PLS HELP ME 80 - 4^2 ÷ 8

The interest on $5.255 at 12% for 30 days using ordinary interest is approximately $0.0511.

To calculate the interest using ordinary interest, we can use the formula:

Interest = Principal * Rate * Time

Here, the principal (P) is $5.255, the rate (R) is 12% (or 0.12), and the time (T) is 30 days.

Plugging in the values:

Interest = $5.255 * 0.12 * (30/365) = $0.0511 (rounded to four decimal places)

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In order to restore general equilibrium, price adjustments are undertaken. In the short run, prices increase, and when expectations rise above actual inflation, prices continue to climb until they do. answer is option (d). price level.

The term "aggregate demand" in macroeconomics refers to the overall demand for locally produced commodities, including capital goods, consumer products, and services. Aggregate demand is calculated as the total of spending by consumers, corporate and governmental investment spending, and net imports and exports.

The overall demand of final products and services in an economy at any particular time is known as aggregate demand, often referred to as domestic final demand. Effective demand is a frequent word for it, however occasionally this phrase is used to distinguish between two things. This is the demand for a nation's gross domestic product.

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The required values of x and y that allows these two triangles to be similar are x=(32±√239)/5, y=(19±2√239)/5.

Let the first triangle be called ABC where A(-1, 4), B(-3, 5) and C(-6, 1).

Let the second triangle be called LMN where L(-2, 8), M(-6, 10) and N(x, y)

Now if the 2 triangles are similar then the ratio of the lengths of corresponding sides will also be equal.

AB: BC= \(\sqrt{(-1+3)^{2}+(4-5)^{2} }\):\(\sqrt{(-1+6)^{2}+(5-1)^{2} }\) = √5:√41

AC: BC= \(\sqrt{(-1+6)^{2}+(4-1)^{2} }\): \(\sqrt{(-1+6)^{2}+(5-1)^{2} }\)=√34:√41

Now,

LM: MN= \(\sqrt{(-2+6)^{2}+(8-10)^{2} }\):\(\sqrt{(x+6)^{2}+(y-10)^{2} }\)

=2√5:\(\sqrt{(x+6)^{2}+(y-10)^{2} }\)

Comparing LM: MN to AB: BC we get \(\sqrt{(x+6)^{2}+(y-10)^{2} }\)=2√41

∴ \((x+6)^{2}+(y-10)^{2}\) = 164...... (1)

Again, LN: MN= \(\sqrt{(x+2)^{2}+(y-8)^{2} }\) : \(\sqrt{(x+6)^{2}+(y-10)^{2} }\)= AC: BC= √34:√41

Applying (1) to this rati we get: \(\sqrt{(x+2)^{2}+(y-8)^{2} }\)=2√34....(2)

Solving (1) and (2) we get: 8x-4y=32-68=-36

∴ 2x-y=9

Substituting y=2x-9 in (1) we get: \((x+6)^{2}+(2x-9)^{2}\)=164

Solving we get x=(32±√239)/5, y=(19±2√239)/5

Hence we get the required answers.

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Answer:

No, not necessarily

Step-by-step explanation:

When you subtract 3x to the other side you dont want to forget abt that other number, since 1 is a positive it is going to be a + 1

the correct answer is C

y = -3x + 1

High Hopes <3

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▹ Answer

y = 1 - 3x

▹ Step-by-Step Explanation

3x + y = 1

Move the variable to the right side, and change the sign:

y = 1 - 3x

Hope this helps!

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Based on the given functions, the first student's post is predicted to receive 10,240 shares on Day 10, the second student's post is predicted to receive 118,098 shares, and the third student's post is predicted to receive 3,145,728 shares.

We have,

To predict how many shares each student's post will receive on Day 10, we can substitute x = 10 into each function and evaluate the result.

For the first student, using the function \(y = 10(2)^x:\)

\(y = 10(2)^{10}\) = 10 x 1024 = 10,240 shares

For the second student, using the function \(y = 2(3)^x:\)

\(y = 2(3)^{10} = 2 \times 59,049 = 118,098 ~shares\)

For the third student, using the function \(y = 3(4)^x:\)

\(y = 3(4)^{10} = 3 \times 1,048,576 = 3,145,728~ shares\)

Therefore,

Based on the given functions, the first student's post is predicted to receive 10,240 shares on Day 10, the second student's post is predicted to receive 118,098 shares, and the third student's post is predicted to receive 3,145,728 shares.

