A student response is selected at random from the results. State the exact probability the student response is from a freshman, given the student prefers to watch reality shows on television.

Answer:

Step-by-step explanation:

x + 5 < 7

x + 5 - 5 < 7 - 5

x < 2

The number line will have a open circle at 2 and be shaded to the left

completely.  The solution is all numbers less than positive 2.

Answer:

∠1 = 126°

∠4 = 54°

∠7 = 126°

Step-by-step explanation:

Since line p and line q are parallel lines we can use the angle relations to find the missing angle measures.

∠1 and ∠3 are alternate and congruent, so their measures are equal and 126° each.

∠4 and ∠3 are making a straight line and are supplementary angles, so their sum is adding up to 180°.

To find ∠4 we need to subtract 126 from 180:

180 - 126 = 54°

∠7 and ∠3 are corresponding angles and so they are equal in measurement and 126° each.

The correct equation to isolate principal, P, is:

Simple interest refers to the interest that is earned on an initial amount of money, known as the principal, over a fixed period of time. It is called "simple" because it is calculated based only on the initial principal amount and does not take into account any interest earned on the interest itself, which is known as compound interest.

To isolate principal, P, we need to rearrange the given formula as follows:

[tex]A - P(1 + rt) =[/tex] Interest earned on principal (I)

The interest earned on the principal (I) is given by:

[tex]I = Prt[/tex]

Now, we can rewrite the above formula as:

[tex]A = P + I[/tex]

Substituting the value of I, we get:

[tex]A = P + Prt[/tex]

Now, we can isolate P by subtracting Prt from both sides:

[tex]A - Prt = P[/tex]

Therefore, the correct equation to isolate principal, P, is:

[tex]P = (A - Prt)[/tex]

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The correct equation to isolate P is c. P = A/(1 + rt)

Simple interest is the term used to describe the interest that is accrued over a predetermined amount of time on an initial sum of money, known as the principal. It is known as "simple" interest because it is computed just using the initial principal sum and ignores any interest that has been earned on top of the interest itself, a concept known as compound interest.

The formula for the final amount earned using simple interest is A = P(1 + rt), where A is the total amount at the end of t years, P is the principal amount, r is the interest rate, and t is the time in years.

To isolate P, we can rearrange the formula as:

A = P(1 + rt)

Divide both sides by (1 + rt):

A/(1 + rt) = P

Therefore, the correct equation to isolate P is:

c. P = A/(1 + rt)

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The scale factor of the given triangle is 3/2.

What is triangle?

Triangles are a particular form of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional image shown here. An example of a 3-sided shape is a triangle. The total of a triangle's three angles is 180 degrees.

In triangle ABC and triangle DEF;

AB= 15, BC=18, AC=12 and DE=10, EF=12, DF=8

NOW, we know that scale factors are the REDUCED FORM of corresponding sides of two similar triangles, then;

HERE;

scale factors will be....

AB/DE=15/10=3/2

BC/EF=18/12=3/2

AC/DF=12/8=3/2

Hence, scale factor is 3/2.

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The correct question is:

Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF. If △ABC: BC = 18, AB = 15, AC = 12 △DEF: EF = 12, DE = 10, DF = 8.

Using the equations we know that the square should be finished by adding 9 to both sides.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

So, write the equation so that the terms with x are on the left and the constants are on the right:

x² – 6x = 5

Ensure that the x2 term's coefficient is 1:

x² – 6x = 5

Including a phrase on both sides will complete the left side's square. The x term's coefficient is multiplied by two and squared to achieve this.

To make the equation equal on both sides, add the same amount to the right side.

x² – 6x + 9 = 5 + 9

(x-3)² = 14

Therefore, using the equations we know that the square should be finished by adding 9 to both sides.

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Correct question:

What number should be added to both sides of the equation to complete the square?

x2 – 6x = 5

(a)  Total urine volume is excreted during this time period is 442.34 mL.

