Sophia's parents spent $100 for
new school clothes for the family.
Sophia's new outfit cost $35. Her
sister Emma's clothes cost $40. The
rest of the money was spent on their
brother Mason. How much money
did Mason's clothes cost?

Answer:

1/3

with indices, the brackets mean you multiply the powers - so you need to multiply 1/4 by something to get 1/12, which is 1/3

:)

Answer:

y = 3x + 3

Step-by-step explanation:

If the entire line, or rather, the graph, is translated upwards by 5 units; the slope stays the same, but the y-intercept rises by 5 as well. Thus, the equation of the new graph would be;

y = 3x (-2+5)

y = 3x + 3

Answer:

y = 3x + 3

Explanation:

Let's say you put a point or line on a graph at (2, 3) with 2 being the x-axis, and y being the y-axis, when you translate it left or right, you would move the point or line left or right, which changes the x-axis. If you move it to the right, you would increase the x value, and decrease it if you move it to the right. This is the same thing for going up and down. moving it up increases the y value, and moving it down decreases the y value.

When you place an equation on a graph, y is the result or point on the line when x equals a certain number. If x equaled 3, then the equation would be, y = (3 * 3) - 2. Which would be 9-2 = 7.

The 3x is the slope of the line, for every 1 unit to the right, the line would go 3 units up. the -2 is the intersection of the line through the y axis. so in this equation, the intersection would be -2.

To find the new equation, you would take the first equation, y = 3x - 2, then when you translate it up, you would increase the y intersect of the line by however much you need to, which would be 5. so you would just add 5 to the -2 to get the new equation. So now the new equation you have is y = 3x +3.

Answer:

x = -8

Step-by-step explanation:

We need to know when the output is 4

There are two values

When x = -8 and when x = 7

well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so

\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)

Answer:

y = 28

Step-by-step explanation:

The dashes on line segments AC and BC indicate that the line segments are equal in length.

Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.

Interior angles of a triangle sum to 180°.  

Therefore:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 34° + 34° + 4y° = 180°

⇒ 68° + 4y° = 180°

⇒ 4y° = 112°

⇒ y = 112° ÷ 4°

⇒ y = 28

The correct option for the demand requirement constraint in a production scheduling LP is option (c): beginning inventory + production - ending inventory = demand.

In a production scheduling LP, the demand requirement constraint represents the balance between the available inventory and the demand for the product. The constraint ensures that the production and inventory levels are sufficient to meet the specified demand.

Option (c) represents this relationship accurately by stating that the beginning inventory, production, and ending inventory, when subtracted from each other, should equal the demand. This equation reflects the concept of maintaining a balance between the production output and inventory changes to meet the demand

Option (a) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Option (b) is also incorrect because it uses the equality (=) symbol, which implies an exact balance between the inventory and demand, disregarding the changes in inventory.

Option (d) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Therefore, option (c) is the correct representation of the demand requirement constraint in a production scheduling LP.

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From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

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Diagram isnt given. However, a picture illustribg the possible scenarios has been attached to help.

Answer:

KINDLY CHECK EXPLANATION

Step-by-step explanation:

Given the triangles A and B below :

Using trigonometric ratios :

If triangle A is given ;

Then ; MN will be obtained using the SIN relation :

Sin 20 = opposite (MN) / hypotenus (21)

If triangle B is given ;

Then ; MN will be obtained using the TAN relation :

Tan 20 = opposite (MN) / Adjacent (21)

Answer:

6x+3y=-66

-6x-4y=-35

Step-by-step explanation:

Both of the equations have the same answer-

-66, and -35

The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.

On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.

To summarize:

- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.

- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.

- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.

Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

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A rectangle with its base on the x-axis and its vertices on the curve

y =4 - x² can have a maximum area of 32/3√3.

The formula for calculating a rectangle's area is  A=length*breadth

The base's length is x.

y represents the curve's vertices (width).

Given that a rectangle's area increases as its base moves along the x-axis, our base will be 2x.

The rectangle's surface area will change to:

A = 2x ( 4 - x²)

When the area is at its largest, da / dx should be maximum.

A = 8x - 2x³

da/dx = 8 - 6x²

8 - 6x² = 0

6x² =  8

x² = 8/6

x  = √4/3

   =2/√3

We shall substitute 2/√3 into the region in order to obtain the maximum area.

A=  8x - 2x³

  = 8*2/√3 - 2*(2/√3)³

  =32/3√3

Therefore, the largest area a rectangle with a base on the x-axis and vertices on the curve y = 4 - x² can have is 32/3√3.

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If his total monthly expenditures last month were $826.20, Tino spent $61.20 on the phone last month.

To find out how much Tino spent on the phone, we need to subtract his other expenses from his total monthly expenditures.

