( given)

<KOE =< LOB (Vertically opposite angle)

Now, we have one side and one angle congruent.

There are two possibilities now either we have another pair of side to make SAS Congruence or we have another angle congruent to make ASA congruence.

So, either KO = OL or

<LBO = <OKE.

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Answer:X-3 is a factor of x³+ax²–2x+3

Step-by-step explanation:X-3 is a factor of x³+ax²–2x+3

p(x)=x

3

−ax

2

+2x+a−1

⇒  p(a)=(a)

3

−a(a)

2

+2(a)+a−1

⇒  0=a

+2a+a−1=0

⇒  3a−1=0

⇒  3a=1   a=

3

1

​

Answer:

y= 3/2 x + -4

Step-by-step explanation:

-4 Is the y intercept (the vertical axis)
the 3/2 is the rise over run of the line (how many up over how many across). It's positive because of the slope up to the right.

Answer:

see explanation

Step-by-step explanation:

the equation of a line (linear equation) has slope- intercept form

y = mx + c ( m is the slope (gradient)) and c the y- intercept )

y = 12 + 2x or y = 2x + 12 ← is in slope- intercept form

with gradient m = 2

--------------------------------------------------------

the only graphs in linear form are

y = [tex]\frac{1}{2}[/tex] x and y = 12 - x

the other 2 have an x² term which indicates they are quadratic

The coordinates of the image after 90° about the​ origin is (6, -5)

A 90 degrees rotation denoted by R(90, 0) is a rotation that has the same effect as the 270 degrees counterclockwise of a figure.

The coordinate of the point is given as

(5, 6)

The rotation is given as 90° about the​ origin

So, we have

(x, y) => (y, -x)

Substitute (5, 6) in (x, y) => (y, -x)

So, we have

(5, 6) => (6, -5)

Hence, the coordinates of the image is (6, -5)

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Using algebraic expression, if Jeff made the fruit salad using one pineapple, then he use 10 oranges, 10 apples and 20 bananas

Number of pineapples = 1 pineapple

Number oranges equal to the 10 times the number of pineapples

We have to multiply number of pineapples by 10

Number of oranges = 1×10

= 10  oranges

Number of oranges equal to the number of apples

Number of apples = 10 apples

Number of bananas equal to the twice the number of apples

Number of bananas = 2×10

= 20 bananas

Hence, using algebraic expression, if Jeff made the fruit salad using one pineapple, then he use 10 oranges, 10 apples and 20 bananas

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95% confidence interval for the true population mean watermelon weight. is (69.94, 72.06)

Confidence Interval formula = Mean ± z × Standard deviation/√n

Mean = 71 ounces

Standard deviation = 2.8 ounces

z score = 95% confidence interval = 1.96

Confidence Interval = 71 ± 1.96 × 2.8/√27

= 71 ± 1.96 × 0.5388602512

= 71 ± 1.0561660924

71 - 1.0561660924

= 69.943833908 ounces

Approximately = 69.94 ounces

71 + 1.0561660924

= 72.0561660924 ounces

Approximately = 72.06 ounces

95% Confidence Interval = (69.94, 72.06).

the complete question is

You measure 27 watermelons' weights, and find they have a mean weight of 71 ounces. Assume the population standard deviation is 2.8 ounces. Based on this, construct a 95% confidence interval for the true population mean watermelon weight.

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Answer:

Positive

Step-by-step explanation:

Below sea level would be negative and at sea level would be zero.

The student that raised the least amount based on the information is student C.

For student A, the equation illustrated is y = 14x and this represents the amount of money raised (y) for walking (x) miles.

For student B, $42 is raised after walking 3 miles. The amount raised per mile will be:

= $42 / 3

= $14 per mile

For C, The miles walked 6 and 9 and the money raised $72 and $108. This shows that the amount is:

= $72 / 6

= $12 per mile.

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Three students are participating in a walkathon. The data for each student is shown. Student A: the equation y = 14x represents the amount of money raised (y) for walking (x) miles

Student B:$42 is raised after walking 3 miles.

Student C: miles walked 6 and 9 money raised $72 and $108

Who raised the least amount

Answer:

The student that raised the least amount based on the information is student C.

Step-by-step explanation:

The number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.

What is an integer ?

Integer is the collection of whole numbers and negative numbers. It does not include the fractional part.

It is given that square root of a decimal number is 9.2371 and we have to find out that the number lies between which 2 integers.

We know that the integer 9 is less than 9.2371 , so the square of 9 will be :

9² = 81

And

The square of next integer 10 is equal to 100.

The square of 9.2371 will be equal to :

= (9.2371)²

= 85.32

So , the number is 85.32 and it lies between 2 integers which are 81 and 100.

Therefore , the number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.

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For 26 rides in a month, a monthly pass should be made, while for rides less than 26 using a one-way ticket will be a cost-effective method

Cost of one way train ticket = $.195

Cost of monthly pass = $50

Monthly pass: It is a prepaid fare card good for one month of limitless travel. This saves cost and time in terms of commuting costs and time of getting the tickets issues

Let x represent the number of rides one takes

Formulating the equation we get:

Cost of one-way ticket*Number of rides = Cost of a monthly pass

= 1.95*x = 50

x = 25.64 or 26 rides

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Answer: 1, 2, and 4

Step-by-step explanation:

1. Cooper included ALL truthful information.

2. Brianna KNOWS she has the funds.

3. Allison makes a large purchase WITHOUT knowing how she will pay.

4. Greg discloses ALL fees.

Answer:

After 2 1/3 hours.

Step-by-step explanation:

For this you have to calculate how much hours is 1/3 of 7 hours. The word 'of' implies a multiplication function.

1/3 * 7 = 7/3 = 2 1/3

Answer:

1.264×10^-5

Step-by-step explanation:

If you are allowed to use a calculator, it will totally do this question for you. Check mode for Sci Not or use the ^ or EE button.

If no calculator allowed, factor out the 10^-6 and add the numbers. Change back to Scientific Notation and fix the first number. It has to have one digit to the left of the decimal. Adjust the exponent to account for changing 12.64 to 1.264 See image.

The most appropriate choice for linear equation will be given by -

First option is the correct option

Adding 4 units negative tiles to both sides.

What is linear equation?

Equation shows  the equality between two algebraic expressions by connecting the two algebraic expression by an equal to sign.

A one degree equation is called linear equation.

Here,

The equation is 3x + 4 = 2x + 6

For the second option,

If we have to add 4 units negative tiles to left side, we will also have to add 4 units negative tiles to right side.

Second option is wrong

For the third option

We have to add four units negative tiles to both sides, not 4 units positive tiles.

For the fourth option

Adding 6 units negative tiles to left side and 4 units negative tiles to right side will not eliminate any of 6 or 4.

So the first option is correct.

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Complete Question

The diagram has been attached below

12. The statement ' x+3 = 9'  is true sometimes.

How is this explained?

Let x= 6,

6 + 3 = 9 (true)

Let x= 5 ,

5 + 3 = 8 (not true)

13. Option c. The statement 'multiplicative inverse of a number is less than the original number' is true for all numbers greater than 1.

How is this explained?

Let us consider some numbers,

a) 1

The multiplicative inverse of 1 = 1

Thus, multiplicative inverse of this number is not less than the original number.

b) 2 (greater than 1)

The multiplicative inverse of 2 = 1/2

multiplicative inverse of this number is less than the original number.

c) 8/7 (greater than 1)

The multiplicative inverse of 8/7 = 7/8

Here, multiplicative inverse of this number is less than the original number.

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