Solve the equation for x:
| 4x - 3] = 7

Answer:

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

Step-by-step explanation:

All lines take the form

\(y = mx + c\)

Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.

To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:

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

Answer:

G: 135

Step-by-step explanation:

The plot has a trend of increasing every year by some number so in year 1980 the participants should be more than 120 (because 1972 has 120 people) to follow the given trend. Thus, best answer is G = 135 countries.

Answer:

slope(m)=(-33/2)

Step-by-step explanation:

Answer: I would say a but not sure sorry if you get it wrong

Step-by-step explanation:

The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

Ang mga Babae sa Relihiyon at Pilosopiya sa Asya. Limang Ugnayan. emperador-mamamayan. ama-anak na lalaki.

Answer:

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

Step-by-step explanation:

Assuming that the tape diagram shows the ratio of adult tickets to child tickets as 3:2, we can represent this as follows:

  AAA

  AAA

  AAA

  CCC

  CCC

In this diagram, each square represents a certain number of tickets. To determine how many tickets each square represents, we need to know the total number of squares in the diagram.

There are a total of 3 + 3 + 3 + 2 + 2 = 13 squares in the diagram. Since the theater sold 126 tickets in total, we can divide 126 by 13 to find out how many tickets each square represents:

126 ÷ 13 ≈ 9.69

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

Rearrange first

9,13,37,39

median=13+37÷2

=25

median is 25

mean=9+13+37+39÷4

=98÷4=24.5

Mean=24.5

A trinomial is a polynomial with three terms that has a leading coefficient of 3 and a constant term of -5 is

3m²+m-5

Here the degree of the trinomial is 2, so the leading coefficient is the coefficient of the term with m², which is 3.

The constant term is the term without a variable, which is -5

To find the coefficient of middle term of the trinomial, formula is:

coefficient of middle term =

(sum of the coefficients of the first and last terms)

                                    2

The sum of the coefficients of the first and last terms is 3 - 5 = -2.

Dividing by 2, we get -1 as the coefficient of the middle term.

Putting all of this together, we can write the trinomial as:                     3m² +m - 5

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The divergence theorem states that the surface integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the surface

we are given the vector field F = (11x, 2y, \(z^{2}\)) and the surface S defined by the equation \(x^2 + y^2 + z^2\)= 1, which represents a unit sphere.

To evaluate the surface integral ∬S F · ds using the divergence theorem, we first need to calculate the divergence of the vector field F. The divergence of F, denoted as ∇ · F, is given by the sum of the partial derivatives of the components of F with respect to their corresponding variables. Therefore, ∇ · F = ∂(11x)/∂x + ∂(2y)/∂y + ∂(z^2)/∂z = 11 + 2 + 2z.

Applying the divergence theorem, the surface integral ∬S F · ds is equal to the triple integral ∭V (∇ · F) dV, where V represents the volume enclosed by the surface S.

Since the surface S is a unit sphere centered at the origin, the triple integral ∭V (∇ · F) dV can be evaluated by integrating over the volume of the sphere.

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Answer:

  yes

Step-by-step explanation:

You want a graph of P = 125 +50W.

The given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.

Usually, the independent variable is graphed on the horizontal axis, which you have done.

The dependent variable is graphed on the vertical axis, which you have done.

The axes are correctly labeled and graduated.

The "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.

The slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.

Yes, you properly graphed the equation.

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Answer:

1.53

Step-by-step explanation:

because 21 minus 19.47= 1.53

Answer:

1  minute and 13 seconds

Step-by-step explanation:

The length of the required chord is approximately equal to 11.8 units.

In Mathematics and Geometry, the chord of a circle refers to a line segment that typically join any two (2) points on a circle.

Based on the equation of the circle, the radius can be determined as follows;

x² + y² = 36

Radius, r = √36

Radius, r = 6 units.

By applying Pythagorean's theorem, side OA can be calculated as follows;

6² - 1² = OA²

OA² = 36 - 1

OA = √35

OA = 5.9

Length of chord = 2 × OA

Length of chord = 2 × 5.9

Length of chord = 11.8 units.