(b) Equations for the velocity of urine is v = (-3 x [tex]V_t[/tex] + 7.35) / 2.46 x [tex]10^{-5}[/tex]

(a) To determine the total urine volume excreted during this time period, we need to integrate the flow rate function over the given time period. However, we are given two different equations for the flow rate for different ranges of time:

For t < 12 seconds, V = -0.306 x  [tex](t-7)^2[/tex]  + 15

For 12 ≤ t < 26.7 seconds, V = -3 x [tex]V_t[/tex]  + 7.35

To find the total urine volume, we need to first determine the time at which the flow rate changes from the first equation to the second.

We can do this by setting the two equations equal to each other and solving for t:

-0.306 x  [tex](t-7)^2[/tex]  + 15 = -3 x [tex]V_t[/tex] + 7.35

0.306 x  [tex](t-7)^2[/tex] + 3 x [tex]V_t[/tex]  = 7.65

0.306 x [tex](t-7)^2[/tex] = 7.65 - 3 x [tex]V_t[/tex]

[tex](t-7)^2[/tex] = (7.65 - 3 x [tex]V_t[/tex] ) / 0.306

t = 7 +/- [tex]\sqrt{((7.65 - 3 \times Vt) / 0.306)}[/tex]

Since t < 12 for the first equation, we can ignore the negative root and use the positive root to find the time at which the flow rate changes:

t = 7 + [tex]\sqrt{((7.65 - 3 \times 12) / 0.306)}[/tex]= 10.76 seconds

Now we can integrate each equation separately over their respective time ranges:

For 0 ≤ t < 10.76 seconds:

∫ V dt = ∫ (-0.306 x [tex](t-7)^2[/tex] + 15) dt

= [-0.102 x [tex](t-7)^3[/tex] + 15t] from t=0 to t=10.76

= 121.86 mL

For 10.76 ≤ t < 26.7 seconds:

∫ V dt = ∫ (-3 x [tex]V_t[/tex] + 7.35) dt

= [-1.5 x [tex]V_t^2[/tex] + 7.35t] from t=10.76 to t=26.7

= 320.48 mL

Therefore, the total urine volume excreted during this time period is:

121.86 mL + 320.48 mL = 442.34 mL

(b) To develop equations for the velocity of urine as it exits the body, we need to use the continuity equation, which states that the flow rate (V) is equal to the cross-sectional area (A) multiplied by the velocity (v):

V = A x v

We are given that the urethra has a diameter of 5.6 mm, which means the radius is 2.8 mm (or 0.0028 m).

The cross-sectional area can be calculated using the formula for the area of a circle:

A = π x [tex]r^2[/tex]

A = 3.14 x [tex](0.0028)^2[/tex]

A = 2.46 x   [tex]10^{-5}[/tex] [tex]m^2[/tex]

Now we can rearrange the continuity equation to solve for the velocity:

v = V / A

Substituting the given equations for V, we get:

For t < 12 seconds:

v = (-0.306 x [tex](t-7)^2[/tex] + 15) / 2.46 x  [tex]10^{-5}[/tex]

For 12 ≤ t < 26.7 seconds:

v = (-3 x  [tex]V_t[/tex] + 7.35) / 2.46 x [tex]10^{-5}[/tex]

Note that the velocity will be in units

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Question:-

The flow of urine from the bladder, through the urethra, and out of the body, is induced by increased pressure in the bladder resulting from muscle contractions around the bladder with simultaneous relaxation of the muscles in the urethra. The mean pressure in the bladder can be estimated using the velocity of urine as it exits the body. Assume that the bladder is about 5 cm above the external urethral orifice. (This height is different for males and females.) The flow rate of urine from the bladder can be approximately described with the following equations, where t is time in seconds, and V is flow rate in mL/s:

V = -0.306 X (t – 7)2 + 15 Osts 12

V = -3 X Vt 12 + 7.35 12 st < 26.7

(a) How much total urine volume is excreted during this time period?

(b) Develop equations for the velocity of as it exits the body. Assume that the urethra is 5.6 mm in diameter.

When two numbers appear side by side, the number and number should be written together for clarity. The statement is true.

