Find the midpoint between (9, -1) and (1, 15).

The number of students who drink coffee with cream is 1800.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that in a recent survey of college students, it was determined that 4 out of 5 students drink coffee. Of those students who drink coffee, 1 out of 8 students adds cream. If a college campus has 18000 students.

The number of students who drink coffee with cream is calculated as:-

Number = ( 4 / 5 ) x ( 1 / 8 ) x 18000

Number = 1800

Therefore, there are 1800 students who like their coffee with cream.

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Answer:

1/ a, c, d

2/ You are missing the option in the picture.

Step-by-step explanation:

If a relation is a function, one input can only have one output!

1/

b is wrong because 1 has two outputs -3 and 0. So, the answer for 1 is: a, c, d

2/

To test whether the graph is a function, we have to see if one x has 2 y or not! If it has 2 y, then it is not a function.

You are missing the options for question 2! So I can't answer number 2.

Answer:

E 1/4 (-8y+6x+7)

Step-by-step explanation:

"a" can be expressed as a function of "R" as:

[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex].

What are logarithmic properties?

The 4 laws of logarithms are product property, division property, power property and change of base property.

To solve for "a" in terms of "R," we need to isolate "a" on one side of the equation. We can do this by rearranging the equation and applying logarithmic properties.

Starting with the equation R = 3 log(a + 2) + 15, we'll subtract 15 from both sides:

R - 15 = 3 log(a + 2)

Next, we'll divide both sides by 3:

(R - 15) / 3 = log(a + 2)

Finally, we'll use the inverse logarithmic function, denoted as "exp" or "10^," to solve for "a":

[tex]a+2 = 10^{\frac{(R - 15)}{3} }[/tex]

And finally, we'll subtract 2 from both sides to obtain the solution:

[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex]

So, "a" can be expressed as a function of "R" as:

[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex]

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The value of the equation is A = 1/2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( 1/5 )r + 9/20   be equation (1)

On simplifying the equation , we get

when r = ( 1/4 )

Substituting the value of r in the equation , we get

A = ( 1/5 ) ( 1/4 ) + 9/20

A = ( 1/20 ) + ( 9/20 )

On further simplification , we get

A = 10/20

A = 1/2

Hence , the equation is A = 1/2

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Correct option is C, A triangle can be formed with these side lengths since 8 cm, which is greater than the third side's 7 cm, is possible.

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.

Straight angle refers to the angle that is 180 degrees in length.

The side length combinations that can result in a triangle include

2, 7, and 6 centimeters; 2 meters; 5, and 7 meters

6, 6, and 12 feet

According to the triangle inequality theorem, the third side of a triangle is greater than or equal to the sum of any two of its sides.

In other words, in a triangle with sides a, b, and c,

a + b ≥ c

When examining the sets of provided side lengths,

2 cm, 7 cm, and 6 cm in a triangle,

2 + 6 = 8,

Thus, a triangle can be formed with these side lengths since 8 cm, which is greater than the third side's 7 cm, is possible.

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Answer:

3 3/13 hours

Step-by-step explanation:

you will first find out how many hours it will take for each gardener to do 1 part of the job. gardener 1 is 1/6 and the second is 1/7. you will next add the two fractions. this will equal 13/42. you will then multiply by the reciprocal to get 1, this stands for the whole job done together. The reciprocal is the answer, 42/13. You will then simplify that to 3 3/13 hours.

The value of the expression,

F(x) + G(x) is -6x⁴ -2x³ + 8x² -x + 11.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

An expression,

F(x) = -6x⁴ + 2x² + 12

And G(x) = -2x³ + 6x² - x - 1

To solve F(x) + G(x):

F(x) + G(x)

= -6x⁴ + 2x² + 12 -2x³ + 6x² - x - 1

Simplifying,

=  -6x⁴ -2x³ + 8x² -x + 11

Therefore, the value is -6x⁴ -2x³ + 8x² -x + 11.

