The equation c = 2b + 6 represents the total cost c of b sets of beads and one necklace string. Graph the relationship on the coordinate plane.

Answer:

The greatest possible distance between two points on the walls in the room is 17 feet.

Step-by-step explanation:

The room can be modelled as a rectangular prism with the following dimensions:

The greatest possible distance between two points on the walls in the room is the line between diagonally opposite corners. This is marked as the blue line (x) on the attached 3D diagram.

This distance is the hypotenuse of a right triangle with a base of the diagonal of the floor and a height of the height of the room.

The diagonal of the floor (marked "y" on the attached diagram) is the hypotenuse of a right triangle with legs of the width and length of the room.  To calculate the diagonal of the floor, use Pythagoras Theorem.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Substitute a = 8, b = 12 and c = y into the formula and solve for y:

[tex]\implies 8^2+12^2=y^2[/tex]

[tex]\implies 64+144=y^2[/tex]

[tex]\implies y^2=208[/tex]

[tex]\implies y=\sqrt{208}\; \sf ft[/tex]

Therefore, the diagonal of the floor (y) is √(208) feet in length.

We can now use Pythagoras Theorem again to find the length x.

Substitute a = y, b = 9 and c = x into the formula:

[tex]\implies y^2+9^2=x^2[/tex]

Substitute the found value of y and solve for x:

[tex]\implies (\sqrt{208})^2+9^2=x^2[/tex]

[tex]\implies 208+81=x^2[/tex]

[tex]\implies 289=x^2[/tex]

[tex]\implies x=\sqrt{289}[/tex]

[tex]\implies x=17 \sf \; ft[/tex]

Therefore, the greatest possible distance between two points on the walls in the room is 17 feet.

Dennis must work for at least 10.81 hours to earn at least $100.

What is inequality in mathematics?

An inequality in mathematics is a statement that compares two values or expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, x < 5 is an inequality that says that the value of x is less than 5. Another example is y ≥ 2x + 3, which is an inequality that says that the value of y is greater than or equal to 2 times x plus 3.

Inequalities are often used to describe ranges of values, such as the set of all numbers that are less than or equal to 5 (written as x ≤ 5) or the set of all numbers that are greater than 2 and less than 7 (written as 2 < x < 7). Inequalities can be solved, graphed on a number line, and used to make comparisons between values or expressions.

Let's start by writing an expression for the total amount of money Dennis earns in x hours:

Total earnings = 1.75x + 7.5x

Simplifying this expression, we get:

Total earnings = 9.25x

Now, we want to find the inequality that represents the number of hours Dennis must work to earn at least $100. We can set up the inequality as follows:

9.25x ≥ 100

This inequality states that Dennis must earn at least $100, which is represented by the value on the right-hand side of the inequality. The left-hand side of the inequality represents Dennis's earnings, which we found to be 9.25x. Since we want to find the minimum number of hours Dennis must work to earn at least $100, we need to solve for x:

9.25x ≥ 100

x ≥ 100/9.25

Simplifying the right-hand side of the inequality, we get:

x ≥ 10.81

Therefore, the inequality that represents the number of hours Dennis must work to earn at least $100 is:

x ≥ 10.81

This means that Dennis must work for at least 10.81 hours to earn at least $100.

To know more about inequality visit:

brainly.com/question/25275758

#SPJ1

It will take 6.5 minutes to grade 338 test by the electronic grading machine.

The quality of the answer papers is a key element. The machine might not be able to reliably scan and evaluate the answers if the answer sheets are not filled out completely or if the paper has rips or smudges on it. Similar to this, the computer might not be able to recognize the right answers if the answer sheets are not properly aligned.

Given that, the machine can grade 52 test in 1 minute.

The, we can calculate the time taken to grade 338 test as follows:

time = number of tests / rate of grading

Plugging in the given values, we get:

time = 338 / 52 = 6.5 minutes

Hence, it will take 6.5 minutes to grade 338 test by the electronic grading machine.

Learn more about rate here:

https://brainly.com/question/29518179

#SPJ1

The value of x in the equation below 18 = x - 10 is equal to 28.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

18 = x - 10

By rearranging and collecting like-terms, we have the following:

x = 18 + 10

x = 28.

Read more on expression here: brainly.com/question/25767785

#SPJ1

Complete Question:

Find the value of x in the equation below. 18 = x - 10

Answer:

A. Lancaster

Lancaster is on the edge of the yellow area.

Answer: Y = X2

Step-by-step explanation:
A and C aren't proportional and D is increasng

for a f(5) is 1 and f(7) is 1/4

for b the domain is 16-1/4

for c the value is decreasing by 1/2 every time

Note that with respect to the above problem,

Plan:

Let P1 be the proportion for the treatment group (low-fat diet), and P2 the proportion for the control group (normal diet).