The term numeric expression consists of two words, number for a number and expression for a sentence. Therefore, it is a word containing numbers. Teaching mathematics is the combination of numbers and mixed numbers using mathematical operations such as addition, subtraction, division, or division. There are many number expressions such as word form and number form. Numerical expressions are mathematical expressions that contain only numbers and one or more operators.

Examples of symbol operations are addition, subtraction, multiplication, and division. It can be represented by a radical symbol (square root symbol) or a real value.

Equations consist of numbers and contain multiple digits. There is no limit to the number of operators a shared account can have. Some numbers use only one operator of the two numbers, while others may have more than one operator. The only requirement for a numeric expression is that it only contains a number and an operator. Some numbers have only one operator code others have two or more.

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The following formula is used: P(n,r) = n! / (n - r)! to the calculate  the number of permutations.

The formula used to calculate the number of permutations when a permutation is any arrangement of r objects

selected from n possible objects is P(n,r).

P(n,r) is the formula used to calculate the number of permutations.

Let us try to understand the concept of permutations first.

Permutations refer to the different ways of arranging elements.

It is represented as nPr called as n-permute-r.

Here, n represents the total number of elements present, and r represents the number of elements taken for each

permutation.

To calculate the number of permutations, the following formula is used:

P(n,r) = n! / (n - r)!

Where n! is equal to n-factorial that refers to the product of all numbers starting from 1 up to n.

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The slope intercept form of the given line whose coordinate of point is (- 5,9) and slope is - 5 would be y = -5x - 16.

Equation of a straight line: y = mx + b ------(i)

Given that

y = 9, x = -5

and slope, m = - 5

By putting above values in equation (i)

9 = -5 (-5) + b

9 = 25 + b

-16 = b

b = -16

y = -5x - 16

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

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Step-by-step explanation:

See image

Answer:

Step-by-step explanation:

The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.

Example: What is the Geometric Mean of 2 and 18?

First we multiply them: 2 × 18 = 36

Then (as there are two numbers) take the square root: √36 = 6

In one line:

Geometric Mean of 2 and 18 = √(2 × 18) = 6

Answer: 4

Step-by-step explanation:

2x6 = 3xd

12=3d

d=4

You can trust this answer because I answered it right now and it was correct. <3

The value of length of segment d is,

⇒ d = 4

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A circle is shown in figure.

Now, We can formulate;

⇒ 6 × 2 = d × 3

Solve for d;

⇒ 12 = 3d

⇒ 3d = 12

⇒ d = 12/3

⇒ d = 4

Thus, The value of length of segment d is,

⇒ d = 4

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The limit of the given function as x approaches infinity is 2.

Infinity is a concept used in mathematics to represent a quantity that is unbounded or without limits. It is often used to describe a value or set of values that increases or decreases indefinitely without ever reaching a final value.

To find the limit of the given function as x approaches infinity, we need to determine the behavior of the function as x becomes very large (positive or negative).

Let's examine the expression inside the limit as x approaches infinity:

StartFraction 4 - 3x + x² Over 2x² + 1 EndFraction

As x approaches infinity, the highest power term in the numerator and denominator dominates. In this case, the term x² dominates in the numerator and denominator. So we can simplify the expression by dividing both numerator and denominator by x²:

Start Fraction 4/x² - 3/x + 1 Over 2 + 1/x² End Fraction

As x approaches infinity, both the terms 3/x and 1/x² become very small and can be ignored. Therefore, the expression approaches:

Start Fraction 4/x² - 0 + 1 Over 2 + 0 End Fraction

which simplifies to:

Start Fraction 4 Over 2 End Fraction = 2

Therefore, the limit of the given function as x approaches infinity is 2.

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Answer:

1 over 36

Step-by-step explanation:

Answer: D Mario owes the bank a little less than $50

Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.

Long-distance travel refers to a journey between two locations that are far apart. The best option for long-distance travel is the train because it is dependable and affordable. Communication that takes place over a long distance is referred to as long-distance. His lover in Colorado gave him a long-distance call.

We may construct a proportion to calculate how long it will take Scott to complete 52 kilometers at the same speed:

52 km/m at 20 km/85 min.

