Tiffany and Clara work as lifeguards at a community pool during the summer. The table shows Tiffany's earnings and the graph shows Clara's earnings for working different numbers of hours. Who is earning money at a faster rate? How much more per hour does that person earn?

Answer:

[tex]-\frac{5}{3}[/tex]

Step-by-step explanation:

[tex]m (slope)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-1-(-6)}{5-8}[/tex]

[tex]m=-\frac{5}{3}[/tex]

A particular type of cell doubles in number every hour.Write an exponential function that can be used to findthe number of cells present, y, at the end of x hours ifthere are initially 4 of these cells?The exponential function that can be used to find the number of cells present, y, at the end of x hours, given that there are initially 4 cells is: y = 4 * 2^x This is because the number of cells doubles every hour, so if there are 4 cells to start with, after one hour there will be 8 cells (doubling the initial number), after two hours there will be 16 cells (doubling the number after one hour), and so on. The exponent in the function represents the number of hours elapsed, and the base of the exponent is 2, representing the doubling of cells every hour.

Answer:

No

Step-by-step explanation:

A prime number cannot be divided exactly by any number other than itself and 1.

For example, 17 is a prime number, since it can only be exactly divided by 17 and 1.

85 is NOT a prime number, since it CAN be divided by 5.

Answer:2

Step-by-step explanation:

When raising an exponential expression to a power, you need to multiply the exponents. Applying this rule to (y^3)^5, we get (y^3)^5 = y^(3*5) = y^15.

So, (y^3)^5 • y^4 = y^15 • y^4 = y^(15+4) = y^19.

Therefore, the simplified expression is y^19, and the answer is 2.

The correct statements are:

The median is six and one-fourth.

The mode cannot be determined from the given information.

The range is five and three-fourths.

The median measures the central tendency in a dataset, which is the middle value when the data is arranged in order from lowest to highest (or highest to lowest). If the dataset has an odd number of values, the median is the middle value. If there is an even number of values in the dataset, the median is the average of the two middle values.

The median is six and fourth: This statement is true based on the given information that there are 11 marks on the line plot above 6 and fourth, and 11 marks below.

The mode is seven and two-fourths: This statement is false based on the given information. The mode is the value that appears most frequently in the dataset, and there are no values that appear more than once in the given data.

The range is five and three-fourths: This statement is true based on the given information. The range is the difference between the highest and lowest values in the dataset, which in this case is 5 and three-fourths (8 minus 2 and one-fourth).

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The equations of the functions from the zeros are f(x) = 4x² + 5x - 6 and f(x) = 3x² - 15

Function (a)

Given that

(3/4,0) and (-2,0).

Since the two points have the same y-coordinate of 0, the quadratic function is of the form

f(x) = (x - p)(x - q), where p and q are the x-coordinates of the two points.

Plugging in the given values, we get

f(x) = (x - 3/4)(x + 2)

So, we have

f(x) = 4x² + 5x - 6

Function (b)

Here we have

(-√5, 0), (√5, 0) and (-3, 12)

This function can be represented as

f(x) = a(x - p)(x - q)

So, we have

f(x) = a(x - √5)(x + √5)

Expand

f(x) = a(x² - 5)

Using the last point, we have

a((-3)² - 5) = 12

4a = 12

a = 3

So, we have

f(x) = 3(x² - 5)

Expand

f(x) = 3x² - 15

Hence, the function is f(x) = 3x² - 15

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The distance between Patrick and Clarissa cannot be determined as only one variable has been given in the question. Not sufficient data provided.

Using congruency, length of the missing side of the triangle =- 8.5 units.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.

In the 1st image:

The distance between Patrick and Clarissa cannot be determined as only one variable has been given in the question. Not sufficient data provided.

In the 2nd image:

Let x be the missing length of the triangle.

As the ray is an angle bisector,

Due to congruency:

11.9/7 = x/5

⇒ (11.9 × 5)/7 = x

⇒ x = 8.5 units.

Therefore, length of the missing side of the triangle =- 8.5 units.

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Answer:

127°

Step-by-step explanation:

I added a photo of my solution

Answer:

--------------------------------

The formed quadrilateral has two right angles, because of tangent segments.

One angle is marked as 53°, and the missing angle is x.

We know the sum of interior angles of a quadrilateral is 360°.

Find the missing angle:

Answer:

4.275 L

Step-by-step explanation:

Pitcher starts with 6.2 L.

7 glasses

each glass has 0.275 L

total water in 7 glasses: 7 × 0.275 L = 1.925 L

water remaining in pitcher: 6.2 L - 1.925 L = 4.275 L

Answer: 4.275 L is left in the pitcher.

The measure of angle T in the given quadrilateral is 92.5 degrees.

