Oak and Maple streets are parallel to each other. Main Street has a traffic
light at (5, 1) and is perpendicular to Oak and Maple. What is the equation
of the line representing Main Street?
Oak St.: y =
A. Y
1
22
+3 Maple St.: y = 22
C. y = -2x + 11
B.y=2x-9
D. y = -2x + 15
+6

The solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.

In mathematics, a logarithm is the inverse operation to exponentiation. Given a base b and a positive number y, the logarithm of y with respect to the base b is the exponent to which b must be raised to yield y. In other words, if x is the logarithm of y with respect to base b, then bˣ = y.

We can begin solving this equation by isolating the exponential term on one side of the equation and taking the logarithm of both sides.

2,401 = 7⁶⁻²ˣ

Taking the logarithm base 7 of both sides:

log₇(2,401) = log₇(7⁶⁻²ˣ )

Using the property of logarithms that states that log base a (aᵇ) = b, we can simplify the right-hand side of the equation:

log₇(2,401) = (6-2x)log₇(7)

Since log₇(7) = 1, we can further simplify:

log₇(2,401) = 6-2x

-2x = log₇(2,401) - 6

x = (6 - log₇(2,401))/2

Using a calculator, we find:

x ≈ 1.4076

Therefore, the solution to the equation 2,401 = 7⁶⁻²ˣ  is x ≈ 1.4076.

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Harriet ate a total of 3/4 of the total pizza

Given data ,

On Monday Harriet ate 1/4 of a 8 slice of pizza

And , on Tuesday she ate 1/2 of the same pizza

Now , If the pizza has 8 slices, then Harriet ate 1/4 of 8 slices on Monday, which is 2 slices.

On Tuesday, Harriet ate 1/2 of the same pizza, which is 4 slices.

So, in total, Harriet ate 2 + 4 = 6 slices of pizza

On simplifying the equation , we get

The whole pizza has 8 slices, so Harriet ate 6/8 of the pizza, which simplifies to 3/4.

Hence , Harriet ate 3/4 of the whole pizza

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The equation of circle whose center is at (4,-7) and radius is "5 units", is (b) (x − 4)² + (x + 7)² = 25.

We know that the equation of a circle which have center at the coordinate (h, k) and has a radius as "r" is represented by the formula ⇒ (x - h)² + (y - k)² = r²,

In this case, the center of the circle is situated at the coordinate (4, -7) and the radius is 5.

So, we substitute these values into the "circle-equation" to get;

⇒ (x - 4)² + (y + 7)² = 5²,

⇒ (x - 4)² + (y + 7)² = 25,

Therefore, the correct option is (b): (x − 4)² + (y + 7)² = 25.

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The given question is incomplete, the complete question is

A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?

(a) (x − 4)² + (x + 7)² = 5,

(b) (x − 4)² + (x + 7)² = 25,

(c) (x + 4)² + (x − 7)² = 5,

(d) (x + 4)² + (x − 7)² = 25.

Answer:

6

Step-by-step explanation:

To find the highest price Jenny can charge to earn $125 in profit, first write an equation.

total profit = profit per card * number of cards

You want to know when Jenny will earn $125 in profit, and the price per card, x, is the variable. The expression 0.7x represents the profit per card.

125=0.7x(–15x+120)

Now, solve for x. Start by writing the equation in standard form

125=0.7x(–15x+120)

125= –10.5x2+84x

0= –10.5x2+84x–125

Now to solve for x, you can use the quadratic formula with a= – 10.5, b=84, and

So, to the nearest dollar, the highest price Jenny can charge per card to earn $125 in profit is $6.0236 or $6.

There are 25% chance of 5 more people in the party.

Hence option (a) is correct.