We can cross-multiply to find the value of m:

20 km * m equals 85 min * 52 km.

Simplifying:

20m = 4420

20 divided by both sides:

m = 221

Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.

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Based on the amount predicted to be spent, the hypotheses Null Hypothesis = $1,007.24 and Alternate Hypothesis ≠ $1,007.24

The null hypothesis, or H0, in statistics science is the exact reverse of what the researcher wants to investigate. Generally, unless there is compelling proof to the contrary, the null hypothesis is taken to be correct. Another theory that will demonstrate the area one wants to investigate and be reflected by H1 must be developed.

The forecast is confirmed by the null hypothesis, which in this instance is that the typical consumer will indeed spend $1,007.24. According to the Alternate Hypothesis, the predicted occurrence won't occur, so in this instance, the shopper wouldn't spend $1,007.24. In conclusion, the variant contradicts the null hypothesis and supports it.

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Using the area formula,

Area of the prism = 40mm².

Define area?

The word "area" designates a vacant region. The length and width of a form are used to calculate its area. The units of unidimensional length are feet (ft), yards (yd), inches (in), etc. Yet, the area of a shape is a two-dimensional quantity. Measurements like square inches (in²), square feet (ft²), square yards (yd²), etc. are used to measure anything in a square.

In the figure,

We have 2 equal rectangles and 2 equal triangles.

Now dimensions of the rectangles, l = 4mm and b = 3mm.

Area of 2 rectangles = 2 × 4 × 3

= 24mm².

Height of triangle, h = 4mm and base, b = 4mm.

Area of 2 triangles = 2 × 1/2 × b × h

= 4 × 4

= 16mm².

Therefore, total area of the prism = 24 + 16 = 40mm².

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A 0.025kg golf ball is hit off a tee with a force of 450N. If the golf club was in contact with the ball for 0.012 s, the velocity of the golf ball will increase by 216 m/s.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

To solve this problem, we can use the equation:

F = m*a

where F is the force applied, m is the mass of the object, and a is the acceleration.

We can rearrange this equation to solve for acceleration:

a = F/m

Using this equation, we can find the acceleration of the golf ball:

a = 450N / 0.025kg = 18000 m/s²

Next, we can use the equation:

v = v0 + a*t

where v is the final velocity, v0 is the initial velocity (which we'll assume is 0 m/s), a is the acceleration, and t is the time.

We know the acceleration and the time, so we can solve for the final velocity:

v = 0 + (18000 m/s²) * 0.012 s

v = 216 m/s

Therefore, the velocity of the golf ball will increase by 216 m/s.

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Answer:

Frequency is high hope this help you

r offers to pay $1,000 over the dealer' cost for a luxury coupe. The base price is $62.685 and options total $5,209. There is no destination charge. If the dealer' costs are 87 percent of the base price and 89 percent of the options, what is Huster's offer?The dealer's cost for the base price would be 87% of $62,685, which is $54,508.95. The dealer's cost for the options would be 89% of $5,209, which is $4,638.01. Therefore, the total dealer's cost would be $54,508.95 + $4,638.01 = $59,146.96. Brad Huxter's offer is $1,000 over the dealer's cost, so his offer would be $59,146.96 + $1,000 = $60,146.96.

The fact that PC is less than 50% indicates a higher probability of underage.

However, without additional information on the costs associated with overage and underage, we cannot determine which cost is higher.

From the information given in the student question, it is clear that the probability of underage (PC) is less than 50%, as indicated by the shaded area under the graph.

To determine whether the cost of overage or the cost of underage is higher, follow these steps:
1. Identify the costs associated with overage and underage in the given context. Overage cost refers to the cost incurred when the inventory is higher than demand, while underage cost refers to the cost incurred when the inventory is lower than demand.
2. Analyze the graph or data provided to compare the costs of overage and underage. Since the student question does not provide any specific data or graph, we cannot accurately determine which cost is higher based on the given information.
3. Interpret the results. If the cost of overage is higher than the cost of underage, this means that having excess inventory is more expensive than having insufficient inventory.

Conversely, if the cost of underage is higher than the cost of overage, this means that not having enough inventory is more expensive than having excess inventory.

