The sum of two numbers is 207. The difference between the two numbers is 11. Find the greater number?

Answer: $31.50 for the four brushes after using the coupon

Step-by-step explanation:

$10.50 (Amount for EACH brush) * 0.75 (coupon 25% off)  = $7.875 (Amount for each after coupon)

$7.875* 4 brushes = $31.5

or

$10.50 (regular price) * 4 brushes = $42 (4 brushes at regular price)

$42 * 0.75(25% coupon) =$ 31.5

Answer:

See below.

Step-by-step explanation:

(4x^2-3x^3)+(2x^2+4x^3)

6x^2-x^3

(-8x^2-2x+7)+(x^2-3x+2)

-7x^2-5x+9

-hope it helps

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

Learn more about sine rule here: https://brainly.com/question/28523617

#SPJ1

Answer:

B

Step-by-step explanation:

Equation of line II:

y-intercept = b = -1

y = mx + b

y = mx - 1

Plugin the point(2,0) in the above equation,

0 = 2m- 1

2m = 1

m = 1/2

Equation of line :

\(y = \dfrac{1}{2}x - 1\)

Both have same y-intercept and the same rate of change.

Answer:

Step-by-step explanation:

5 1/4

Answer:là

5

với số dư

1

.

5

1

4

Step-by-step explanation:

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

for more such question on mean visit

https://brainly.com/question/1136789

#SPJ8

Answer:

Step-by-step explanation:

Let the point P is origin (0, 0), segment AB lies on the x-axis and segment PC on the y-axis,

Coordinates of A, B and C will be (1, 0), (2, 0) and (0, 2).

When triangle ABC is dilated by a scale factor 4 about the origin,

Rule for dilation;

(x, y) → (4x, 4y)

New coordinates of the points A, B and C will be,

A(1, 0) → A'(4, 0)

B(-2, 0) → B'(-8, 0)

C(0, 2) → C'(0, 8)

By plotting points A', B' and C' we can get the dilated image A'B'C'.

Dilation involves changing the size of a shape.

Assume point P is the center of origin, then we have the following coordinates of ABC

\(A = (1,0)\)

\(B = (-2,0)\)

\(C = (0,2)\)

The scale factor (k) is given as:

\(k= 4\)

So, the dilation rule is represented as:

\((x,y) \to (4 \times (x,y)\)

Using the above dilation rule, the following coordinates represent the image of triangle ABC

\(A' = (4,0)\)

\(B' = (-8,0)\)

\(C = (0,8)\)

See attachment for the image of the dilation.

Read more about dilation at:

https://brainly.com/question/8532602

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

-57.6=x

Step-by-step explanation:

-22.3= x/3-3.1
-19.2=x/3
-57.6=x

It should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

In geometry, it should be noted that a polygon is a plane figure which is described by a finite number of straight line segments that are connected in order to form a closed polygonal chain.

In this case, the bounded plane region, the bounding circuit, may be called a polygon. Also, a similarity transformation is the conformal mapping whose transformation matrix are identical.

In this case, it should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

Learn more about polygon on:

https://brainly.com/question/24966296

#SPJ1

Answer:

2

Step-by-step explanation:

1+1=2

Answer: 12 and 13

Step-by-step explanation:

a(a + 1) = 156

\(a^{2} + a - 156 = 0\)

(a + 13)(a - 12) = 0

a1 = -13 (Room number can't be negative so this is impossible)

a2 = 12, a2 + 1 = 12 + 1 = 13

So the room numbers are 12 and 13

Using a system of equations, it is found that:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, we consider the variable x as Pratham's velocity, with variable y as Roshan's velocity.

If they walk in opposite directions, they will meet in 4 hours, which means that each hour they get 16 miles closer, that is, the sum of their velocities is of 16, hence:

x + y = 16.

In the same direction, they will meet in 16 hours, which means that the subtraction of their velocities is of 4, hence:

x - y = 4 -> x = 4 + y.

Replacing on the first equation:

x + y = 16.

4 + y + y = 16.

2y = 12.

y = 6.

x = 4 + y = 10.

More can be learned about a system of equations at https://brainly.com/question/24342899

Answer:

(0,5) (-5,0) (-5,10) (-10,5)

Step-by-step explanation:

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

Learn more about piecwise functions:

https://brainly.com/question/3628123

#SPJ1

Answer:

none.

Step-by-step explanation:

because FTP=ATJ,

P=A

J=F

The two triangles are not congruent. The correct answer is option A.

If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

In the image two triangles, ETP and ATJ are given. Angle F and angle J are equal due to the opposite angle property. Similarly, angle P and angle A are also equal by alternate angle property. But all the angles are not congruent.

Hence, the triangle FTP and ATJ are not congruent with each other.

