What is 475. 189 475. 189 rounded to the nearest hundredth? ​

Answer:

y=5x-6

Step-by-step explanation:

Therefore, the solution to the equation 10ˣ = 23 is: x = log(23) that is option B.

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be solved to find the value(s) of the variable(s) that make the equation true.

Here,

Taking the logarithm of both sides of the equation 10ˣ = 23:

log(10ˣ) = log(23)

Using the power rule of logarithms, the left-hand side simplifies to:

x log(10) = x

Since log(10) = 1, we have:

x = log(23)

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The ladder should she placed 12 feet from the base of her house

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

Using the above as a guide, we have the following:

We make use of the pythagoras theorem to calculate how far the ladder should be placed

Represent this with x

So we have

x^2 = 20^2 - 16^2

Evaluate

x^2 = 144

So, we have

x = 12

Hence. the ladder should she placed 12 feet from the base of her house

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lines a and b are perlendicularr and the equation of line a is y=x+3.Therefore, after calculation, the equation of line b is y = -x + 3.

Perpendicular refers to a line, ray, or segment that intersects another line or segment at a right angle, or 90-degree angle. The point of intersection is called the point of perpendicularity and is equidistant from the endpoints of the segment.

An equation of a line is a mathematical representation of a straight line. It can be written in various forms, including slope-intercept form, point-slope form, and standard form, and relates the variables x and y.

According to the given information:

If line a has the equation y = x + 3 and line a is perpendicular to line b, then the slope of line b is the negative reciprocal of the slope of line a.

The slope of line a is 1, so the slope of line b is -1/1, which simplifies to -1.

To find the equation of line b, we need to find the y-intercept (b) using the point-slope form of a linear equation. We can choose any point on line b, but since we don't have any specific point given, we can use the y-intercept of line a, which is 3.

So, the equation of line b is y = -x + 3.

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The graph that represents f(x) =3x-2 is the graph (b)

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

The equation: f(x) = 3x - 2

From the above equation, we have

f(x) = 3x - 2

The above equation is a linear function with the following features

Slope = 3

y-intercept = -2

This means that the graph intersects with the y axis at y = -2

Using the above as a guide, we have the following:

The graph intersects with the y axis at y = -2 and has a slope of 2 is graph (b)

Hence, the graph that represents f(x) =3x-2 is graph (b)

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The new cost after the discount and tax are applied is $872.10, which is option (d).

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

First, let's calculate the amount of discount Angel will receive using the coupon code:

Discount = 15% of $950 = 0.15 x $950 = $142.50

Next, let's calculate the new price of the jacket after the discount is applied:

New price = $950 - $142.50 = $807.50

Now, let's calculate the amount of tax that will be applied to the new price:

Tax = 8% of $807.50 = 0.08 x $807.50 = $64.60

Finally, let's add the tax to the new price to get the total cost:

Total cost = $807.50 + $64.60 = $872.10

Therefore, the new cost after the discount and tax are applied is $872.10, which is option (d).

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18x9=162

18 cubes and 9 layers of the 18 cubes. so thats just eighteen, nine times.

a. The length of one side of the cube  shape x ≈ 3.633 ft

b. The length of one side of the cube  shape is roughly 3.633 feet.

c. The case has a more noteworthy surface region than the block by roughly 10.325 square feet.

Let x be the length of one side of the cube. Since the cube has equal length, width, and height, its volume is  = x^3.

The volume of the box  = (4 feet 5 in) * (3 feet 2 in) * (4 feet 3 in),

which can be converted to feet as Volume of box =

(4 + 5/12) * (3 + 2/12) * (4 + 3/12) = 4.3135 * 3.1667 * 4.25 =

55.0448 cubic feet.

Since the cube has the same volume as the box, we can set Volume of cube = Volume of box and

solve for x:

[tex]x^3 = 55.0448\\x = (55.0448)^{1/3}\\[/tex]

x ≈ 3.633 ft

b. The length of one side of the cube is approximately 3.633 feet.

c. We must determine the surface area of each to compare the cube's and box's surfaces. A cube with side length x has the surface area given by

Surface area of cube = [tex]6x^2[/tex], and

Surface area of a box = 2lw + 2lh + 2wh is the formula for the surface area of a box with the dimensions l, w, and h. Based on the box's dimensions, we have:

Surface area of cube = [tex]6(3.633)^2[/tex] ≈ 79.342 sq. feet

Surface area of box = 2(4.4167 * 3.25) + 2(4.4167 * 4.25) + 2(3.25 * 4.25) ≈ 89.667 sq. feet

By about 10.325 square feet, the surface area of the box is greater than that of the cube.

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The electrician needs approximately 296.26 feet of wire.

The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).

The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.

Using trigonometry, we can write:

sin(17°) = opposite / hypotenuse

where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:

hypotenuse = opposite / sin(17°)

To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:

tan(17°) = opposite / 85

Solving for the opposite side, we get:

opposite = 85 tan(17°)

Substituting this into the formula for the hypotenuse, we get:

hypotenuse = (85 tan(17°)) / sin(17°)

hypotenuse ≈ 296.26 feet

Therefore, the electrician needs approximately 296.26 feet of wire.

