Ava has more than 15 coins in her collection.
Which inequality shows the number of coins in Ava's collection?

Answer:

-2.6112

Step-by-step explanation:

= 0.510 (3+0.2) x -1.6

= 0.510 x 3.2 x -1.6

= -2.6112

hence answer is -2.6112.

Answer:

Step-by-step explanation:

-( -1 ) = 1

-| -1 | = -1

-| 1 | = - 1

| 1 | = 1

| -1 | = 1

Answer: 4=X

Step-by-step explanation:

You divide 4x by itself, and divide 16 by 4x leaving you with X and 4 (I'm pretty sure)

Answer:

x=2,-2

Step-by-step explanation:

first you subtract x^4 from both sides

second subtract 16  from both sides

third Divide both sides by -1

fourth take root.

Answer:

360 cubes

Step-by-step explanation:

EXPLANATION:

-We must first find the value of x in the given equation for AC=4y-48.

-After obtaining the value we must add the value of AD = 18

The exercise is as follows:

Now we must replace the value in the equation; is as follows:

Answer:

-15 degrees

Step-by-step explanation:

3 times 5 is 15 and its negative because it says it DROPS every hour and its taking the temp every 5 hrs

The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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Answer:

x = 13

Step-by-step explanation:

The tirangle ABC is given as equilateral. Every angle is therefore =. Not only that, each angle is 60 degrees.

If you need proof of that, remember that x + x + x  = 180. Every triangle has 180 degrees.

if 3x = 180 then 1 x is 60

8x - 44 = 60       Add 44 to both sides.

8x = 60 + 44

8x = 104             Divide by 8

x = 104/8

x = 13

Answer:

h = 22.91 cm

Step-by-step explanation:

Given that,

The volume of a vase, A = 1330.2 cm³

Radius of the vase, r = 4.3 cm

We need to find the height of the vase. The formula for the volume of a cylinder is given by :

\(V=\pi r^2 h\\\\h=\dfrac{V}{\pi r^2}\\\\h=\dfrac{1330.2 }{3.14\times (4.3)^2}\\\\h=22.91\ cm\)

or

h = 23 cm

So, the height of the vase is equal to 23 cm.

Answer:

15.10$

Step-by-step explanation:

you would multiply 4.20x3 and 2.50x1 get the product of both answers and add them im pretty sure.

The office and living room in a tiny house share a wall. The office area is 28 square feet, while the living room area is 63 square feet.

In a tiny house where the office and living room share a wall, the office area measures 28 square feet, while the living room area is 63 square feet. The shared wall creates a physical boundary between these two spaces, allowing for separation while maximizing the efficient use of space.

Despite the shared wall, the office and living room can be distinct areas with their own functionality and design. The office, with its 28 square feet, can accommodate a small desk, chair, and necessary office equipment. It provides a dedicated workspace for tasks that require focus and concentration.

On the other hand, the living room, with its larger area of 63 square feet, offers more space for relaxation and entertainment. It can house a comfortable seating arrangement, a television or entertainment center, and other elements that promote a cozy and inviting atmosphere.

By sharing a wall, the tiny house optimizes its available area. This design allows for separate zones for work and leisure without sacrificing precious square footage. The shared wall also offers the advantage of shared utilities, such as electrical outlets or internet connections, reducing the need for additional installations. Overall, this setup provides a compact yet functional living space that maximizes efficiency and comfort in a tiny house setting.

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A slope is also known as the gradient of a line. The slope of the function is -4, Thus, the correct option is D.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

The slope of the function is,

m = (13-5)/(-2-0) = 8/-2 = -4

Hence, the slope of the function is -4, Thus, the correct option is D.

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Answer:

3x(2x - 3)

Step-by-step explanation:

Given

y = 6x² - 9x ← factor out 3x from each term

  = 3x(2x - 3)

Answer: Solution: \(a=\dfrac{-19}{3}\) and \(b=\dfrac{1}{3}\) .