To know more about congruency follow

https://brainly.com/question/2938476

#SPJ5

Out of the population being surveyed, the one that could result in a sample statistic but not a parameter is; B: 50

A sample statistic is a piece of information you get from a fraction of a population.

A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

Now, we are told that a population consists of 5000 people. This means that the sample statistic could be the sample mean which could be 50 but certainly not 5000 as the sample statistic can't be same as the population.

Read more about Sample Statistic at; https://brainly.com/question/7301139

#SPJ1

Answer:

there is a formula...

Sn = a1 (1 - r^n) / (1 - r)

a1 = first term = 3

n = number of terms = 8

r = common ratio = 1/2

now we sub

S(8) = 3(1 - 1/2^8) / (1 - 1/2)

S(8) = 3(1 - (1/2^8) / (1/2)

S(8) = 3(1 - 1/256) / (1/2)

S(8) = 3 (256/256 - 1/256) / (1/2)

S(8) = 3(255/256) / (1/2)

S(8) = (765/256) / (1/2)

S(8) = 765/256 * 2/1

S(8) = 1530/256

S(8) = 765/128 or 5 125/128 or 5.9765625

Step-by-step explanation:

Hundredths is at t

fifty three hundredths as decimal = 0.53

The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

More can be learned about union and intersection at brainly.com/question/4699996

#SPJ1

The coordinates of the other endpoint  of the segment, given its midpoint and one endpoint are (-14, -9)

The Midpoint Formula for a line with endpoints as (x₁, y₁) and (x₂, y₂) is;

((x₁ + x₂)/2, (y₁ + y₂)/2)

We are given the  following;

Midpoint (-15,-6)

End point (-16,-3)

Let x₁ = -16, the x coordinate of the endpoint

Let x₂ = the x coordinate of the unknown endpoint

Let y₁ = -3, the y coordinate of the endpoint

Let y₂ = the y coordinate of the unknown endpoint

Thus, for the x coordinate of the unknown endpoint;

(x1 + x2)/2

(-16 + x₂)/2 = -15

-16 + x₂ = -30

x₂ = -14

For the y coordinate of the unknown endpoint;

(y1 + y2)/2

(-3 + y₂)/2 = -6

-3 + y₂ = -12

y₂ = -12 + 3

y₂ = -9

Read more about Line coordinate at; https://brainly.com/question/18315903

#SPJ1

The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

Learn more about domain on

https://brainly.com/question/26098895

#SPJ1

Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.

Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:

Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.

Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.

Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.

Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.

However, mathematical models also have limitations and potential disadvantages:

Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.

Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.

Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.

Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:

Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.

Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.

Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.

Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.

Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.

These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.

For such more questions on Advantages of Mathematical Models

https://brainly.com/question/12653211

#SPJ8

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

One axis is used for kilograms, the other for pounds. When the x-axis is kilograms, the line includes points (1, 2.2), (2, 4.4), and (3, 6.6). The graph is a straight line that passes through the origin. The line is straight because unit conversions are proportional.

9514 1404 393

Answer:

  A (first choice), F (last choice)

Step-by-step explanation:

Formulas for arithmetic sequences are generally written in one of two forms. The form you're given here is called an "explicit" formula. For some value of n, you can find the n-th term by evaluating the formula.

The form used in the first three answer choices is called a "recursive" formula. The value of the n-th term depends not on 'n', but on the previous term.

These two forms can be converted to each other like this:

  explicit formula   ⇔   recursive formula

  \(A(n)=A_1+d(n-1)\quad\Leftrightarrow\quad\begin{cases}a_1=A_1\\a_n=a_{n-1}+d\end{cases}\)

The values of the first term (A₁), the common difference (d), and the term index number (n) are the same in both forms. Once you see this relationship, you should be able to find ...

__

Here, the given function tells you ...

This means the formulas that describe the same sequence are ...

  \(\square\ \begin{cases}a_1=5\\a_n=a_{n-1}+4\end{cases}\\\\\square\ A(n)=5+4(n-1)\)

_____

Additional comment

The commutative property of multiplication tells you that (n-1)(4) = 4(n-1). The order of the operands makes no difference. The given function has the first of these forms, the offered answer choices have the second of these forms.

Answer:

In that one week, his commision was $896, over all 52 weeks, he made $46592

Step-by-step explanation:

So, he makes 14% commision on any stock he sells. This week, he sold $6,400 worth of stocks, and, hes going to make 14% on it. So, take 6400 and divide that by 14%, and what do you get? $896! So, he made $896 that week. Now, say he made that amount EVERY WEEK. so, all you have to do is know how many weeks are in a year (52) and multiply that by 896, which gives you 46592.

Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).

Answer:

Neither

Step-by-step explanation:

I just took the quiz.