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The point estimate for the parameter B based on the sample is approximately 0.284. We can calculate it in the following manner.

Given that X1, X2, X3, ... X14 is a random sample of size 14 taken from a Gamma distribution with unknown parameters a and B.

The method of moments is used to find the point estimate for the parameter, B, based on the following sample. The moment estimator for a parameter is a sample statistic that is used to estimate an unknown parameter. When the sample moments are equated to their corresponding population moments, these are called method of moments estimators. The population mean of a gamma distribution with parameters a and B is μ = a/B

The population variance of a gamma distribution with parameters a and B is σ² = a/B²

The first moment is the mean of the distribution, which is the same as the expected value of the gamma distribution. The second moment is the variance of the distribution. The method of moments estimation method is as follows: First Moment Estimation:μ = X = {X1+ X2+ X3+ ... X14}/14

Second Moment Estimation:σ² = S² = {Σ(Xi - X)²}/14 where X is the sample mean and S² is the sample variance.

By equating these to the corresponding population moments of gamma distribution, we get the estimators for a and B respectively. They are as follows: a = (X)² / S²B = (S²) / X

Now, we have the values of X and S² from the given sample. They are as follows: X= {0.50+0.88+0.40+0.80+1.14+0.71+0.49+1.45+0.65+0.62+1.04+1.89+0.29+0.79+0.2522}/14 = 0.84208S² = {Σ(Xi - X)²}/14 = 0.3058We need to find the point estimate for the parameter, B, based on the given sample.

B = (S²) / X = 0.3058/0.84208 ≈ 0.3632

Therefore, the estimate of parameter B is approximately 0.3632, using the method of moments. The correct option is the third option.
To estimate the parameter B using the method of moments, we first need to calculate the sample mean and the sample variance. However, you provided 17 data points instead of 14. We will use the first 14 data points for our calculation.

Data: 0.50, 0.88, 0.40, 0.80, 1.14, 0.71, 0.49, 1.45, 0.65, 0.62, 1.04, 1.89, 0.29, 0.79

1. Calculate the sample mean (µ):
µ = (ΣXi) / n = (0.50+0.88+0.40+0.80+1.14+0.71+0.49+1.45+0.65+0.62+1.04+1.89+0.29+0.79) / 14 ≈ 0.859

2. Calculate the sample variance (s²):
s² = (Σ(Xi - µ)²) / (n-1) ≈ 0.243 (after calculating)

Now, we can use the method of moments. For Gamma distribution, the mean and variance are:

Mean: µ = aB
Variance: s² = aB²

We have already estimated a point estimate for a (a-hat) using the method of moments:
a-hat = µ² / s² ≈ 0.859²/ 0.243 ≈ 3.023

Now we can estimate the point estimate for B (B-hat):
B-hat = µ / a-hat ≈ 0.859 / 3.023 ≈ 0.284

The point estimate for the parameter B based on the sample is approximately 0.284.

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The point estimate for the parameter B is 9.14.

To use the method of moments to find a point estimate for the parameter B, we first need to set up the equations using the sample moments.

The sample mean is:

mu1 = (X1 + X2 + ... + X14) / 14

And the sample variance is:

mu2 = [(X1 - mu1)²+ (X2 - mu1)² + ... + (X14 - mu1)²] / 14

For a Gamma distribution with parameters a and B, the theoretical mean and variance are:

E(X) = a / B
Var(X) = a / B²

Setting the sample moments equal to the theoretical moments, we get:

mu1 = a / B
mu2 = a / B²

Solving for B in the first equation, we get:

B = a / mu1

Substituting this into the second equation, we get:

mu2 = a / (a / mu1)²

mu2 = a * mu1² / a²
mu2 = mu1²/ a

Solving for a in terms of the sample moments, we get:

a = mu1^2 / mu2

Substituting this into the equation for B, we get:

B = (mu1 / mu2)²

Now we can plug in the values from the sample:

mu1 = (0.50 + 0.88 + 0.40 + 0.80 + 1.14 + 0.71 + 0.49 + 1.45 + 0.65 + 0.62 + 1.04 + 1.89 + 0.29 + 0.79 + 0.2522 + 0.0011 + 0.2099) / 14 = 0.865

mu2 = [(0.50 - 0.865)² + (0.88 - 0.865)²+ ... + (0.2099 - 0.865)²] / 14 = 0.286

Plugging these values into the equation for B, we get:

B = (0.8691 / 0.2375)² = 9.14.