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Answer:

100 or 10²

Step-by-step explanation:

8² = 64

36 = 6²

64 + 36 = 100

8² + 6² = 10²

Answer:

800$

Step-by-step explanation: not sure

Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Part A:

To predict how many votes each candidate for president will get in the election, we can set up a proportion between the sample and the population

Let x be the number of votes each candidate will receive in the election.

For Henry:

36/150 = x/1500

x = (36/150) * 1500

x = 360

For Christy:

42/150 = x/1500

x = (42/150) * 1500

x = 420

For Celina:

22/150 = x/1500

x = (22/150) * 1500

x = 220

Therefore, Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.

Part B:

Based on the survey results, Christy is most likely to get the highest percentage of votes for the president’s position with 42/100 votes, which is approximately 42%.

Part C:

To predict how many votes each candidate for vice president will get in the election, we can set up a proportion between the sample and the population.

Let x be the number of votes each candidate will receive in the election.

For Tristan:

14/150 = x/1500

x = (14/150) * 1500

x = 140

For Kenny:

46/150 = x/1500

x = (46/150) * 1500

x = 460

For Madison:

40/150 = x/1500

x = (40/150) * 1500

x = 400

Therefore, Tristan is predicted to receive 140 votes, Kenny is predicted to receive 460 votes, and Madison is predicted to receive 400 votes for the vice president’s position.

Part D:

Based on the survey results, Kenny is most likely to get the highest percentage of votes for the vice president’s position with 46/100 votes, which is approximately 46%.

Part E:

To predict how many votes each candidate for treasurer will get in the election, we can set up a proportion between the sample and the population.

Let x be the number of votes each candidate will receive in the election.

For Priscilla:

53/150 = x/1500

x = (53/150) * 1500

x = 530

For Reuben:

24/150 = x/1500

x = (24/150) * 1500

x = 240

For Erica:

23/150 = x/1500

x = (23/150) * 1500

x = 230

Therefore, Priscilla is predicted to receive 530 votes, Reuben is predicted to receive 240 votes, and Erica is predicted to receive 230 votes for the treasurer’s position.

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The linear equation that passes through the given points is:

y + 9 = -10*(x - 1)

A general linear equation that passes through two points (x₁, y₁) and (x₂, y₂) has a slope given by:

a = (y₂ - y₁)/(x₂ - x₁)

Then using any of these points we can write the line as:

y -  y₁ = a*(x - x₁)

Here the points are (1, -9) and (-10, 101), then the slope is:

a = (101 + 9)/(10 - 1) = 110/-11 = -10

And using the point (1, -9) we can write the line as:

y + 9 = -10*(x - 1)

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Manuel could make up to 24 table runners with the given amount of fabric thus all possible values are 20, 22, and 24.

One or more variables, integers, and mathematical operations like addition, subtraction, multiplication, and division are all included in an algebraic expression. Algebraic expressions are used to simulate events in the actual world and to represent relationships between quantities. Constants (fixed values), variables (unknown values), and coefficients can all be found in an algebraic equation (numbers multiplied by variables).

The expression for the left over fabric is:

Amount of fabric left = 18 - (3/4)t

Solving for t we have:

(3/4)t = 18

t = 24

Hence, Manuel could make up to 24 table runners with the given amount of fabric, thus all possible values are 20, 22, and 24.

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The value of x in the tangent angle formed by the intersecting chords on the circle is 8.

The value of x is calculated by setting up equation for the sum of angles in a circle in order to obtain the value of the opposite arc angle (arc WX) as shown below.

arc WX + arc WV + arc VX = 360 ( sum of angles in a circle)

arc WX + 96⁰ + 64⁰ = 360⁰

arc WX + 160 = 360

arc WX = 360 - 160

arc WX = 200

The value of angle WVX is equal to half of arc angle WX (based on intersecting chord theorem).

m ∠WVX = ¹/₂ arc WX

12x + 4 = ¹/₂ (200)

12x + 4 = 100

12x = 100 - 4

12x = 96

x = 96/12

x = 8

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