Step-by-step explanation:

The given pair of equations:

\(a-8b= -9\ ...(i)\\\\ a-2b= -7\ ...(ii)\)

Eliminate equation (i) from (ii) , we get

\(-2b-(-8b)=-7-(-9)\\\\\Rightarrow\ -2b+8b=-7+9\\\\\Rightarrow\ 6b=2\\\\\Rightarrow\ b=\dfrac{1}{3}\)

Put value of b in (ii) , we get

\(a-2\times\dfrac{1}{3}=-7\\\\\Rightarrow\ a=-7+\dfrac{2}{3}\\\\\Rightarrow\ a=\dfrac{-21+2}{3}\\\\\Rightarrow\ a=\dfrac{-19}{3}\)

Solution: \(a=\dfrac{-19}{3}\) and \(b=\dfrac{1}{3}\) .

Answer:

15.6 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula below, where \((x_1, y_1)\) is the first coordinate and \((x_2, y_2)\) is the second coordinate.

\(\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}\)

Using the distance formula above,

distance between A(-3, 1) and B(7, 13)

= \(\sqrt{(13-1)^{2} + [7-(-3)]^{2} } }}\)

= \(\sqrt{12^2+(7+3)^2}\)

= \(\sqrt{244}\)

= 15.6 units (3 s.f.)

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Answer:

u use the closest number to the number u are rounding up to round it up.if it is 0-4 u round it to 0and add to the number while if it is 5-9 u round it up to 1 and add to the number.after all rounding up the number used to round up downwards will be converted to 0s

Answer:

If the ones place has a number less than 4, the tens stay the same with a zero in the ones place. If the ones place has a number more than 5, the tens will have another ten. If the ones place has a number 5 in the ones place, then you round the tens to the next ten.

Examples: 37=40       73=70          65=70

Answer:

d = 13

Step-by-step explanation:

First, the distance formula is needed:

\(d = \sqrt{(x_{2} - x_{1} )^{2} +(y_{2} - y_{1 })^{2} }\)

Next we assign the points

(2,-4) is point 1, (7,8) is point 2

\(d = \sqrt{(7 - 2 )^{2} +(8 - (-4))^{2} } \\d = \sqrt{5^{2} +12^{2} } \\d = \sqrt{25 + 144}\\ d = \sqrt{169} \\d = 13\)

Given two points (2,-4) and (7,8)

To find - The distance between given points.

We know the formula that is used to find the distance is given as

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We let P = (2,-4)

and Q = (7,8)

\(x_1=2, y_1=-4\\x_2=7,y_2=8\)

on substituting we get

\(d=\sqrt{(7-2)^2+(8+4)^2}\\ d=\sqrt{(5)^2+(12)^2} \\d=\sqrt{25+144} \\d=\sqrt{169}\\ d=13\)

Hence we get the distance between (2,-4) and (7,8) is 13.

Final answer - The distance is 13.

Answer:

(0,-18)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The phase change line, also known as the phase boundary or phase transition line, is a line on a graph that represents a change in conditions for a substance. This line shows the temperature and pressure conditions at which a substance will change from one phase to another, such as from a solid to a liquid or from a liquid to a gas.

The phase change line is represented on a graph by a diagonal line that separates two regions where the substance is in different phases. This line usually slopes upwards from left to right, indicating that higher temperatures and pressures are needed to change the substance from one phase to another.

The phase change line is an important concept in thermodynamics and is used to understand the behavior of substances under different conditions. For example, the phase change line for water shows that at normal atmospheric pressure, water will freeze at 0°C and boil at 100°C. However, at higher pressures, the freezing and boiling points will change, and water may exist in different phases, such as a supercritical fluid.

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The values of x that satisfy the equation are x = 13 and x = 1. The other two options, x = -29 and x = 42, are not solutions to the equation.

A mathematical statement proving the equality of two expressions is known as an equation. The left-hand side (LHS) and the right-hand side (RHS), which are commonly joined by the equal sign (=), make up this structure.

Many mathematical operations, such as addition, subtraction, multiplication, division, exponents, and roots, can be used in equations. Finding the variable value or variables that make an equation true is the aim when solving an equation.

Based on their degree, or the highest power of the variable in the equation, equations can be categorized. A quadratic equation, for instance, has a degree of 2, while a linear equation has a degree of 1. Moreover, the number of solutions to an equation can be used to categorize it.