Total monthly expenses = Rent + Cable + Phone

We know that Tino pays $725 for rent and $40 for cable, so:

Total monthly expenses = $725 + $40 + Phone

We also know that Tino pays $3.60 per hour for local telephone service. Let's say he used the phone for x hours last month. Then the cost of his phone service would be:

Phone = $3.60/hour x hours = $3.60x

Now we can set up an equation to solve for x:

$826.20 = $725 + $40 + $3.60x

Simplifying the equation:

$61.20 = $3.60x

Dividing both sides by $3.60:

x = 17

So Tino used the phone for 17 hours last month. To find out how much he spent on the phone:

Phone = $3.60/hour x 17 hours = $61.20

Therefore, Tino spent $61.20 on the phone last month.

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The probability that all three wires will meet the specifications is approximately 0.173 .

Expected value (mean) of wire resistance = 0.13 ohms Standard deviation of wire resistance = 0.005 ohms

the probability for each wire, we need to standardize the range of resistance values using the expected value and standard deviation. We can use the Z-score formula:

Z = (X - μ) / σ

Z is the standard score (Z-score) X is the observed value (resistance) μ is the mean (expected value) σ is the standard deviation

For the lower specification of 0.10 ohms

Z1 = (0.10 - 0.13) / 0.005

For the upper specification of 0.17 ohms

Z2 = (0.17 - 0.13) / 0.005

Using a standard normal distribution table , we can find the probability associated with each Z-score.

Lower bound of standardized range = (0.10 - 0.13) / 0.005 = -0.06

Upper bound of standardized range = (0.17 - 0.13) / 0.005 = 0.80

Let's calculate the probabilities for each wire

P(z < -0.60) ≈ 0.2743

P(z < 0.80) ≈ 0.7881

Since we want the probability that all three wires meet the specifications, we need to multiply these probabilities together since the wires are selected independently.

P(all three wires meet specifications) = P(z < -0.60) × P(z < 0.80) × P(z < 0.80)

P(all three wires meet specifications) ≈ 0.2743 × 0.7881 × 0.7881 ≈ 0.1703

Therefore, the probability that all three wires will meet the specifications is approximately 0.173, or 17.3% .

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To compute the characteristic polynomial p(λ) for the matrix A, we need to find the determinant of (A - λI), where λ is the eigenvalue and I is the identity matrix.

The matrix (A - λI) is:

A - λI = [20 - λ, 16; -24, -20 - λ]

The determinant of (A - λI) is:

det(A - λI) = (20 - λ)(-20 - λ) - (16)(-24)

           = λ^2 + 20λ + 400 + 384

           = λ^2 + 20λ + 784

Therefore, the characteristic polynomial p(λ) is λ^2 + 20λ + 784.

To solve for the roots, we set p(λ) equal to zero and solve the quadratic equation:

λ^2 + 20λ + 784 = 0

Using the quadratic formula:

λ = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation, a = 1, b = 20, and c = 784. Substituting these values into the quadratic formula:

λ = (-20 ± √(20^2 - 4(1)(784))) / (2(1))

  = (-20 ± √(400 - 3136)) / 2

  = (-20 ± √(-2736)) / 2

  = (-20 ± √(2736)i) / 2

Since the discriminant is negative, the roots of the equation are complex numbers. Simplifying the expression:

λ1 = (-20 + √(2736)i) / 2

   = -10 + √(684)i

λ2 = (-20 - √(2736)i) / 2

   = -10 - √(684)i

Therefore, the two eigenvalues of the matrix A, with λ1 < λ2, are:

λ1 = -10 + √(684)i

λ2 = -10 - √(684)i

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Answer:

Step-by-step explanation:

It is 48.

A. Graph the points. Course Hero graph of the points FGHJFGHJ is a trapezoid. A trapezoid is a quadrilateral with one set of parallel sides. In this case, the parallel sides are FG and HJ. The other two sides, GH and FJ, are not parallel.

F(-4, -1)

G(-2, -5)

H(4, -2)

J(2, 2)

graph of the points FGHJOpens in a new window.

To justify that FGHJ is a trapezoid, we can use the following steps:

Draw a line segment connecting the midpoints of any two parallel sides. In this case, we can draw a line segment connecting the midpoints of FG and HJ. The line segment drawn in Step 1 will be parallel to the other set of parallel sides. In this case, the line segment drawn in Step 1 will be parallel to GH and FJ.

If the line segment drawn in Step 1 is parallel to the other set of parallel sides, then the quadrilateral is a trapezoid.Therefore, FGHJ is a trapezoid.

In addition to the above, we can also see that FGHJ is a trapezoid by looking at the graph of the points. The graph shows that the sides FG and HJ are parallel, and the sides GH and FJ are not parallel. This is the defining characteristic of a trapezoid.