A quadrilateral is said to be inscribed in a circle if all four of its vertices are located on the circumference of the circle. In other terms, the quadrilateral is "enclosed" by the circle. The opposing angles of a quadrilateral are supplementary (add up to 180 degrees) and the product of the measurements of the two diagonals equals the sum of the products of the measures of the pairs of opposite sides when a quadrilateral is inscribed in a circle, both of which are important features. Inscribed quadrilateral geometry difficulties can be resolved by using these characteristics.

The sum of the angles in a quadrilateral is 360 degrees.

angle R + angle S + angle T + angle U = 360 degrees

79 degrees + 96 degrees + x + angle U = 360 degrees

Angle T and angle U are opposite angles in quadrilateral RSTU, therefore congruent.

175 degrees + 2x = 360 degrees

2x = 185 degrees

x = 92.5 degrees

Hence, the measure of angle T is 92.5 degrees.

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The equation of parabola for the given equation through which it satisfied the relation is     [tex]( \frac{1}{30} )x^2 + (\frac{1}{30} )x - 1[/tex].

What about parabola?

A parabola is a U-shaped curve that is formed by the graph of a quadratic function of the form y = [tex]ax^2 + bx + c[/tex]. The parabola is symmetric around its axis of symmetry, which is a vertical line passing through the vertex of the parabola. The vertex is the point where the parabola changes direction, either from increasing to decreasing or from decreasing to increasing. The direction of the opening of the parabola (upward or downward) is determined by the sign of the coefficient a in the quadratic equation. Parabolas are used in various fields, such as physics, engineering, and mathematics, to model various real-life phenomena.

Define equation:

An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). It represents a mathematical relationship between two or more variables or constants, and is used to solve problems and make predictions.

In mathematics, equations can take various forms, including linear equations, quadratic equations, trigonometric equations, differential equations, and more. Depending on the type of equation, the variables may represent real or complex numbers, vectors, matrices, functions, or other mathematical objects.

According to the given information:

As, we know about the condition of the parabola,

Hence:

[tex]y = Ax^2 + Bx + C y-intercept: x=0 and y = -1\\\\ C = -1 y = Ax^2 + Bx - 1 (5,0) \\ \\0 = 25A + 5B - 1 (-6,0) \\\\ 0 = 36A - 6B - 1 1 \\\\ = 25A + 5B1 = 36A - 6B \\ \\ 0 = -11A - 11B 11B = -11A B = -A kX^2 - kx - 1 , k=A=-b (5,0)\\\\25k + 5k - 1 = 030k = 1k = 1/30 \\\\(-6,0)36k - 6k - 1 = 0\\\\30k = 1k=30 (\frac{1}{30} )x^2 + (\frac{1}{30} )x - 1 ,[/tex]

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Answer:

it's above

Step-by-step explanation:

yeah

Answer:

Step-by-step explanation:

Rate of commission = commission / total sales

Rate of commission = $1,393.74 / $15,486

Rate of commission = 0.0898 or 8.98%

Diego's rate of commission is 8.98%.

a)The function that describes the height of the rocket in terms of time t can be expressed as: h(t) = -16t² + 224t + 98

b) the maximum height of the rocket is 1378 feet at t=7sec.

c)the rocket will be more than 702 feet above ground level during the time interval [1.95, 18.55].

d)14.13 seconds will take it to hit the ground

The quadratic formula is a formula that gives the solutions (or roots) of a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients, and x is the variable:

x = (-b ± √(b² - 4ac)) / (2a)

a) The function that describes the height of the rocket in terms of time t can be expressed as:

h(t) = -16t² + 224t + 98

where h(t) represents the height of the rocket (in feet) at time t (in seconds).

The -16t² term represents the effect of gravity, which causes the rocket's height to decrease over time. The 224t term represents the initial velocity of the rocket, which causes its height to increase over time. The constant term 98 represents the initial height of the rocket (at t = 0).

b) To determine the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function h(t). The x-coordinate of the vertex is given by:

t = -b / (2a)

where a = -16 (the coefficient of t²) and b = 224 (the coefficient of t). Substituting these values, we get:

t = -224 / (2×(-16)) = 7

Therefore, the rocket reaches its maximum height at t = 7 seconds.

To find the maximum height, we can substitute t = 7 into the function h(t) and simplify:

h(7) = -16(7)²+ 224(7) + 98 = 1378

Therefore, the maximum height of the rocket is 1378 feet.

c) To find the time interval during which the rocket is more than 702 feet above ground level, we need to solve the inequality:

h(t) > 702

Substituting the expression for h(t), we get:

-16t² + 224t + 98 > 702

Simplifying and rearranging terms, we get:

16t² - 224t - 604 < 0

Using the quadratic formula, we can solve for the roots of the equation:

t = [224 ± √(224²- 4(16)(-604))] / (2(16))

t ≈ 1.95 or t ≈ 18.55

Therefore, the rocket will be more than 702 feet above ground level during the time interval [1.95, 18.55].

d) To find the time at which the rocket hits the ground, we need to find the root(s) of the function h(t) where h(t) = 0. This occurs when the rocket returns to ground level (i.e., h(t) = 0) after reaching its maximum height.

