Dan bought 5 new baseball trading cards to add to

his collection. The next

day his dog ate half of his collection. There are now

only 32 cards left.

How many cards did Dan start with ?

f(x)>=-7

Functions:

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.

If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x

Given :

f(x) = -3|x+1|-4

using the table of values for g(x) = |x|

Solution :

f(x) = -3|x+1|-4

f(x) = -3|g(x)+1|-4

f(x) = -3||x|+1|-4

which means |x| is always positive |x|>0

f(x) = -3||x|+1|-4

f(x) = -3x-3-4

f(x) = -3x-7

f(x)>=-7

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Answer:

F  = (9/5)C  + 32 is a function because every Celsius temperature is associated with only one Fahrenheit temperature.

hope this helps!!

Answer:

\(y=-\frac{2}{3}x+1\)

Step-by-step explanation:

Parallel means same slope.

\(y=-\frac{2}{3}x+b\)

\(5=-\frac{2}{3} (-6)+b\)

5 = 4 + b

b = 1

\(y=-\frac{2}{3}x+1\)

the molecular formula is obtained by multiplying the empirical formula (CH) by the molecular formula ratio: Molecular formula = (CH) * 6 = C6H6

To determine the percent composition, empirical formula, and molecular formula of the substance, we need to use the given masses of the elements and the molecular mass.

a. Percent Composition:

The percent composition represents the proportion of each element's mass in the total mass of the substance.

For carbon:

Percent composition of carbon = (mass of carbon / total mass of substance) * 100

Percent composition of carbon = (43.910 g / 47.593 g) * 100

Percent composition of carbon ≈ 92.09%

For hydrogen:

Percent composition of hydrogen = (mass of hydrogen / total mass of substance) * 100

Percent composition of hydrogen = (3.683 g / 47.593 g) * 100

Percent composition of hydrogen ≈ 7.74%

Therefore, the percent composition of carbon and hydrogen in the substance is approximately 92.09% and 7.74%, respectively.

b. Empirical Formula:

The empirical formula represents the simplest ratio of the elements in a compound.

To determine the empirical formula, we need to find the mole ratios of the elements. First, we calculate the moles of each element using their masses and molar masses:

Moles of carbon = mass of carbon / molar mass of carbon

Moles of carbon = 43.910 g / 12.01 g/mol

Moles of carbon ≈ 3.659 mol

Moles of hydrogen = mass of hydrogen / molar mass of hydrogen

Moles of hydrogen = 3.683 g / 1.01 g/mol

Moles of hydrogen ≈ 3.649 mol

Next, we divide the number of moles of each element by the smallest number of moles to get the simplest ratio:

Carbon : Hydrogen ≈ 3.659 mol / 3.649 mol ≈ 1:1

The empirical formula of the substance is CH.

c. Molecular Formula:

To determine the molecular formula, we need the molecular mass of the substance.

The molecular mass is given as 78.11 u.

The empirical formula mass can be calculated by adding the molar masses of carbon and hydrogen:

Empirical formula mass = (molar mass of carbon * number of carbon atoms) + (molar mass of hydrogen * number of hydrogen atoms)

Empirical formula mass = (12.01 g/mol * 1) + (1.01 g/mol * 1)

Empirical formula mass = 13.02 g/mol

To find the molecular formula, we divide the molecular mass by the empirical formula mass and determine the whole-number ratio:

Molecular formula ratio = molecular mass / empirical formula mass

Molecular formula ratio = 78.11 g/mol / 13.02 g/mol

Molecular formula ratio ≈ 6

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The value based on the iterative formula will be 4.556.

An iterative formula is a mathematical formula that generates a sequence of values by repeatedly applying a set of rules or operations to an initial value. The output of each iteration is used as the input for the next iteration.

In this case, to work out the value of x3 using the given iterative formula, we need to apply the formula three times, starting with x1 = 8:

x₁ = 8 (given)

Using n = 1:

x₂ = 5 - 2 ln(x₁) = 5 - 2 ln(8) ≈ 1.153

Using n = 2:

x₃ = 5 - 2 ln(x₂) = 5 - 2 ln(1.153) ≈ 4.556

Therefore, x3 ≈ 4.556.

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The value of the vector \(proj_{vu}\) is <-972/169, -405/169>. (option d).

The projection of one vector onto another vector can be thought of as the shadow of one vector onto another in the direction of the second vector. Mathematically, the projection of vector v onto vector u can be calculated as follows:

\(proj_{vu}\) = (v · u / ||u||²) x u

Here, · denotes the dot product of two vectors, and ||u|| denotes the magnitude or length of vector u.