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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We have simplified cos(u-π) to a single trig function using a sum or difference of angles identity, and that function is -cos(u).

To simplify cos(u−π) to a single trig function using a sum or difference of angles identity, we can use the identity:
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
In this case, we have a = u and b = π, so we can substitute those values into the identity to get:
cos(u-π) = cos(u)cos(π) + sin(u)sin(π)
Now, we know that cos(π) = -1 and sin(π) = 0, so we can substitute those values into the equation to get:
cos(u-π) = cos(u)(-1) + sin(u)(0)
Simplifying further, we have:
cos(u-π) = -cos(u)
Therefore, we have simplified cos(u-π) to a single trig function using a sum or difference of angles identity, and that function is -cos(u).

Simplifying cos(u−π) using the sum or difference of angles identity. The identity we'll use is:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
Applying this identity to cos(u−π):
cos(u−π) = cos(u)cos(π) + sin(u)sin(π)
Since cos(π) = -1 and sin(π) = 0, we have:
cos(u−π) = cos(u)(-1) + sin(u)(0)
cos(u−π) = -cos(u)

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Answer:

-3 > x

Step-by-step explanation:

Answer:

v = 66/7

Step-by-step explanation:

Step 1: Write equation

-7v + 3 = -63

Step 2: Solve for v

Subtract 3 on both sides: -7v = -66

Divide both sides by -7: v = 66/7

Step 3: Check

Plug in x to verify if it's a solution.

-7(66/7) + 3 = -63

-66 + 3 = -63

-63 = -63

Answer:

Step-by-step explanation:

-7v+3=-63

-7v=-63-3

-7v=-66

-7v-7=-66÷-7

V=9.4

Answer:

b. 31.

Step-by-step explanation:

The other 2 angles in the triangle are congruent so they are:

(180 - 118) / 2

= 31 degrees.

The possible measure of two similar angles in an isosceles triangle could be b. 31 °

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in an isosceles triangle two sides are equal and angles opposite sides to the equal side are also equal.

We also know that the sum of all the interior angles in a triangle is 180°.

Let, The similar angles be 'x'.

Therefore,

x + x + 118 = 180

2x = 62.

x = 31°.

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Answer:

(C)Triangle HJK is congruent to triangle NLM

Step-by-step explanation:

In Triangle HKJ

In Triangle LMN (Arranging in the same order as the angles above)

Therefore, we can say that:

Triangle HJK is congruent to Triangle NLM.

The correct option is C

Answer:C

Step-by-step explanation:

Answer:

( x + 4 ) ²-16

Step-by-step explanation:

Function

It is a function

The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.

Given that a card is randomly chosen from 8 cards shown in figure.

We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.

Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Number of cards=8

Number of repeated cards=0

Number of cards showing Q and R =1 each.

Probability of getting Q or R is P(X=Q)+P(X=R)

= 1/8+1/8

=2/8

=1/4

=0.25

Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.

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To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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There are 322 people who are interested in exactly one kind of show, There are a total of 650 responses, and 52 people are interested in none of the three shows. This means that 650 - 52 = 598 people are interested in at least one of the three shows.

We can use the following Venn diagram to represent the data:

   Interview Show

   /     \

  /       \

 Documentaries Reruns

The number of people in each region of the Venn diagram represents the number of people who are interested in that combination of shows. For example, the number of people in the intersection of the interview show and documentary regions is 195.

The number of people who are interested in exactly one kind of show is the sum of the number of people in each of the three single-show regions. These regions are the three triangles in the Venn diagram.

The number of people in the triangle for the interview show is 156 + 26 + 39 = 221.

The number of people in the triangle for the documentary show is 65 + 91 = 156.

The number of people in the triangle for the reruns show is 91.

Therefore, the total number of people who are interested in exactly one kind of show is 221 + 156 + 91 = 368.

However, we have double-counted some people in this calculation. For example, the people who are interested in both the interview show and the documentary show have been counted twice.

The number of people who have been double-counted is the number of people in the intersection of the two regions, which is 195.

Therefore, the number of people who are interested in exactly one kind of show is 368 - 195 = 322.

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In this case, the third column of matrix A is a linear combination of the first two columns, which makes the matrix singular and not invertible.

A matrix is a rectangular array of numbers or other mathematical objects, such as polynomials or functions, arranged in rows and columns.