Substituting the expression for h(t), we get:

-16t²+ 224t + 98 = 0

Using the quadratic formula, we can solve for the roots of the equation:

t = [224 ± √(224² - 4(-16)(98))] / (2(-16))

t ≈ 14.13 or t ≈ -0.38

the rocket hits the ground after approximately 14.13 seconds.

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Answer:

Step-by-step explanation:

The triangles are similar so the ratio of their corresponding sides will be the same. That is, TV/RV is equal to TS/RQ. This gives us the equation 12/x+6=16/x+1. Cross multiplying, this becomes 12x+12=16x+96. Simplifying, we get x=21. Therefore, RV=12+x-6=x+6=21+6=27.

Answer:

TV/RV=TS/RQ, 12/x+6=16/x+1, 12x+12=16x+96, x=21. Therefore, RV=12+x-6=x+6=21+6=27.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

f(4) = (4+2)² = (6)² = 36

The equation [tex]f(x) = -x^2 + 5x + 14[/tex] models the flight path of a quaffle thrown into the air during a game of quidditch.

The equation [tex]f(x) = -x^2 + 5x + 14[/tex] can be used to model the height of the quaffle, where x represents the time in seconds after the quaffle is thrown.

To find the maximum height of the quaffle, we need to find the vertex of the parabola described by the equation. The following formula can be used to determine the vertex's x-coordinate:

x = -b / 2a

where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c[/tex]. In this case, a = -1, b = 5, and c = 14, so we have:

x = -5 / 2(-1) = 5/2

The y-coordinate of the vertex can be found by plugging this value of x into the equation:

[tex]f(5/2) = -(5/2)^2 + 5(5/2) + 14 = 23.5[/tex]

Therefore, the maximum height of the quaffle is 23.5 feet, and it occurs 2.5 seconds after the quaffle is thrown.

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Answer:

Step-by-step explanation:

Short answer? x is 52 degrees and y is 38 degrees.

But how did I get it you probably did not ask?

Let's run it back to the definitions of complementary and supplementary angles.

Complementary angles: 2 angles that add to get you a CLEAN 90 degrees

Supplementary angles: 2 angles that add to get you a CLEAN 180 degrees

So if x is supplementary to 128 degrees, it has to be 52 degrees to fit the definition. So yeah 180-128= 52 degrees

Now for x to be complementary to y, y has to 38 degrees. 90-52=38 degrees.

x: 52 degrees

y: 38 degrees

I teleport here again should you have anymore questions.

The formula for the Pythagorean theorem in 3 dimensions is [tex]d^2 = a^2 + b^2 + c^2.[/tex]

What is Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be extended to 3 dimensions using the same principle.

In the case of a cube with base a, width b, and height c, we can imagine a right triangle that is formed by one of the diagonals of the cube and one of the faces. Let d be the length of this diagonal.

By the Pythagorean theorem in 3 dimensions, we have:

[tex]d^2 = a^2 + b^2 + c^2[/tex]

To see why this is the case, imagine that we have a right triangle in three dimensions, with sides of length a, b, and c.

The hypotenuse of this triangle is the diagonal of a rectangular box with sides of length a, b, and c. By the Pythagorean theorem, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the other two sides, which gives us the formula above.

Therefore, the formula for the Pythagorean theorem in 3 dimensions is [tex]d^2 = a^2 + b^2 + c^2.[/tex]

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The answer is ,the statement  that are true are: A. The small popcorn has  volume of about 25.13 cubic inches , C. The volume of two small popcorn is less than  volume of one large popcorn , E. The volume of  large popcorn is about 34.68 cubic inches greater than  volume of small popcorn (135.09 - 25.13 = 109.96).

A cone is  three-dimensional geometric shape that tapers smoothly from  flat, usually circular base to  point called the apex or vertex. The base of  cone can be any closed shape, but is usually a circle. A cone can be right or oblique, depending on whether or not the axis passing through the apex and the center of the base is perpendicular to the base.

The formula for volume of  cone are V = (1/3)πr^2h, where r is radius and h is height.