Relative frequency = (number of times of occurrence of an event )/ (number of trials)

For the given table

relative frequency for 1 people = 0.05 = 5%

relative frequency for 2 people = 0.46 = 46%

relative frequency for 3 people = 0.18 = 18%

relative frequency for 4 people = 0.22 = 22%

relative frequency for 5 people = 0.06 = 6%

relative frequency for 6 people = 0.03 = 3%

Since relative frequency for 1 people is 5%

Therefore,

Relative frequency for 5 people is = 5x5%

                                                         = 25 %

Hence,

Relative frequency of 5 more people 25%.

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Answer:

last choice:  2b²/a³

Step-by-step explanation:

2a⁻³/b⁻² = 2·(1/a³) / (1/b²) = 2·(1/a³)(b²) = 2b²/a³

The answer

4.16666667 yards

According to the information, Sandra charges $2.25 for each necklace. So the correct option would be A.

To find the answer to this problem we must identify the information that the function raises. In this case we must replace the n by a number (in this case it will be 5) to find the value of P as shown below:

Once we identify how much 5 necklaces are worth, we divide that value by 5 to find the unit value.

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Answer:Answer and Explanation: An algebraic expression for the phrase '6 more than the product of 8 and n' is '8n + 6.

Step-by-step explanation:

Answer:

It is 50x or 50*x or 50(x).

The area of the similar triangle B is derived to be equal to 1.8 which makes option B correct.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

We shall represent the hight of triangle B with the letter h so that;

h/2 = 3/5

h = (2 × 3)/5 {cross multiplication}

h = 1.2

area of triangle B = 1/2 × 3 × 1.2

area of triangle B = 1.8

Therefore, the area of the similar triangle B is derived to be equal to 1.8

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Answer:

14:10

Step-by-step explanation:

We are given that the total train journey from Reading to Worle is the same for all trains

For the first train the time taken = 13:45 - 12:05

13:45
   -
12:05
--------
1 : 40
--------

So total travel time = 1 hour 40 minutes

For the third train time taken
15:05  -  13:25

15:05 = 14:05 + 0:60 since there are 60 minutes in an hour (we carry 60 from the hours part)

14:05 + 0:60 = 14:65

15:05 - 13:25 =

14:65
   -
13:25
---------
1 : 40 or 1 hour 40 minutes same as train #1

We want to find the arrival time of train #2 at Worle

Departure time of train #2 from Reading = 12:30

Time of travel = 1 hour 40 minutes

Arrival time = 12:30 + 1:40

12:30 time
   +
 1: 40  hours
----------
13:70   time
------------------
Since there are 60 minutes in 1 hour, to convert 13:70 to proper time units
subtract 60 from 70 to get the minute part of time and add 1 to 13 to get the hour part of time

13:70 = 14:10

Therefore the time that goes into the gap = 14:10

Verify

If the second train leaves Reading at 12:30 and arrives at Worle at 14:10, then time taken =

14:10 - 12:30 = 13:70 - 12:30 = 1:40 = 1 hour 40 minutes

Hope that helps and please don't hesitate to ask more questions if you have not fully understood my explanation

Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.

There are two distinct y values satisfying the given equation.

First, we rewrite the equation as |y-3| = 5 - x² + 8x - 18. Then, we express |y-3| as two cases: y-3 and -(y-3).

Case 1: y - 3 = 5 - x² + 8x - 18

Solving for y, we get y = x² - 8x + 16.

Case 2: -(y - 3) = 5 - x² + 8x - 18

Solving for y, we get y = x² - 8x + 10.

Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.

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The polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6 is f(x) = x³ - x² - 30x.

To find a polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6, we start by using the factor theorem. This theorem tells us that if a polynomial function has a zero at some value c, then it is divisible by the linear factor (x - c).

Therefore, the polynomial with zeros at -5, 0, and 6 can be written as:

f(x) = a(x + 5)(x - 0)(x - 6)

where a is a constant coefficient that we need to determine. Since the leading coefficient of the polynomial is 1, we set a = 1.