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Answer:

7.65$ or 97.65$

Step-by-step explanation:

When making a $90 purchase, an \(8.5\)% tax will be applied to the total amount.

To calculate this tax, we multiply the purchase cost by the tax rate. $\(90 x\) \(0.085 = $7.65 So,\) the tax on the $\(90\) purchase is $\(7.65.\) This means that the total amount including tax will be the sum of the purchase cost and the tax amount. $\(90 + $7.65 = $97.65\)

Hence, the final amount the customer will have to pay is $\(97.65.\) The tax of 8.5% on the $90 purchase adds an additional $7.65 to the total. It's essential to consider such taxes when making budgetary decisions and keeping track of expenses.

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The term used for a line, ray, or segment that intersects a segment at its midpoint is the Perpendicular Bisector.

A perpendicular bisector is a line that intersects another line at the midpoint, forming right angles. It's a line that splits a line segment into two equal pieces at a 90-degree angle.

A line is split into two parts, each of which is the same length and is equidistant from the endpoints of the original line. A perpendicular bisector divides a line into two equal parts, making each one a mirror image of the other.

Perpendicular bisectors have a variety of practical applications.

For example, they can be used in geometry proofs to demonstrate that two lines are parallel or that two line segments are equal in length.

They may also be used in surveying, architecture, and engineering to establish straight lines and points of intersection.

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Answer:

c

Step-by-step explanation:

Answer:

y = -8

Step-by-step explanation:

When two variables vary inversely, their relation is proportional. This means that their product is constant.

We can show the constant of proportionality (k) using the equation:

x · y = k

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Note: you may also see this written as:

y = k / x

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

↓ plugging in the given values

(-4) · 6 = k

    -24 = k

       k = -24

Using this constant, we now solve for y when x = 3 by plugging that value into the proportionality equation above:

x · y = k

↓ plugging in the known values

3 · y = -24

↓ dividing both sides by 3

y = -24/3

y = -8

The option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is B) x1 = 5, x2 = 5.25, Z = 56.5

To determine the correct answer, we can substitute each option into the objective function and check if the constraints are satisfied. Let's evaluate each option:

A) x1 = 5, x2 = 4.63, Z = 52.78

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(4.63) = 85 + 37.04 = 122.04 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(4.63) = 15 + 18.52 = 33.52 ≤ 36 (constraint satisfied)

B) x1 = 5, x2 = 5.25, Z = 56.5

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5.25) = 85 + 42 = 127 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5.25) = 15 + 21 = 36 ≤ 36 (constraint satisfied)

C) x1 = 5, x2 = 5, Z = 55

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5) = 85 + 40 = 125 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5) = 15 + 20 = 35 ≤ 36 (constraint satisfied)

D) x1 = 4, x2 = 6, Z = 56

Checking the constraints:

17x1 + 8x2 = 17(4) + 8(6) = 68 + 48 = 116 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(4) + 4(6) = 12 + 24 = 36 ≤ 36 (constraint satisfied)

From the calculations above, we see that options B), C), and D) satisfy all the constraints. However, option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is: B) x1 = 5, x2 = 5.25, Z = 56.5.

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Thus, the time rocket spent in the air before it impacted the ground by keeping in mind that after it reaches the ground, the rocket's height is zero is 0.168 seconds.

Quadratics and parabolas are frequently used in practical settings. Situations that can be approximated by quadratic functions include tossing a ball, firing a cannon, jumping off a platform, and hitting a golf ball.

Input/ output data for the quadratic regression equation

Time (s) 1 2 3 4

Height (ft) 91.1 135.7 148.5 129.1

quadratic regression equation is found using the calculator for the values given in table.

y = 14.4x² + 92.68x - 16

You may calculate how long that rocket spent in the air before it impacted the ground by keeping in mind that after it reaches the ground, the rocket's height is zero.

Put x = t and y  = 0

0 =  14.4t² + 92.68t - 16

Using the quadratic formula, find the time t.

t = [-b ± √(b² - 4ac)] / 2a

a = 14.4 , b = 92.68 , c = -16

Put the values:

t = [-92.68 ± √(92.68² - 4* 14.4* (-16))] / 2* 14.4

t =  [-92.68 ± 97.52] / 28.8

t = (-92.68 + 97.52)/28.8 and t =  (-92.68 - 97.52)/28.8

t = 0.168 seconds  and  t = -6.6  seconds

Negative values not taken.

Thus, the time that rocket spent in the air before it impacted the ground by keeping in mind that after it reaches the ground, the rocket's height is zero is 0.168 seconds.