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The angles formed by the bisector are equal in measure, adjacent, supplementary, form a linear pair, and are congruent.

When a line bisects an angle, it divides the angle into two equal parts. The resulting angles have several properties

They have equal measures: The two angles formed by the bisector have the same degree measurement.

They are adjacent: The two angles share a common side and vertex.

They are supplementary: The sum of the two angles formed by the bisector is 180 degrees.

They form a linear pair: The two angles, together with the adjacent angle on the other side of the bisector, form a straight line or a linear pair.

They are congruent: The two angles formed by the bisector are congruent to each other.

These properties are useful in solving problems involving angle bisectors in geometry.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

What are some properties of the angles formed by the bisector?

We can conclude that a quadratic model is appropriate for the given set of points {(-2,4. 5),(0,8),(1,10. 67),(3,18. 96)}.

To determine which model is appropriate for the given set of points {(-2,4.5),(0,8),(1,10.67),(3,18.96)}, we need to examine the pattern in the data and choose a model that fits the pattern well.

One common approach to fitting a model to data is to use regression analysis. In this case, we can start by plotting the points on a graph and visually examining the pattern.

When we plot the points, we see that they form a curved shape that resembles a quadratic function. To confirm this, we can use regression analysis to fit a quadratic model to the data.

Using a quadratic regression model, we obtain an equation of the form y = ax^2 + bx + c, where a, b, and c are constants to be determined. The regression analysis yields the following coefficients: a = 2.138, b = 1.959, and c = 5.48.

We can now use this quadratic equation to predict y for any given value of x within the range of the data.

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The percent increase for the dinner is 25%

The first step is to calculate the increase

The price rose from $7 to $8.75

Increase= 8.75-7

= 1.75

Therefore the percent increase can be calculated as follows

1.75/7 × 100

= 0.25 × 100

= 25

Hence the percent increase is 25%

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The sums that prove that the wooden boards can create a triangular outline according to triangle inequality rule are:

The triangle inequality rule states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Testing each combination of sides, we get:

Case 1:

Let 5 feet be the third side

Then,

2.5 + 4 > 5

6.5 > 5

Case 2:

Let 2.5 feet be the third side

Then,

4 + 5 > 2.5

9 > 2.5

Case 3:

Let 4 feet be the third side

Then,

5 + 2.5 > 4

7.5 > 4

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The factored form of the trinomial x² - 7x + 12 is (x - 3)(x - 4).The involved trinomial is x² - 7x + 12.

Here is a detailed explanation:

a = 1 (coefficient of x²),

b = -7 (co - efficient of x), and

c = 12 are the trinomial's coefficients and constant (constant term).

Step 2: Find two numbers that multiply to a*c (1*12) and add up to b (-7).

The two numbers are -3 and -4.

Step 3: Modify the middle word as x²- 3x - 4x + 12 using the two integers

Step 4: Factor by grouping. Group the first two terms and the last two terms separately: (x² - 3x) + (-4x + 12).

Step 5: Factor out the greatest common factor (GCF) from each group: x(x - 3) - 4(x - 3).

Step 6: Factor out the common binomial (x - 3) from both terms: (x - 3)(x - 4).

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The chord length is approximately 1.397 centimeters where 0.7 centimeters is the separation from the center of the circle to the chord.

We can use the properties of circles to find the angle formed by the chord at the center of the circle to evaluate the length of the chord.

0.7 centimeters is the separation from the center of the circle to the chord. This remove is additionally the stature of the isosceles triangle shaped by the chord and the two radii of the circle. 

Let θ be the angle between the chord and the center of the circle. You can use trigonometry to find θ.

sin(θ/2) = 0.7/2.5

[tex]θ/2 = sin⁻¹(0.7/2.5)[/tex]

θ/2 = 0.2793

θ=2×0.2793

θ ≈ 0.5586 radians

Now that we know θ, we can use the formula for the chord length of a circle.

chord length = 2 × radius × sin(θ/2)

Chord Length = 2 × 2.5 × sin(0.2793)

String length ≈ 1.397 cm

Therefore, the chord length is approximately 1.397 centimeters.

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An inequality that correctly models the situation is:

4x² + 50x + 154 ≤ 320

The correct answer is an option (D)

Let us assume that l represents the length (height) and w represents the width of the poster and frame together.

Here, the original poster is 11 inches wide and 14 inches tall and the frame will be x inches thick on each side.

So, the height l would be,

l = (14 + 2x) inches

and the width w would be,

w = (11 + 2x) inches

We know that the formula for the area of rectangle.

A = l × w

So, the expression for the area of the poster and frame together would be,

A = (14 + 2x) × (11 + 2x)

A = 154 + 22x + 28x + 4x²

A = 4x² + 50x + 154

The total area of the poster and frame together to be no more than 320 square inches.

So, we get an inequality

A ≤ 320 in²

4x² + 50x + 154 ≤ 320 in²

Thus, the correct answer is an option (D)

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Find the complete question below.