State the hypotheses for your test:

H₀: P1 = P2 (There is no significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups)

Ha: P1 ≠ P2 (There is a significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups)

To test this claim, we can use a two-sample z-test for proportions. We calculate the test statistic as follows:

z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled proportion. The pooled proportion is calculated as:

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of successes in each sample.

Using the given data, we have:

p1 = 1642/3311 = 0.495

p2 = 1480/3176 = 0.466

n1 = 3311

n2 = 3176

x1 = 1642

x2 = 1480

p = (1642 + 1480) / (3311 + 3176)

p = 0.480

Then, the test statistic is:

z = (0.495 - 0.466) / sqrt(0.480*(1-0.480)*(1/3311 + 1/3176))

z = 3.22

Using a standard normal distribution table or calculator, we find the p-value associated with a two-tailed z-score of 3.22 is approximately 0.001.

Therefore, the p-value is 0.001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is a significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups.

Answer: The difference between the sample proportions is significant at the 0.10 significance level. Therefore, we reject the null hypothesis and conclude that there is evidence that the two proportions differ.

Learn more about P-Value at:

https://brainly.com/question/30078820

#SPJ1

The growth rate of the plant shown in the graph is 1/2 centimeter per week

From the question, we are to determine the growth rate of the plant

To determine the growth rate of the plant, we will determine the slope of the line

To determine the slope of the line passing through the points (1, 1/2) and (3, 1 1/2), we can use the slope formula:

Slope = (Change in y) / (Change in x)

We first calculate the change in y by subtracting the y-coordinate of the first point from the y-coordinate of the second point:

Δy = 1 1/2 - 1/2 = 1

Next, we calculate the change in x by subtracting the x-coordinate of the first point from the x-coordinate of the second point:

Δx = 3 - 1 = 2

Finally, we can calculate the slope by dividing the change in y by the change in x:

Slope = Δy / Δx = 1 / 2

The slope of the line is 1/2.

Hence, the growth rate is 1/2 centimeter per week

Learn more on Calculating growth rate here: https://brainly.com/question/7040405

#SPJ1

Janice packed 32 cookies.

A system of equations is a set of two or more equations that are to be solved simultaneously. The solutions to a system of equations are the values that satisfy all the equations in the system. There are different methods to solve systems of equations, such as substitution, elimination, and graphing. Systems of equations are used in many areas of mathematics, science, engineering, and economics to model and solve real-world problems.

Substitution method is a common technique for solving systems of equations. In this method, one equation is solved for one of its variables in terms of the other variable, and then the expression for that variable is substituted into the other equation. This results in an equation in one variable that can be solved using algebraic methods. Once the value of one variable is found, it can be substituted back into one of the original equations to solve for the other variable.

In the given question,

Let's use a system of equations to solve the problem:

Let x be the number of cookies Janice packed.

Let y be the number of cookies Siti packed.

Let z be the number of cookies Huiling packed.

From the problem, we know:

x + y = 146 (equation 1)

x + z = 374 (equation 2)

z = 3y (equation 3)

We can use equation 3 to substitute z in equation 2:

x + 3y = 374

We can then use equation 1 to substitute y in the new equation:

x + (146 - x)/2 * 3 = 374

Simplifying and solving for x, we get:

x + 219 - 3x/2 = 374

2x/2 - 3x/2 = 374 - 219

-x/2 = 155

x = -2 * 155

x = -310 (discard this solution)

Since we can't have negative number of cookies, we discard the solution x = -310. Therefore, we can conclude that Janice packed:

x = 146 - y

x = 374 - z

z = 3y

Substituting z in the second equation, we get:

x = 374 - 3y

Substituting this expression for x in the first equation, we get:

374 - 3y + y = 146

Simplifying and solving for y, we get:

-2y = -228

y = 114

Therefore, Siti packed 114 cookies, and since Janice and Siti packed 146 cookies altogether, we have:

x + y = 146

x + 114 = 146

x = 32

So Janice packed 32 cookies.

To know more Substitution method,visit:

https://brainly.com/question/14619835

#SPJ1

Answer: The empirical rule for normal distributions states that for a normal distribution with mean μ and standard deviation σ:

Approximately 68% of the data falls within one standard deviation of the mean, i.e., in the interval (μ - σ, μ + σ).

Approximately 95% of the data falls within two standard deviations of the mean, i.e., in the interval (μ - 2σ, μ + 2σ).

Approximately 99.7% of the data falls within three standard deviations of the mean, i.e., in the interval (μ - 3σ, μ + 3σ).