Now, let's apply this formula to the given vectors u and v:

u = <-12,-5>

v = <3,9>

To calculate \(proj_{vu}\), we first need to find the dot product of vectors u and v:

u · v = (-12 x 3) + (-5 x 9) = -36 - 45 = -81

Next, we need to find the magnitude of vector u:

||u|| = √((-12)² + (-5)²) = √(144 + 25) = √169 = 13

Now, we can substitute the values we have found into the formula for \(proj_{vu}\):

\(proj_{vu}\) = (-81 / (13²)) x <-12,-5> = <-81/13, -405/169>

Therefore, the answer to the given question is option (d): \(proj_{vu}\) = <-972/169, -405/169>.

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Answer:

about -4, 0.5 I believe

Step-by-step explanation:

the distance between AB is 7 theres is 4 on 1 side and 3 on the other making it lean towards the bottom side specifically -0.5 now using basic knowledge we can conclude that the horizo tal coordinate is -4 hope this helps

Using half angle formula,

Half angle formulas are equations that contain the half angles of the trigonometric ratios.

Given that tanα = -1/2 and π/2 < α < π

To find sin(α/2), we use the half angle formula

sin(α/2) = √[(1 - cosα)/2]

Also, tan²α + 1 = sec²α = 1/cos²α

⇒ cosα = ±1/√(1 + tan²α)

Since π/2 < α < π

cosα = -1/√(1 + tan²α)

Substituing this into the equation for sin(α/2), we have

sin(α/2) = √[(1 - cosα)/2]

sin(α/2) = √[(1 - (-1/√(1 + tan²α)))/2]

Substituting  tanα = -1/2 into the equation, we have

sin(α/2) = √[(1 + 1/√(1 + tan²α))/2]

sin(α/2) = √[(1 + 1/√(1 + (-1/2)²))/2]

sin(α/2) = √[(1 + 1/√(1 + 1/4))/2]

sin(α/2) = √[(1 + 1/√(5/4))/2]

sin(α/2) = √[(1 + 1/√5/2)/2]

sin(α/2) = √[(1 + 2/√5)/2]

sin(α/2) = √[(√5 + 2)/√5)/2]

sin(α/2) = √[(√5 + 2)/2√5

sin(α/2) = √[(√5 + 2)/2√5 × √5/√5

sin(α/2) = √[5(√5 + 2)]/2 × 5

sin(α/2) = √[5(√5 + 2)]/10

So, sin(α/2) = √[5(√5 + 2)]/10

Using the half angle formula,  

tan(α/2) = sinα/(1 + cosα)

Using the trigonometric identity cosα = ±1/√(1 + tan²α)

cosα = ±1/√(1 + (-1/2)²)

cosα = ±1/√(1 + 1/4)

cosα = ±1/√(5/4)

cosα = ±1/√5/2

cosα = ±2/√5

Since π/2 < α < π

cosα = -2/√5

Also, since the trigonometric identity sinα = ±√(1 - cos²α)

So, sinα = ±√(1 - (-2/√5)²)

sinα = ±√(1 - 4/5)

sinα = ±1/√5

Since π/2 < α < π

sinα = +1/√5

Substituting cosα = -2/√5 and sinα = +1/√5 into the equation for tan(α/2), we have

tan(α/2) = sinα/(1 + cosα)

tan(α/2) = +1/√5/(1 + (-2/√5))

tan(α/2) = +1/√5/(1 - 2/√5)

tan(α/2) = +1/√5/(√5 - 2)/√5)

tan(α/2) = 1/(√5 - 2)

So, tan(α/2) = 1/(√5 - 2)

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Answer:

324cm³

Step-by-step explanation:

Volume of a triangular prism = (height x width x base length) / 2

We are given:

If we plug this into the formula we get (9 x 6 x 12) / 2

==> multiply numbers in parenthesis

volume = 648/2

==> simplify division

volume = 324cm³

Answer:

1,000 friends will get 1 gram of gold bar each from 1 kilogram of gold bar

Step-by-step explanation:

1 kilogram of gold bar = 1,000 grams of gold bar

You have 1 kilogram of gold bar

You want each of your friends to get 1 gram

Number of friends that will get 1 gram of gold bar each = 1 kilogram of gold bar / 1 gram

= 1000 gram / 1 gram

= 1,000

Number of friends that will get 1 gram of gold bar each = 1,000 friends

The component form of the velocity vector becomes ⟨150√2, -150√2⟩. This represents the velocity vector's magnitude and direction in terms of its x and y components.

The component form of the velocity vector of an airplane traveling at 300 mph in the direction of S 45° E can be represented as ⟨300cos(45°), -300sin(45°)⟩. This breaks down the velocity vector into its horizontal (x) and vertical (y) components.