Multiplying out the factors, we get:

f(x) = (x + 5)(x)(x - 6)

= x³ - x² - 30x

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The probability that he passes Math and does not pass Physics is given as follows:

0.28 = 28%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probabilities for each event is given as follows:

The events are independent, hence the probability that he passes Math and does not pass Physics is given by the multiplication of the probabilities of each event, as follows:

0.7 x 0.4 = 0.28 = 28%.

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Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

The correct answers for the quadratic equation are:

Roots of a quadratic equation are the points where y = 0.

Abscissa of a quadratic equation are the points where x = 0.

If the equation of a quadratic equation is in the vertex form,

         y = a(x - h)² + k

         Vertex of the U-shaped curve will be (h, k)

Given in the question, where the equation of the u-shaped curve is
y = 2x(x - 11)

Convert the equation in the vertex form,

y = 2x² - 22x

y = 2(x² - 11x)

y = 2 *  (x² - 2 ( 5.5x) + (5.5)² - (5.5)²)

y = 2[(x - 5.5)² - 30.25]

y = 2(x - 5.5)² - 60.5

Hence, the vertex of the U-shaped curve will be (5.5, -60.5).

For x-intercepts,

Substitute y = 0,

0 = 2x(x - 11)

⇒ x = 0, 11

   Therefore, roots of the parabola will be (0, 0) and (11, 0).

and the  ordinate of the vertex is x = 5.5

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Answer:

I'm sorry, but there is no feature for this in this game.  But, there is a grid and a sizing tool.  You'll just have to make an educated guess based on the size of your character and your character's stage of life (baby, toddler, kid, teen, adult).  Hope I helped!  I once had the same question, but just did this.  I think each big grid square maybe is 3-5 ft?

The quadratic equation is solved and intersect at the points (4, 1) and (-1, 16)

Given data ,

To find the intersection points of the two functions, we can set them equal to each other and solve for x:

x² - 6x + 9 = -x² + 17

Bringing all the terms to one side:

2x² - 6x - 8 = 0

Dividing by 2:

x² - 3x - 4 = 0

We can factor this quadratic equation as:

(x - 4)(x + 1) = 0

So the solutions are:

x = 4 or x = -1

To find the corresponding values of y, we can substitute each value of x into either of the original equations

y = x² - 6x + 9

When x = 4:

y = 4² - 6(4) + 9 = 1

So one intersection point is (4, 1).

When x = -1:

y = (-1)² - 6(-1) + 9 = 16

So the other intersection point is (-1, 16).

Hence , the two functions intersect at the points (4, 1) and (-1, 16)

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Chebyshev's inequality is a statistical tool that provides a bound on the probability that a random variable deviates from its mean by a certain amount. It can be used to determine whether there is statistical evidence to support a hypothesis based on sample data.

Suppose we have a random variable D that represents the proportion of defective lightbulbs in a population. We want to test the hypothesis that the average proportion of defective lightbulbs in the population is greater than 0.10, i.e., H₀: D ≤ 0.10 vs H₁: D > 0.10. Let's assume that we have a sample of n lightbulbs and that the sample proportion of defective lightbulbs is W.

Chebyshev's inequality states that for any random variable X, the probability that X deviates from its mean by k standard deviations is at most 1/k². In other words,

P(|X - μ| ≥ kσ) ≤ 1/k²,

where μ and σ are the mean and standard deviation of X, respectively.

Now, let's apply Chebyshev's inequality to our sample proportion W. Since we don't know the true mean and standard deviation of D, we can use the sample mean and sample standard deviation as estimates. The sample mean is W/n and the sample standard deviation is √[W(1-W)/n]. We want to find the probability that D is greater than 0.10, which is equivalent to finding the probability that W/n is greater than 0.10.

Let k = (0.10 - W/n)/(√[W(1-W)/n]). Then,

P(D > 0.10) = P(W/n > 0.10) = P(W - 0.10n > 0) = P(W - μ ≥ (0.10 - μ)n) ≤ σ²/[(0.10 - μ)n]²,

where μ = E(W) = D and σ² = Var(W) = D(1-D)/n. Thus,

P(D > 0.10) ≤ D(1-D)/n[(0.10 - D)n]².