Starting with the equation:

(x – 7)^2 = 36

Taking the square root of both sides, we get:

x – 7 = ±6

Solving for x in each case, we get:

x – 7 = 6, which gives x = 13

or

x – 7 = -6, which gives x = 1

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Answer:

(C) ¹/₂

Step-by-step explanation:

Given;

A standard number cube with the numbers 1 through 6 = 1, 2, 3, 4, 5, 6

The probability of rolling a number less than 4 = 3, 2, 1

The probability of rolling 3, P(3) = ¹/₆

The probability of rolling 2, P(2) = ¹/₆

The probability of rolling 1, P(1) = ¹/₆

Probability of rolling a number less than = P(3) or P(2) or P(1)

                                                                   = ¹/₆ + ¹/₆ + ¹/₆

                                                                   = ³/₆

                                                                   = ¹/₂

Therefore, the probability of rolling a number less than 4 is ¹/₂

Option (C) ¹/₂

To find the area of a triangle with three given vertices, P(2,0,-3), Q(1,4,5) and R(7,2,9), we can use the formula for Heron's Formula. Heron's Formula states that the area of the triangle is equal to the square root of the semi-perimeter multiplied by the semi-perimeter minus the length of each side. To calculate the length of each side, we can use the distance formula. The distance formula states that the length of a line connecting two points (x1, y1, z1) and (x2, y2, z2) is equal to the square root of (x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2.

To calculate the area of the triangle, we must first calculate the length of each side. The length of PQ is 5.196, the length of QR is 8.602, and the length of PR is 11.402. To calculate the semi-perimeter, we must add the three lengths together and divide by 2. The semi-perimeter is (5.196 + 8.602 + 11.402) / 2 = 12.200.

Finally, we can use Heron's Formula to calculate the area of the triangle. The area of the triangle is equal to the square root of the semi-perimeter multiplied by the semi-perimeter minus the length of each side. Thus, the area of the triangle is equal to the square root of 12.200 x 12.200 - 5.196 - 8.602 - 11.402 = 6.127 units.

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Answer:

y + 9 = \(\frac{1}{5}\)(x + 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = \(\frac{1}{5}\) and (a, b) = (- 4, - 9) , thus

y - (- 9) = \(\frac{1}{5}\)(x - (- 4) ) , that is

y + 9 = \(\frac{1}{5}\)(x + 4)

Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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The probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50, is approximately 11.90%.

Probability plays a significant role in statistics and helps us understand the likelihood of an event occurring. In this case, we will discuss the probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50.

To calculate the probability of selecting a sample with a mean of 1450 or less, we will use the concept of the standard normal distribution. The standard normal distribution is a probability distribution that has a mean of 0 and a standard deviation of 1.

We can convert any normal distribution to a standard normal distribution by using the formula z = (x - μ) / σ, where z is the standard score, x is the raw score, μ is the population mean, and σ is the standard deviation.

In this case, we know the population mean is 1500, and the standard error of the mean is 42.50. The standard error of the mean is the standard deviation of the sample means, and we can calculate it using the formula σ/√n, where σ is the population standard deviation and n is the sample size. However, in this case, we already know the standard error of the mean.

Using the formula z = (x - μ) / σ, we can find the z-score for a sample mean of 1450:

z = (1450 - 1500) / 42.50

z = -1.18

We can then use a standard normal distribution table to find the probability of a z-score of -1.18 or less.

The probability of a z-score of -1.18 or less is 0.1190, or approximately 11.90%.

Therefore, the probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50, is approximately 11.90%.

This means that if we were to randomly select samples from the population, about 11.90% of them would have a mean of 1450 or less.

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a) "You will get an A in this course if and only if you learn how to solve discrete mathematics problems."
b) "You will be informed if and only if you read the newspaper every day."
c) "It will rain if and only if it is a weekend day."
d) "You can see the wizard if and only if the wizard is not in."
e) "My airplane flight will be late if and only if I have to catch a connecting flight."

These propositions are written in the form "p if and only if q" in English, which means that both p and q must be true for the entire statement to be true.

This form is also known as a biconditional statement, and it is often used in logic and mathematics to express the relationship between two propositions.

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