To determine the component form of the velocity vector, we need to consider the given direction and magnitude. The direction S 45° E can be broken down into two components: south (negative y-axis direction) and east (positive x-axis direction).

The magnitude of the velocity is given as 300 mph. The horizontal component of the velocity can be found by multiplying the magnitude by the cosine of the angle (45°) since cosine represents the adjacent side divided by the hypotenuse. Thus, the horizontal component is 300 * cos(45°) = 300 * √2 / 2 = 150√2.

Similarly, the vertical component of the velocity can be found by multiplying the magnitude by the sine of the angle (45°) since sine represents the opposite side divided by the hypotenuse. Therefore, the vertical component is 300 * sin(45°) = 300 * √2 / 2 = 150√2.

Combining these components, the component form of the velocity vector becomes ⟨150√2, -150√2⟩. This represents the velocity vector's magnitude and direction in terms of its x and y components.

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Answer B stands For Base and h stands for Height

Answer:

Step-by-step explanation:

it shows the maximum rise in temperature.

Answer:

b answer, will show the rise in temperature

Answer:

C-5m

Step-by-step explanation:

Answer:

answer is ( b )

The general equation of the vertical parabola is

\(y= ax^2+bx+c\), where a,b and c are constant.

The parabola passes through the points D(1,-2), E(-3,10), and F(4,31).

For point D:

\(-2=a(1)^2+b(1)+c\)

\(\Rightarrow -2=a+b+c\cdots(i)\)

For point E:

\(10=a(-3)^2+b(-3)+c\)

\(\Rightarrow 10=9a-3b+c\cdots(ii)\)

For point F:

\(31=a(4)^2+b(4)+c\)

\(\Rightarrow 31=16a+4b+c\cdots(iii)\)

All the three equations can be written in the matrix for as:

\(\[ \left[ {\begin{array}{cc} -2 \\ 10 \\31 \end{array} } \right]\]= \left[ {\begin{array}{ccc} 1 & 1 & 1 \\ 9 & -3 & 1 \\ 16 & 4 &1\end{array} } \right]\] \left[ {\begin{array}{cc} a \\ b \\c \end{array} } \right]\]\)

The value of all the three coefficients can be determined by solving the above equation as

\(\left[ {\begin{array}{ccc} a \\ b \\c \end{array} } \right]= \left[ {\begin{array}{ccc} 1 & 1 & 1 \\ 9 & -3 & 1 \\ 16 & 4 &1\end{array}\right]^{-1} \left[ {\begin{array} -2 \\ 10 \\31 \end{array} } \right]\)

On solving this, we have

\(\Rightarrow \[ \left[ {\begin{array}{ccc} a \\ b \\c \end{array} } \right]\]= \left[ {\begin{array}{ccc} 2 \\ 1 \\-5 \end{array} } \right]\)

So, values of the constants,

a=2, b=1, and c=-5

Hence, the required equation of parabola is

\(y=2x^2+x-5\)

The correct option is:

c. Action research

What type of research is conducted by professionals in any type of school to investigate a problem, with findings that may have limited generalizability?

The type of research conducted by professionals in any type of school to investigate a problem, with findings that may have limited generalizability, is known as action research.

c. Action research.

Action research is a type of research that is intended to be carried out by professionals in any type of school setting to investigate a specific problem or issue. The focus of action research is on practical solutions and making improvements within a particular context.

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Answer:

Brother there's nothing there

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

these angles are supplementary, which means they add up to 180°

using this, you can make the following equation:

6x + 60 = 180

subtract 60 from both sides of the equation

6x + 60 - 60 = 180 - 60

6x = 120

divide both sides of the equation by 6

6x/6 = 120/6

x = 20

a. The expression to show how many more miles Libby ran than Sarah is 3x - 4.

b. Libby ran 27 - 22 = 5 more miles than Sarah when they each ran for 3 hours.

a. The expression 9x - (6x + 4) represents the number of miles Libby ran more than Sarah. To simplify the expression, we can combine like terms. This gives us: 9x - 6x - 4 = 3x - 4. Therefore, the expression to show how many more miles Libby ran than Sarah is 3x - 4.

b. If Sarah and Libby both ran for 3 hours, Sarah ran 6x + 4 miles in that time. Plugging in 3 for x, we get 6(3) + 4 = 22 miles. On the other hand, Libby ran 9x miles in 3 hours, which is 9(3) = 27 miles. Therefore, Libby ran 27 - 22 = 5 more miles than Sarah when they each ran for 3 hours.

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Maintaining a balanced budget while influencing the output level of the economy is not necessarily macroeconomically neutral and requires careful consideration of the policy trade-offs involved.