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The complete question:

F(x) = -6x⁴ + 2x² + 12

And G(x) = -2x³ + 6x² - x - 1

Find out, F(x) + G(x)?

Answer:     212  +-  360 n    

Step-by-step explanation: Everytime you go full circle (360 degrees  )    either positive or negative you will land back at the 212 degree mark.

The value of c is zero and a and b can be something else, because the vector are linearly independent.

A set of vectors is linearly independent if no vector can be expressed as a linear combination of the others (i.e., is in the span of the other vectors). A set of vectors is linearly independent if no vector can be expressed as a linear combination of those listed before it in the set.

Assume the following:

[tex]a\left[\begin{array}{ccc}2\\2\\0\end{array}\right] + b\left[\begin{array}{ccc}1\\-1\\1\end{array}\right] +c\left[\begin{array}{ccc}4\\2\\-2\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

Determine if a=b=c=0

[tex]2a+b+4c =0 (1)\\ 2a-b+2c =0 (2)\\b-2c=0(3)\\[/tex]

Subtract (2) from (1)

[tex]b+c = 0\\b-2c=0[/tex]

Substitute (5) into (4), we get c=0.

So now what do I do with this fact? I'm tempted to say that only c=0, and a and b can be something else.

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The two equations, y = 53x + 10 and y = 55x, represent the cost of x tickets for option 1 and option 2, respectively.

The equation y = 53x + 10 represents the cost of x tickets for option 1, which includes a ticket cost of $53 per ticket plus a shipping fee of $10. So, if Mrs. Curtis buys 1 ticket, the cost would be 53 * 1 + 10 = 63. If she buys 2 tickets, the cost would be 53 * 2 + 10 = 116, and so on.

The equation y = 55x represents the cost of x tickets for option 2, which includes a ticket cost of $55 per ticket and free shipping. So, if Mrs. Curtis buys 1 ticket, the cost would be 55 * 1 = 55. If she buys 2 tickets, the cost would be 55 * 2 = 110, and so on.

By comparing the values of y for different values of x in these two equations, Mrs. Curtis can determine the cost-effective option for buying the tickets.

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The result of the 10th iteration is 1.689, rounded to the nearest ten-thousandth.

The initial value for this question is 2 + 0.01 = 2.01. If we iterate this initial value using the function "f" ten times, we get the following sequence:

1st iteration: f(2.01) = 3.07 - [tex](2.01)^{2}[/tex]= 0.1599

2nd iteration: f(0.1599) = 3.07 - [tex](0.1599)^{2}[/tex]= 2.868201

3rd iteration: f(2.868201) = 3.07 - [tex](2.868201)^{2}[/tex]= 0.34459799

4th iteration: f(0.34459799) = 3.07 - [tex](0.34459799)^{2}[/tex] = 2.46306801

5th iteration: f(2.46306801) = 3.07 - [tex](2.46306801)^{2}[/tex] = 0.86121799

6th iteration: f(0.86121799) = 3.07 - [tex](0.86121799)^{2}[/tex] = 2.11255201

7th iteration: f(2.11255201) = 3.07 -[tex](2.11255201)^{2}[/tex] = 1.47511099

8th iteration: f(1.47511099) = 3.07 -[tex](1.47511099)^{2}[/tex]  = 1.87593299

9th iteration: f(1.87593299) = 3.07 -[tex](1.87593299)^{2}[/tex] = 1.28972499

10th iteration: f(1.28972499) = 3.07 -[tex](1.28972499)^{2}[/tex] = 1.68900499

So, the result of the 10th iteration is 1.689, rounded to the nearest ten-thousandth.

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Answer: 12/37

Step-by-step explanation:

sin A= bc/ab = 12/37

The sine of the angle is equal to the ratio of the opposite to the hypotenuse (Ik this probably made 0 sense but I hope it helps! :D)

Answer: If a 21.0 kg rock rests on the edge of a cliff 32.0 m high, the gravitational potential energy gained by the rock would be 6585.6 Joules.