To decide whether there is statistical evidence to support the hypothesis H₁, we need to compare this upper bound on the probability of D being greater than 0.10 to the significance level α = 0.05. If the upper bound is less than α, then we reject the null hypothesis H₀ in favor of the alternative hypothesis H₁.

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The calculated length of XY in the right triangle XYZ is 6

From the question, we have the following parameters that can be used in our computation:

The right triangle

The value of XY in the right triangle can be calculated using the following sine ratio

sin(30) = XY/XZ

So, we have

sin(30) = XY/12

Cross multiply the equation

So, we have

XY = 12 * sin(30)

Evaluate the products

XY = 6

Hence, the length of XY in the right triangle is 6

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Answer:

1/8

Step-by-step explanation:

The absolute value of positive numbers (decimals, fractions, etc.) is the same number. The absolute value of negative numbers (decimals, fractions, etc.) is the same, but positive.

What is Absolute value?

Absolute value is a set of lines that if any number is placed in it, the number would be positive

Absolute signs: | |

Examples:

|-6|= 6 (Absolute value of -6 is 6)

|9|=9 (Absolute value of 9  is 9) (Because 9 is already positive)

Your Question

Since 1/8 is already positive, the absolute value of it would just be 1/8

Please feel free to ask questions

The equation of the circle in this problem is given as follows:

x² + y² = 90000

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The center for this problem is given as follows:

(0,0).

The radius is given as follows:

300 ft.

Hence the equation is of:

x² + y² = 90000

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Answer:$578.81

Step-by-step explanation:

✨magic✨

The resulting function is given as follows:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

The parent function in the context of this problem is given as follows:

[tex]y = e^{-2x}[/tex]

When the function is vertically compressed by a factor of 3, we have that it is divided by three on the range, hence:

[tex]y = \frac{e^{-2x}}{3}[/tex]

When the function is reflected across the x-axis, we multiply by -1 on the domain, hence:

[tex]y = \frac{e^{2x}}{3}[/tex], as -2x x -1 = 2x.

When it is shifted down two units, we subtract by two on the range, hence:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

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Answer:

Perimeter of rhombus = 4(9.7) = 38.8 cm

Area of rhombus = 4(1/2)(6.2)(7.4)

= 91.76 cm^2

Therefore , the solution of the given problem of area comes out to be the trapezium has a surface area of 39 square centimetres.

Calculating how much space would be needed for fully covering its exterior will reveal its overall dimensions. The surrounding environment is considered while selecting a comparable product with a rectangular shape. The surface area of anything determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal shapes determines how much water it can contain.

Here,

We can use the formula for a trapezoid's area if we assume that the shape is a trapezoid with parallel sides that are 9 cm and 4 cm and a height of 6 cm.

=> A = (a + b)h/2

where h is the height, and a and b are the lengths of the parallel sides.

When we enter the values we have, we obtain:

=> A = (9 + 4)(6)/2

=> A = 13(3)

=> A = 39

Consequently, the trapezium has a surface area of 39 square centimetres.

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Answer:

a. 3x = 23-2

3x = 21

x = 21÷3

x = 7

b. 5x - 2 = 4

5x = 4+2

5x = 6

x = 6÷5

x = 1.2

c. 3x = 23-2

3x = 21

x = 21÷3

x = 7

d. 7 = 2x+0.5x

7 = 2.5

x = 2.5÷7

x = 2.8

The surface area of the rectangular prism is 2200 square mm

From the question, we have the following parameters that can be used in our computation:

Dimensions = 5 mm by 40 mm by 20 mm

The surface area of the rectangular prism is calculated as

Area = 2 * (5 * 40 + 5 * 20 + 40 * 20)

Evaluate

Area = 2200

Hence, the area is 2200 square mm

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