For the small popcorn cone:

radius =diameter/2 =4/2=2 inches

V = (1/3)π(2²)(6) ≈ 25.13 cubic inches

For the large popcorn cone:

radius = diameter/2 = 5/2 = 2.5 inches

V = (1/3)π(2.5²)(9) ≈ 59.81 cubic inches

Therefore, the statements that are true are:

A. The small popcorn has  volume of about 25.13 cubic inches

C. The volume of two small popcorn is less than volume of one large popcorn

E. The volume of  large popcorn is about 34.68 cubic inches greater than  volume of small popcorn (135.09 - 25.13 = 109.96)

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Step-by-step explanation:

The correct statement is: The amplitude will decrease, and the sound will become quieter.

When the compressions in a sound wave are very close together, the amplitude of the wave decreases. Amplitude is the measure of the maximum displacement of the particles of the medium from their rest position. As the amplitude of the wave decreases, the energy supplied by the vibrating source decreases, and the sound becomes quieter.

Answer:

Step-by-step explanation the answer will be 20 each

:

Waymon's hourly wage for the first 40 hours of labour was thus S9.68. equation

An equation in mathematics is a declaration of the equality of two expressions. Two sides of an equation are divided using the algebraic symbol (=). As an example, the assertion "2x + 3 = 9" is supported by the argument that it is true. Finding the value or values of the variable(s) needed to make the equation true is the aim of equation solving. It is possible to create regular or nonlinear, straightforward or complex equations that include one or more elements.

Let's name Waymon's usual hourly wage for the first 40 hours of labour "x". Based on the facts provided, we can then construct the following equation:

[tex]40x + 3(x + 1.5x) = 479.27[/tex]

Waymon's normal compensation for 40 hours of work is represented by the first term, while his overtime pay for 3 hours of work at time-and-a-half is represented by the second term (or 1.5 times his regular rate).

When we simplify this equation, we get:

[tex]40x + 4.5x = 479.27 - 48.4744.5x = 430.80 \\x = 9.68[/tex]

Waymon's hourly wage for the first 40 hours of labour was thus S9.68.

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The standard deviation for the given Poisson distribution is 0.8.

A Poisson distribution is used to model the number of events occurring in a fixed time interval when the events occur independently and at a constant rate. The mean and variance of a Poisson distribution are equal, and both are given by λ, the rate parameter.

Here, the given information is that the company receives an average of 0.64 purchase orders per minute. Therefore, λ = 0.64.

The formula for the variance of a Poisson distribution is σ² = λ, where σ is the standard deviation. Thus, substituting λ = 0.64 in this formula, we get σ² = 0.64. Taking the square root of both sides, we get σ = √0.64 = 0.8.

Therefore, the correct answer is 0.8.

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Answer:

28

Step-by-step explanation:

Average of first 6 scores is 12, so the total of those 6 scores is 6 × 12 = 72.

Average of next 12 scores is 36, so the total of those 12 scores is 12 × 36 = 432.

Total of all 18 scores is 72 + 432 = 504.

Overall average is 504 ÷ 18 = 28.

This proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To simulate the probability that Chad will get a hit on more than 2 of every 10 pitches he receives using random digits, follow these steps:

1. Divide the pitches into groups of 10. For each group of 10 pitches, record the number of hits that Chad gets.

2. Generate a random digit between 0 and 9 for each pitch in the group. If the digit is 0, 1, 2, or 3, consider it a hit. If the digit is 4, 5, 6, 7, 8, or 9, consider it a miss. Repeat this process for each group of 10 pitches.

3. Count the number of groups of 10 pitches in which Chad gets more than 2 hits.

4. Repeat steps 2 and 3 a large number of times (for example, 1000 times) to get an estimate of the probability that Chad will get a hit on more than 2 of every 10 pitches he receives.

5. Calculate the proportion of times in which Chad gets more than 2 hits in a group of 10 pitches.

Therefore, this proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.

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Answer: -3

Step-by-step explanation: 3-3=0

Answer:

Step-by-step explanation:

bonsoir aider moi plus vite possible

3+?=0

3 + x = 0

x = -3

5000 parts must be tooled by the machine to ensure 4500 are acceptable as One tenth of the parts tooled by a machine are rejects.

One-eighth of the parts tooled by a machine are rejected.

Now, let's take the number of parts made by the machine to be x.

Now, the number of acceptable parts will be:

Total number of parts - number of rejected parts

x - (x/10)

(10x-x)/10

9x/10

Now, we have the number of acceptable parts as 4500.

So, we have:

9x/10 = 4500

9x = 4500*10

x = (4500*10)/9

x = 5000

Hence, the total number of parts tooled by the machine is 5000 in which 4500 are acceptable one.

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Answer: 2

Step-by-step explanation:

7x-5 =3x+9

x = 4

7x4-5= 23

3x4+9=21

∠PQT=∠PQS+∠SQT

23=21+∠SQT

∠SQT=2