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Answer:

7:40

Step-by-step explanation:

first driver(every 20 min)         second driver( every 25 min)

6:00                                            6:00

6:20                                            6:25

6:40                                             6:50

7:00                                             7:15

7:20                                             7:40

7:40

8:00

both have 7:40 so they will both stop then

Answer:

WELL 17

Step-by-step explanation:

60 DIVED BY 5 IS 12

SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS

Answer:

yo we need the data lol how many

Answer:

20%

if there are 300 students and 60 of them chose the lion, 20% of the students chose lion

Ryan Neal has a loss of approximately $1,826. To calculate Ryan Neal's gain or loss, we need to consider the cost of buying the shares, the commission fees for buying and selling, and the selling price of the shares.

1. Cost of buying the shares:

Ryan bought 1,900 shares of Ford at $15.87 per share, so the total cost of buying the shares is:

Cost = Number of shares * Price per share = 1,900 * $15.87 = $30,153

2. Commission fees for buying:

The commission fee for buying is 19% of the purchase price, which is:

Commission fee for buying = 19% * $30,153 = $5,729.07

3. Selling price of the shares:

Ryan sells the shares for $20.18 per share, so the total selling price is:

Selling price = Number of shares * Price per share = 1,900 * $20.18 = $38,342

4. Commission fees for selling:

The commission fee for selling is also 19% of the selling price, which is:

Commission fee for selling = 19% * $38,342 = $7,285.98

Now, let's calculate the gain or loss:

Gain or Loss = Selling price - Cost - Commission fees for buying - Commission fees for selling

Gain or Loss = $38,342 - $30,153 - $5,729.07 - $7,285.98

Calculating the value, we have:

Gain or Loss ≈ $38,342 - $30,153 - $5,729 - $7,286

Gain or Loss ≈ $-1,826

Therefore, Ryan Neal has a loss of approximately $1,826.

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The equilibrium E2 corresponds to a stationary point where p increases (p' > 0) and q does not change (q' = 0).

To construct the phase plane for the given system of differential equations, we first need to find the nullclines and identify the equilibria.

(a) Nullclines and Equilibria:

For the first equation, p' = p(1 - p - q), we set p' = 0 and solve for p:

p(1 - p - q) = 0

This equation has two solutions:

p = 0

1 - p - q = 0

For the second equation, q' = q(2 - 3p - q), we set q' = 0 and solve for q:

q(2 - 3p - q) = 0

This equation also has two solutions:

q = 0

2 - 3p - q = 0

Now we can plot the nullclines on the phase plane:

Nullcline for p' = 0: p = 0 (horizontal line)

Nullcline for 1 - p - q = 0: q = 1 - p (diagonal line)

Nullcline for q' = 0: q = 0 (vertical line)

Nullcline for 2 - 3p - q = 0: q = 2 - 3p (diagonal line)

Next, we identify the equilibria by solving the equations:

Equilibrium for p = 0 and q = 1 - p: p = 0, q = 1 (Equilibrium E1)

Equilibrium for q = 0 and 2 - 3p - q = 0: p = 2/3, q = 0 (Equilibrium E2)

Now we can plot the equilibria on the phase plane.

To indicate the direction of motion, we can choose a few points in different regions of the phase plane and evaluate p' and q' at those points. This will help us determine the direction of the vector field arrows.

(b) Expression for each equilibrium:

For Equilibrium E1: p = 0, q = 1

Substituting these values into the given system of differential equations:

p' = 0(1 - 0 - 1) = 0

q' = 1(2 - 3(0) - 1) = 1

The equilibrium E1 corresponds to a stationary point where p does not change (p' = 0) and q increases (q' > 0).

For Equilibrium E2: p = 2/3, q = 0

Substituting these values into the given system of differential equations:

p' = (2/3)(1 - 2/3 - 0) = 2/9

q' = 0(2 - 3(2/3) - 0) = 0

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Answer:

13 Blocks Away From School

Step-by-step explanation:

5 + 8 Is 13

Answer: 13 blocks from school

Step-by-step explanation:

Answer:

\(\boxed{\boxed{\sf 1 }}\)

Step-by-step explanation:

\(\sf 9p^2 \:if\: \:p=\cfrac{1}{3}\)

__________

\(\sf 9\left(\cfrac{1}{3}\right)^2\)

\(\sf {Calculate\: 1 \:to \:the \:power\: of \:1=1}\)

\(\longmapsto \sf 9\times \left(\cfrac{1}{3}\right)^2\)

\(\sf Now, \: calculate \: \frac{1}{3} \: to\: the\: power\: of \:2 \:which\: will\: give\: you\: \frac{1}{9}\)

\(\longmapsto \sf 9\times \left(\cfrac{1}{9}\right)\)

\(\sf Multiply\: 9\: and\: \frac{1}{9} =1\)

\(\longmapsto 1\)

___________________________