In this problem, the mean is μ = 20 points and the standard deviation is σ = 3 points. To estimate the probability that the player scored less than 26 points, we need to find the z-score for the value 26, which is given by:

z = (x - μ) / σ = (26 - 20) / 3 = 2

Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, the probability that the player scored less than 26 points is approximately:

P(X < 26) = P(Z < 2) ≈ 0.9772

Converting to a percentage and rounding to one decimal place, we get:

P(X < 26) ≈ 97.7%

Therefore, the estimated probability that the player scored less than 26 points in a randomly selected game is 97.7%.

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

If A file that is 278 megabytes is being downloaded and the download is 19.7% complete, then you just need to multiply the 278 megabytes with 19.7%

The calculation would be: 278 megabytes x 0.197 = 54.766 megabytes.

If you round up the answer to nearest tenth it will be 54.8 megabytes.

Volume of the cone is 1/3 of the volume of the cylinder, so volume of the cone = 40in³.

One-third of the volume of a cylinder is the formula for the volume of a cone. The product of the base area and the height is used to calculate a cylinder's volume. As a result, the formula for a cone's volume is given as V = (1/3) r²h, where "h" stands for the cone's height and "r" for its base radius.

A cylinder's volume is determined by how many unit cubes (cubes of the same length) can fit inside of it. It is the area the cylinder takes up, just as any three-dimensional shape's volume is the area it occupies.

We are aware that a circle serves as the base of a right circular cylinder and that r² is the area of a circle of radius r. As a result, using the formula above, V = r²h is the right circular cylinder's volume.

Now in the given question, volume of the cylinder = 120in³.

Volume of cone = 1/3(volume of the cylinder)

= 1/3 × 120

40in³.

Therefore, volume of the cone = 40in³.

To know more about volume of cylinder, visit:

https://brainly.com/question/16134180

#SPJ1

The length of the mid segment is 8 feet.

The bases of a trapezoid have lengths of 6 feet and 10 feet. Let's find the length of the mid segment of the trapezoid.

A midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

The length of the midsegment of trapezoid is half the sum of the lengths of the two parallel sides

Hence,

mid segment = 1  /2 (6 + 10)

mid segment = 16 / 2

mid segment = 8 feet

Therefore,

mid segment = 8 feet.

learn more on trapezoid here: brainly.com/question/22607187

#SPJ1

The amount that I spent by using the equation y = 1/2x , according to my friend's expense is $7.5.

In its simplest form in algebra, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. 

There are two types of equations:

Identities and conditionals. The identity applies to all values ​​of the variable. Constraint expressions apply only to specific values ​​of variables. Equations are written as two expressions separated by an equal sign ("="). 

Solution:

Given, amount spent by friend = $15

           Equation: y = 1/2x

So, amount spent by me is as follows

y = (1/2)×15

  =15/2

y  = $7.5

To learn more about equation, visit the link below

https://brainly.com/question/29657992

#SPJ1

The amount of money you are spending is $7.50 according to the given equation.

A mathematical equation is a statement that expresses the relationship between two values using mathematical symbols. An equation typically involves a variable, which is a symbol that stands for a number that can change, and an equals sign. Equations can be used to solve a variety of problems in mathematics.

The equation y = 1/2x states that 'y' is equal to one half of 'x'. This equation can be used in many different ways to solve real-life problems. In this case, 'x' represents the amount of money your friend spent at the carnival. 'y' represents the amount of money you spent. To solve for 'y', we divide the value of 'x' by 2.

In the question, your friend spent $15 at the carnival. Therefore, 'x' is equal to 15. We then divide 15 by 2, which gives us 7.5. This means that you spent $7.50 at the carnival.

The equation y = 1/2x is a simple but powerful tool for solving problems. It can be used for a variety of tasks, including finding out how much money you spent at the carnival if you spent half as much as your friend. All you have to do is plug in the value of 'x' and divide it by two.

To know more about real-life problems,

https://brainly.com/question/30051951

#SPJ1

Answer:

$104,000

Step-by-step explanation:

For simple interest,

I = Prt

where I = interest earned

P = principal, amount invested

r = annual interest rate

t = time in years

I = $40,000 × 0.08 × 20

I = $64,000

The total amount saved is the principal amount plus the interest.

$40,000 + $64,000 = $104,000

Answer:

-6a - 48

Step-by-step explanation:

−6(a + 8)

= -6a - 48

So, the answer is -6a - 48

Answer: -6a - 48

Step-by-step explanation: distribute -6

Total amount/Working days

Step-by-step explanation:

Answer:4

Step-by-step explanation:12/3

As a result, there is roughly 0.4664 of an area under the standard normal curve between Z= -1.83 and Z= 0.

Area is the overall space occupied by a three-dimensional object's surface. Square units like square meters or square feet are used to quantify it. By adding up the areas of all an item's faces or surfaces, the surface area of the object can be calculated. For instance, since a cube has six faces, the surface area of a cube can be determined by finding the area of one face and multiplying it by six. Similar to this, one can determine the surface area of a sphere by calculating the area of its surface using the formula 4r2, where r is the sphere's radius.

given

To determine the region under the standard normal curve between Z=-1.83 and Z=0, we can use a standard normal chart or a calculator.