Therefore, the point estimate for the parameter B based on the sample is 9.14.

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Answer:

-81

Step-by-step explanation:

(-3)^4 is 81, but - (3)^4 is -81

Answer:

7.5 x 10^4

Step-by-step explanation:

The sample mean of the given observations {3, 6, 9, 12, 20} is 10. It represents the average value of the data points in the sample and provides a measure of central tendency.

To calculate the sample mean, we sum up all the observations in the sample and divide it by the total number of observations. In this case, we have a sample of size 6 with the observations {3, 6, 9, 12, 20}.

To find the sample mean, we add up all the numbers: 3 + 6 + 9 + 12 + 20 = 50. Then, we divide this sum by the total number of observations, which is 6.

Sample Mean = (Sum of Observations) / (Number of Observations)

Sample Mean = 50 / 6 = 8.33 (rounded to two decimal places)

Therefore, the sample mean of the given observations {3, 6, 9, 12, 20} is 10. It represents the average value of the data points in the sample and provides a measure of central tendency.

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Answer:

\(y = - 2x + 5\)

Step-by-step explanation:

Simply simplify the equation from what it is to the slope intercept format:

\(y = mx + b\)

Step-by-step explanation:

Hey there!

We know;

The slope intercept form of equation is;

y = mx+c

So, let's try to take it in this form.

(y-1) = -2(x-2)

Multiply -2 and (x-2)

(y-1) = -2x + 4

Take '-1' to right side.

y = -2x+4+1

y = -2x+5

Therefore, the equation is y = -2x+5.

Hope it helps...

Step-by-step explanation:

5:2:3 a+b+c:5a

5+2+3:5(5)

10/25=2/5 = 2:5

Answer:

The relationship between altitude and atmospheric pressure is exponential, as shown by the function f(x) in this problem.

Step-by-step explanation:

a. To find the pressure at sea level, we need to evaluate f(x) at x=0:
f(0) = 1038(1.000134)^0 = 1038 millibars.

Therefore, the pressure at sea level is approximately 1038 millibars.

b. To find the atmospheric pressure at an altitude of 2000 meters, we need to evaluate f(x) at x=2000:
f(2000) = 1038(1.000134)^(-2000) ≈ 808.5 millibars.

Therefore, the approximate atmospheric pressure at the McDonald Observatory in Texas is 808.5 millibars.

c. As altitude increases, atmospheric pressure decreases. This is because the atmosphere becomes less dense at higher altitudes, so there are fewer air molecules exerting pressure.

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The value of the composite function is 2x - 15

A function can be defined as a rule, law ore equation that explicitly shows the relationship between two variables.

These variables are called;

From the information given, we have the functions;

To determine the composite function (fog)(x), we have to substitute the value of g(x) as the variable 'x' in the function, f(x), we have;

(fog)(x) = 2 - (18 -2x) + 1

Now, expand the bracket

(fog)(x) = 2 - 18 + 2x + 1

collect like terms

(fog)(x) = 2x - 15

Hence, the function is 2x - 15

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The amount in gallons of each milk containing 9% butterfat and milk containing 4% butterfat which must be used to obtain the desired 365 gallons are;

It follows from the task content that the quantity of each type of milk required to arrive at the targeted fat content and quantity of milk are to be determined.

Let x = quantity of 9% fat milk and

Let y = quantity of 4% fat milk

Therefore, by mass balance; we have;

x + y = 365.

Where; y = 365 - x.

Also, by fat balance; we have;

(9% × x) + (4% × y) = (7% × 365)

9x + 4y = 2555

Therefore, the two equations to be solved simultaneously by substituting y from the first equation into the second equation as follows;

9x + 4 (365 - x) = 2555

5x = 1095

x = 1095/5

x = 219 gallons.

Also, y = 365 - 219 = 146 gallons.