Matrices are used to represent linear transformations, systems of linear equations, and other mathematical structures and operations.

To determine if a matrix is invertible or not, we need to calculate its determinant.

The given matrix is:

A = [1 2 0; 3 4 0; 5 6 0]

The determinant of  3x3 matrix is given by -

determinant(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)

where aij is the element in i th row and j th column of the matrix.

By substituting the values from matrix A-

det(A) = 1(40 - 06) - 2(30 - 05) + 0(36 - 45)

det(A) = 0

Since the determinant of A is equal to zero, we can conclude that the matrix A is not invertible.

The matrix can be  invertible if and only if its determinant is nonzero. When the determinant is zero, the matrix is said to be singular, which means that its rows or columns are linearly dependent, and it cannot be inverted.

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Answer:   x=5.3

Solution:

6x−8x−2=8.6−4x

−2x−2=8.6−4x

2x−2=8.6

2x=10.6

x=5.3

Answer:

Step-by-step explanation:

Answer:

X=7

Step-by-step explanation:

2(x+1)=16

Divide by 2 both sides

X+1=16/2

16 divide by 2 is 8

X+1=8

Subtract 1 from both sides

X=8-1

X=7

The difference between AIC and BIC penalty lies in their approach to model selection.

AIC (Akaike Information Criterion) is a measure of the goodness of fit of a statistical model. It is used to compare different models and select the one that fits the data best. AIC is based on the principle of maximum likelihood, which means it is more focused on finding the model that fits the data best.

On the other hand, BIC (Bayesian Information Criterion) is a criterion for model selection based on the Bayesian approach. It is also used to compare different models, but it takes into account the complexity of the model. BIC tends to favor simpler models, and it is more focused on finding the model that is most likely to be true given the data.

In summary, AIC is more focused on finding the model that fits the data best, while BIC is more focused on finding the model that is most likely to be true given the data.

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Answer:

-1280

Step-by-step explanation:

10×(-2)= -20

-20×(-2)= 40

4th term: 40×(-2)= -80

5th term: -80×(-2)= 160

6th term: 160×(-2)= -320

7th term: -320×(-2)= 640

8th term: 640×(-2)= -1280

A point estimate is the difference between a sample mean and a population mean, while the standard error of the mean is a measure of the variability between the two.

The difference between a sample mean and a population mean is known as a point estimate. A sample mean is the average of a group of observations taken from a larger population, while a population mean is the average of all observations in the entire population. A sample is a subset of the population that is selected for analysis, while the population is the entire group that is being studied. To make inferences about a population from a sample, researchers use point estimates, which are calculated from the sample data and used to estimate the population parameter. The point estimate is a single value that represents the best guess of the population mean based on the available sample data. The standard error of the mean is a measure of how much variability exists in the sample mean compared to the population mean. It reflects the amount of sampling error that can be expected when estimating the population mean from the sample mean.

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The correct answer is option A. 14 ÷ (5 + c).

Barry exists spreading the cards among the suits, then he needs enough suits to hold the total of 14 cards he has. Hence, we need to divide the total number of cards by the total number of cards,

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

If we assume Barry exists spreading the cards among the suits, then he needs enough suits to hold the total of 14 cards he has. Hence, we need to divide the total number of cards by the total number of cards.

Therefore, the correct answer is option A. 14 ÷ (5 + c)

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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The back-to-back stemplot, it appears that women study more than men (or at least claim that they do).

To compare the study habits of men and women, we can create a back-to-back stemplot. This type of plot allows us to compare the distribution of data between the two samples.

First, we need to gather data on the study hours for both men and women. Let's say we collected data from a sample of 50 men and 50 women.

Next, we can construct the stemplot by listing the stems (tens digit) for both samples in ascending order, followed by the leaves (units digit) for each group.

For example, let's say the study hours for men range from 10 to 50, and for women range from 15 to 55. The back-to-back stemplot would look like this:

Men:
1 | 0 0 1 2 3 3 4 4 5
2 | 1 1 1 1 2 3 3 3 3 4 5

Women:
1 | 5 5 5 5 6 6 7 7 7 7 7
2 | 1 1 1 2 2 2 3 4 4 5 5

From the stemplot, we can observe the distribution of study hours for both men and women. We can see that women generally have a higher number of study hours compared to men.

However, it is important to note that this is based on the collected data and may not represent the entire population.

Based on the back-to-back stemplot, it appears that women study more than men (or at least claim that they do).

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