Using a normalised standard table:

Z=-1.83 corresponds to a region of 0.0336. (from the table).

The region is 0.5 to the west of Z= 0. (from the table).

Therefore, 0.5 - 0.0336 = 0.4664 is the region between Z= -1.83 and Z= 0.

Calculator usage

Calculator's normalcdf algorithm can be used to determine the region between Z=-1.83 and Z=0. We calculate normalcdf(-1.83, 0) = 0.4664 using the tool.

As a result, there is roughly 0.4664 of an area under the standard normal curve between Z= -1.83 and Z= 0.

To know more about surface area visit:

https://brainly.com/question/2835293

#SPJ1

By answering the above question, we may state that We still have the expressions same problem because this result is negative once more.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.  

Sheila began with five metres of ribbon and chopped off two and a half to wrap a gift. This may be written as a mixed number:

[tex]2 3/4 = (2 * 4 + 3)/4 = 11/4[/tex]

So, she still has 5 to 11/4 metres of ribbon.

She takes off 0.9 metros of the bracelet's ribbon before cutting it.

She now has the following total quantity of ribbon left:

[tex]5 - 11/4 - 0.9 = 20/4 - 11/4 - 9/10 = (100 - 110 - 36)/20 = -46/20 = -23/10[/tex]

In light of the issue, the outcome is negative, which is illogical.

[tex]5 - 2 3/4 - 0.9 = 5 - 11/4 - 9/10 = (100 - 110 - 36)/20 = -46/20 = -23/10[/tex]

We still have the same problem because this result is negative once more.

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

x= 3 and y = 4

so :

x + y = 3 + 4 = 7

Answer : 7

The statement, Angle 1 and angle 5 are complementary angles,

As ∠2 = ∠5.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know when the sum of two angles is 180° they are supplementary.

Two angles are said to be adjacent angles if they share a common side.

Two angles are said to be complementary when the sum is 90°.

We know vertically opposite angles are in equal measure when a transversal intersects two parallel lines.

Therefore, ∠2 = ∠5.

Hence, ∠1 + ∠2 = ∠1 = ∠5 = 90°.

learn more about transversals here :

https://brainly.com/question/18024908

#SPJ1

The statistical measures for this set of data are as follows:

Minimum: 3

First Quartile (Q1): 8

Median: 13

Third Quartile (Q3): 16

Maximum: 17

Data is information that has been collected and organized to be used for a purpose. It can include numbers, words, images, or any other type of information. Data is used to answer questions, solve problems, and inform decisions. Data can come from a variety of sources such as surveys, experiments, and observations.

A box and whiskers plot can be used to display the distribution of the data set. The box and whiskers plot will use the minimum, maximum, Q1, median and Q3 values to create a visual representation of the data set. The box in the box and whiskers plot is bound by the Q1 and Q3 values, with the median value being represented as a horizontal line inside the box. The whiskers are lines that extend from the box to the minimum and maximum values. The points outside the whiskers are considered outliers in the data set.

For more questions related to number

https://brainly.com/question/17200227

#SPJ9

The volume of water that Keith's kitchen kettle holds when it is full is 1800 ml.

Assume that Keith's kitchen kettle has a "x" ml capacity when it is full.

The kettle is initially 80% full, which means it holds 0.8x ml of water, according to the problem.

20% of the water is poured out, leaving 80% of the original amount of water in the kettle, which is:

0.8x * 0.8 = 0.64x ml

We are informed that the 1152 ml of water that is left equates to:

0.64x = 1152

By multiplying both sides by 0.64, we obtain:

x = 1800

Consequently, Keith's cooking kettle has an 1800 ml capacity when it is full.

To know more similar question visit:

https://brainly.com/question/79178

#SPJ1

Answer: B. 50

Step-by-step explanation:

  To solve this, we will isolate the variable b.

   Given:

[tex]\frac{1}{5}[/tex]b + 4 = 14

   Subtract four from both sides of the equation:

[tex]\frac{1}{5}[/tex]b = 10

   Multiply both sides of the equation by 5:

b = 50

        B. 50

The average rate of change on that interval is r = 7/3.

For any function f(x), we define the average rate of change on an interval [a, b] as

r = ( f(b) - f(a))/(b - a)

here, we have,

In this case, the interval is [0, 6], using the graph we can find the values of the function for these inputs:

f(0) = -8

f(6) =6

Replacing that we get:

r = (6 - (-8))/(6 - 0)

r = (6 + 8)/6

r = 14/6

r = 7/3

The average rate is 7/3.

Learn more about rates of change:

brainly.com/question/8728504

#SPJ1

Answer:

7.75 ; 7.81 ; 7.77 ; 7.84