The problem presents a scenario where governments aim to maintain a balanced budget while trying to influence the output level of the economy through changes in government spending (g) and taxes (t). To assess the macroeconomic neutrality of such policy changes, we use equation (3.8) to find the impact of a unit increase in g and t on the output level y.

(a) The impact of a unit increase in g on the output level y is given by the multiplier (1/1-c1), where c1 is the marginal propensity to consume. Therefore, an increase in g by one unit will increase output by the multiplier times the change in g.

(b) The impact of a unit increase in t on the output level y is given by the negative multiplier (-c1/1-c1). Therefore, an increase in t by one unit will decrease output by the negative multiplier times the change in t.

(c) The answers to (a) and (b) are different because an increase in g will increase aggregate demand, leading to a higher equilibrium level of output, while an increase in t will decrease disposable income and hence decrease consumption and aggregate demand, leading to a lower equilibrium level of output.

In the scenario where the government starts with a balanced budget, any increase in government spending will have to be financed through an increase in taxes or a reduction in government transfers. The impact of such policy changes on the output level will depend on the size of the multiplier and the extent to which the increase in taxes or reduction in transfers affects consumption and aggregate demand.

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Non of the above Statement is true.

Standard deviation is a mathematical measure of how spread out a dataset is. It is a measure of the variation or dispersion of a set of values from the mean. It is calculated by taking the square root of the variance. Standard deviation can be used to measure the risk associated with an investment, to compare data sets, or to measure the accuracy of a data set.

The standard deviation is a measure of the dispersion of a set of data from its mean, and it is always a non-negative number. It can sometimes be zero, and it can also be larger than the variance.

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Answer:

\(y=-3,\:x=6\)

Step-by-step explanation:

hope this helped :P

Answer:

A = pi ft^2

If we approximate by 3.14

A = 3.14 ft^2

or use the pi button

A =3.141592654 ft^2

Step-by-step explanation:

The area of a circle is found by

A = pi r^2

A = pi (1)^2

A = pi ft^2

If we approximate by 3.14

A = 3.14 ft^2

or use the pi button

A =3.141592654 ft^2

Answer:

y = 3/4x - 3

m= 3/4

y = (0,-3)

This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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The number of ways we can put 4 different balls in 3 different boxes is 81 ways.

The number of ways we can put 4 different balls in 3 different boxes is calculated as;

If we select a box for the first ball, there are 3 available boxes, so we have 3 ways of arrangement.

If we select a box for the second ball, there are 3 available boxes, so we have 3 ways of arrangement.

If we select a box for the third ball, there are 3 available boxes, so we have 3 ways of arrangement.

If we select a box for the fourth ball, there are 3 available boxes, so we have 3 ways of arrangement.

Total number of ways of arrangement =  (3 ways)⁴ = 3⁴ = 81 ways

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There is an inverse relationship between the EBP and the required sample size. As the EBP increases, the required sample size decreases, and vice versa.

As the error bound of the proportion (EBP) increases, the required sample size decreases.

The EBP is a measure of the maximum error that is allowed in estimating a population proportion using a sample proportion. It is calculated as the difference between the sample proportion and the true population proportion, divided by the sample proportion. For example, an EBP of 0.02 means that the estimated proportion could differ from the true population proportion by up to 2%.

When the EBP is large, it means that the allowable margin of error is also large, so we do not need as large a sample size to achieve the desired level of precision in our estimate. In other words, if we are willing to tolerate a larger error in our estimate, we can use a smaller sample size to achieve the same level of accuracy.

Conversely, when the EBP is small, it means that the allowable margin of error is also small, so we need a larger sample size to achieve the desired level of precision in our estimate. This is because a smaller margin of error requires a more precise estimate, which in turn requires a larger sample size to reduce the effect of random sampling variability.

Therefore, there is an inverse relationship between the EBP and the required sample size. As the EBP increases, the required sample size decreases, and vice versa.

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Answer:

h(0) = 7

Step-by-step explanation:

by saying h(0) it is asking you to plug in 0 as the x value

3(0)^2 = 0

0 + 7 = 7

The requried new coordinates of the translated points are (2, 3), (3, 5), and (0, -2).

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To translate a point using the given rule, we add 1 to the x-coordinate and 1 to the y-coordinate.

For points (1, 2), the new coordinates are (1+1, 2+1) = (2, 3).

For the point (2, 4), the new coordinates are (2+1, 4+1) = (3, 5).

For the point (-1, -3), the new coordinates are (-1+1, -3+1) = (0, -2).

Therefore, the new coordinates of the translated points are (2, 3), (3, 5), and (0, -2).

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