Step-by-step explanation:

Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.

As given in the problem a 21.0 kg rock rests on the edge of a cliff 32.0 m high, then we have to calculate the potential energy gained by the rock,

The potential energy of the rock = 21 × 9.8 × 32

                                                     = 6585.6 Joules.

Thus ,If a 21.0 kg rock rests on the edge of a cliff 32.0 m high, the gravitational potential energy gained by the rock would be 6585.6 Joules.

Hope this helps.

Answer:

21.0 kg

Step-by-step explanation:

If the length of the model airplane is 12 inches, then the length of the actual airplane is 18 feet.

Rob collects model planes. One of his planes uses a scale in which 1 inch represents 1. 5 feet.

We will use unitary method to find the length of airplane in inches.

This means according to the model,

1 inch in the model = 1.5 feet of the actual

Therefore, if the length of the model airplane is 12 feet

12 inches of the model airplane = 1.5 × 12

                                                     = 18 feet

so, the actual length of airplane is 18 feet.

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Answer:

224 m^2

Step-by-step explanation:

The dimensions of the four walls are:

6x8, 8x8, 6x8, 8x8

The area of all of these walls is 2(6x8 + 8x8) = 224 m^2

The federal income tax for this person is $407 per month.

The person qualifies for five personal allowances because they have five children. As of 2021, the standard personal allowance in the United States is $12,550.

As a result, the person can deduct 5 × $12,550 =$62, 750, from their taxable income to account for the five allowance

Their monthly taxable income is 61320 - $62, 750, or $4070. Based on taxable income, the federal income tax is calculated, and the individual's tax rate is determined by their taxable income bracket.

The tax rate on $4070 in taxable income as of 2021 is 10%.

Therefore, the federal income tax for this person is $4070 × 10% = $407 per month.

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Answer:

x = 40

Step-by-step explanation:

We have to find,

→ the value of x in the equation.

The equation is,

→ (x/2) + 3 = 23

Now the value of x will be,

→ (x/2) + 3 = 23

→ x/2 = 23 - 3

→ x/2 = 20

→ x = 20 × 2

→ [ x = 40 ]

Hence, the value of x is 40.

Answer:

if there anything you dont understand ask me

Tthe the number of smallmouth bass Chelsie caught = 37

and the number of salmon she caught = 15

Here, x represents the number of smallmouth bass Chelsie caught. and y represents the number of salmon she caught.

Chelsie caught 52 fish today.

So we get an equation,

x + y = 52        

Also, for smallmouth bass, she caught seven more than 2 times the amount of salmon she caught.

So we get an equation,

x = 7 + 2y  

So, we get a system of equations:

x + y = 52                      ..........(1)

x = 7 + 2y                .......(2)

Substitute above value of x in equation (1)

(7 + 2y) + y = 52      

7 + 3y = 52

3y = 45

y = 15

Substitute above value of y in equation (2),

x = 7 + 2(15)

x = 37

Therefore, she caught 37 smallmouth bass and 15 salmon.

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The value of x is given as follows:

x = 39.3.

Similar triangles share these two features listed as follows:

The equivalent side lengths on the proportional triangles are given as follows:

Hence the proportional relationship relating the side lengths is given as follows:

25/35 = x/55

Applying cross multiplication, the value of x is obtained as follows:

35x = 55(25)

x = 55(25)/35

x = 39.3.

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y = 1500 + 150x, this is correctly  represents the relationship between x and y in the graph. This can be solved using the slope formula.

Slope, An evaluation of a line's inclination with respect to the horizontal using numbers. The slope of any line, ray, or line segment in analytical geometry is defined as the proportion of the vertically to the horizontally distance between the two points on the line ("slope equals rise over run").

(0, 1500) to (2, 1800)

thus, slope = (y₂ - y₁) / (x₂ - x₁)

or, slope = 300 / 2

or, slope = 150

So, y - 1500 = 150x

thus, y = 1500 + 150x

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The complete question is as follows:

Answer:

Step-by-step explanation:

The percent of the square shaded is 37.5 without including the % sign.