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Answer:

3 3/4 cups

Step-by-step explanation:

We need 3/4 cups of beans for 7 servings, and we need to figure out how many cups we need for 35 servings. You'll notice that 7 times 5 is 35. We can multiply 3/4 by 5 to find the answer to our problem. This thought process looks somewhat like this:

\(\frac{\frac{3}{4} }{7} = \frac{x}{35}\)

Notice that we can multiply 5 by 3/4 to find the value of x.

So, 3/4 times 5 is equal to 15/4, or 3 3/4. So, you need 3 3/4 cups of beans for 35 servings.

Hopefully this was helpful! If you have any more questions, let me know.

Answer:

can you explain more

Step-by-step explanation:

Rational functions are functions written as fractions. The correct function is y = -√x - 6

Rational functions are functions written as fractions. According to the question, we are to select the function for which as y tends to minus infinity, x will tend to positive infinity.

For the function

y = -√x - 6

Substitute y = -∞ into the equation

- ∞ = - √x - 6

x - 6 = ∞

x = ∞ + 6

x = ∞

Therefore Rational functions are functions written as fractions. The correct function is y = -√x - 6

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Answer:

please see answers below

Step-by-step explanation:

13a)

120 books at £4 each = £480

he sells 60 books at £5 each = £300

he sells 40% of 120 books (48 books) at £7 each = £336

he has sold 60 + 48 books = 108 books.

he has 120 - 108 = 12 remaining.

he sells these 12 at £8 each = £96.

his sales are 300 + 336 + 96 = £732.

formula for percentage profit = (profit/cost price) X 100

= [(732 - 480) / 480] X 100

= (252/480) X 100

= 52.5%

13b) £15 is 120% of the price

15/120 = 0.125 is 1% of the price

so 100 X 0.125 = £12.50 is 100% of the price (ie the value in May 2018)

Answer:

Step-by-step explanation:

△D′E′F′ is reflection of △DEF across y = - 1.

The transformation of the △DEF to △D′E′F′ is as follows; The △D′E′F′ is a reflection of △DEF across y = - 1.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given triangle △DEF with vertices D (1, 2) , E (2, 0) , and F (−1, 0) .

The plot of the above triangle has been plotted below,

As per the given triangle △D′E′F with vertices D′ (1, −4) , E′(2, −2) , and F′ (−1, −2) .

The plot of the above triangle has been plotted below,

It is clear that △DEF is reflected and how much is reflected can be known by making equal distance.

Since it equals apart from y = -1 thus it will be a reflection of y = -1.

Hence "The transformation of the △DEF to △D′E′F′ is as follows; The △D′E′F′ is a reflection of △DEF across y = - 1".

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After being fired, a person on Earth would calculate the density of the projectile to be the same as the density of steel, which is 8060 kg/m³.

To calculate the estimated mass of the projectile, we can use the formula:

Mass = Volume × Density

Given:

Length of the projectile (L) = 0.50 m

Diameter of the projectile (D) = 0.20 m

Density of steel (ρ) = 8060 kg/m³

First, let's calculate the volume of the cylinder-shaped projectile. The volume of a cylinder is given by:

Volume = π × (radius)² × height

The radius of the projectile is half the diameter:

Radius = D/2 = 0.20 m/2 = 0.10 m

Now, we can calculate the volume:

Volume = π × (0.10 m)² × 0.50 m

Next, we multiply the volume by the density of steel to find the mass:

Mass = Volume × Density

Substituting the values:

Mass = (π × (0.10 m)² × 0.50 m) × 8060 kg/m³

Calculate the numerical value of the mass, rounding it to the nearest kilogram.

After being fired, a person on Earth would calculate the density of the projectile to be the same as the density of steel, which is 8060 kg/m³.

The density remains constant regardless of the projectile's motion.

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Answer:

1= -25

2=  22

3= 0

4= -34.5

Answer:

1 negative

2 positive

3 zero

4 negative

Step-by-step explanation:

Hope this helps :D

Step-by-step explanation:

x<-5 is the answer

1.

6x=-30

2.

x=-5

3.

x<-5