The square is divided into 4 equal parts

1/4 of the square is fully shaded

The other 1/4 is shaded half

Hence,

When the square is divided into 8 equal parts, 3 parts are shaded

Percent of square shaded= Parts shaded/ Total parts × 100

= 3/8 × 100

= 0.375 × 100

= 37.5%

Ultimately, 37.5 is the percent of the square shaded.

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Answer:

1/3

Step-by-step explanation:

6 faces in a die

1/6 of rolling each side

1/6 of rolling 2 or 3

2/6 chance, 1/3 (simplified)

The solution to the system of equations 4a + 3b = -9 and 2a + 5b = -1 is a = 12, b = -5, found through substitution method.

Simultaneous equations are a set of equations with multiple variables, and the solution of these equations gives us the values of the variables that make all the equations true at the same time. To solve these equations, we can use elimination, substitution or matrices method.

Here, the given set of simultaneous equations is

4a + 3b = -9

2a + 5b = -1

One way to solve this is by substitution, where we solve one equation for one variable and substitute that expression into the other equation. Solving the first equation for "a", we get:

a = -3b - 3

Substituting this expression into the second equation, we get:

2(-3b - 3) + 5b = -1

Expanding the left-hand side, we get:

-6b - 6 + 5b = -1

Combining the like terms, we get:

-b - 6 = -1

Adding b and 6 to both sides, we get:

-b = 5

Finally, dividing both sides by -1, we get:

b = -5

Substituting the value of b back into the expression for a, we get:

a = -3(-5) - 3 = 15 - 3 = 12

So the solution to the system of equations is:

a = 12, b = -5

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Answer:

y = 250x

Step-by-step explanation:

y = 1/[tex]x^{3}[/tex](k)  Solve for k

2 = 1/[tex]5^{3}[/tex](k)

2 = 1/125 (k)  Multiply both sides by 125

250 = k

y = 250x

When the variance of the error term increases in a simple linear regression model, it indicates a less accurate model with a high degree of uncertainty in its predictions.

Regression is a statistical method used to model the relationship between two variables, where one of the variables is dependent on the other.

Simple linear regression is a type of regression where the relationship between the dependent variable and the independent variable is modeled as a linear equation.

Mathematically, let's consider the simple linear regression equation as:

Y = β0 + β1X + ε

Where Y is the dependent variable, X is the independent variable, β0 and β1 are the coefficients of the regression equation, and ε is the error term.

The variance of the error term, Var(ε), is a measure of the spread of the residuals. A large variance of the error term indicates that the residuals are spread out over a large range, and thus, the regression model's predictions may not be very accurate.

In other words, a large variance of the error term means that the model has a high degree of uncertainty in its predictions, leading to a larger deviation between the actual and predicted values.

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The car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).

The depreciation equation for the car can be represented as y = mx + b, where y is the value of the car at time x, m is the slope of the line, and b is the y-intercept.

To find the slope, we can use the information that the car loses all of its marketable value after 9 years. The market value of the car will be 0 after 9 years, so we can set y = 0 when x = 9:

0 = m * 9 + b

To find the y-intercept, we can use the information that Jason purchased the car for $22,995. This means that the value of the car at time 0 was $22,995, so we can set y = 22,995 and x = 0:

22,995 = m * 0 + b

Combining these two equations, we can solve for m and b:

0 = m * 9 + b

22,995 = m * 0 + b

b = 22,995

Now that we have found the y-intercept, we can use it to find the x-intercepts by setting y = 0 and solving for x:

0 = m * x + 22,995

0 - 22,995 = m * x

-22,995 = m * x

x = -22,995 / m

Since we don't know the value of m, we can't find the x-intercepts directly. However, since the car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).

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Answer:

Step-by-step explanation:

The Answer would be -4x

Because 3-7= -4