The new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

To rotate a triangle 270 degrees clockwise with the origin as the centre of rotation, you can follow these steps:

Draw the coordinates of the vertices of the triangle. Let's assume that the coordinates of vertex A are (x₁, y₁), the coordinates of vertex B are (x₂, y₂), and the coordinates of vertex C are (x₃, y₃).

To rotate the triangle 270 degrees clockwise, you need to reflect it first over the x-axis, and then over the y-axis.

To reflect the triangle over the x-axis, you need to change the sign of the y-coordinates of each vertex. So the new coordinates of vertex A would be (x₁, -y₁), the new coordinates of vertex B would be (x₂, -y₂), and the new coordinates of vertex C would be (x₃, -y₃).

To reflect the triangle over the y-axis, you need to change the sign of the x-coordinates of each vertex. So the final coordinates of vertex A would be (-y₁, x₁), the final coordinates of vertex B would be (-y₂, x₂), and the final coordinates of vertex C would be (-y₃, x₃).

These final coordinates represent the vertices of the rotated triangle.

So, the new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

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The expression for the area of the triangle is given as follows:

A = 1.5x^4 + x³ - 0.5x².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5(3x² - x)(x² + x)

A = 0.5(3x^4 + 3x³ - x³ - x²)

A = 0.5(3x^4 + 2x³ - x²)

A = 1.5x^4 + x³ - 0.5x².

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Answer:

(x) = (-19/9)(x + 3)^2 + 5

Step-by-step explanation:f(x) = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola. Given that the vertex is (-3, 5), we can plug in these values into the vertex form equation:

f(x) = a(x - (-3))^2 + 5

which simplifies to:

f(x) = a(x + 3)^2 + 5

Now, we know that the function passes through the point (0, -14). We can plug in these values into the equation and solve for 'a':

-14 = a(0 + 3)^2 + 5

-14 = 9a + 5

Subtracting 5 from both sides:

-19 = 9a

Dividing both sides by 9:

a = -19/9

The midpoint between [tex]-3,5 and 1,6 is (-1,5.5)[/tex]

The midpoint between two points can be found by averaging the coordinates of the points separately for each dimension (x-axis and y-axis). Let's calculate the midpoint between [tex]-3,5 and 1,6[/tex].

The coordinates of the two points are:

Point 1: ([tex]-3,5[/tex])

Point 2: ([tex]1,6[/tex])

To find the midpoint, we can average the x-coordinates and y-coordinates separately.

Midpoint's x-coordinate = (x-coordinate of Point [tex]1[/tex] + x-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]

Midpoint's y-coordinate = (y-coordinate of Point [tex]1[/tex] + y-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]

According to the problem

Midpoint's x-coordinate = [tex](-3+1)/2= -2/2= -1[/tex]

Midpoint's y-coordinate = [tex](5+6)/2= 11/2 = 5.5[/tex]

So, the midpoint between [tex]-3,5[/tex] and [tex]1,6[/tex] is [tex](-1,5.5)[/tex].

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Answer:

The number series 2, 4, 6, 8, 10, 12, . . . . , 80. Therefore, 1640 is the sum of first 40 even numbers.......Sep 23, 2018

PLS MARK BRAINLIEST

Step-by-step explanation:

Answer:

$14.80

Step-by-step explanation:

First you need to subtract .50 from 2.35, which is 1.85.

Next you need to multiply 1.85 times 8.

1.85 x 8 = 14.80

Therefore, she has made $14.80 since the new price.

Quadrilateral ABCD can be dilated by a scale factor 1.25 to create a smaller image and by a scale factor 1.5 to create a bigger image.

To calculate the scale factor of a given shape for its dilation or reduction, the formula that should be used is given as follows:

Scale factor = bigger dimension/smaller dimension.

To create a smaller image;

bigger dimension length AB = 22in

smaller dimension length AB = 17.6in

Scale factor = 22/17.6 = 1.25

To create a bigger image:

Bigger dimension length = 33in

Smaller dimension length = 22in

scale factor = 33/22 = 1.5

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Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

Answer:

  a) '34'

Step-by-step explanation:

You want the result of executing the Python expression "3" +"4".

The tokens "3" and "4" are both strings. In this context, the "+" operator does concatenation of the strings, so the result is the string "34". The Python interpreter outputs this as '34'.

Answer: D

Step-by-step explanation:

The value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

To solve this problem, we can use the standard normal distribution table or a calculator that provides the inverse of the standard normal distribution. Let X be the weekly earnings of the bus drivers, then we have:

P(X > $429.35) = 0.011

Using the standard normal distribution table or calculator, we can find the z-score that corresponds to a probability of 0.011, which is approximately -2.33. We can then use the formula for standardizing a normal variable:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution. Substituting the given values, we have:

-2.33 = ($429.35 - $395) / σ

Solving for σ, we get:

σ = ($429.35 - $395) / (-2.33) = $14.57

Therefore, the value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

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The critical z-value for a 98% confidence level is 2.33.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

Statistics plays a significant role in various fields, including business, economics, social sciences, medicine, engineering, and many others.

To find the critical z value for a 98% confidence level, we need to look up the z-value associated with an area of 0.01 in the upper tail of the standard normal distribution table (since 98% of the area lies within the confidence interval, leaving 2% in the tails).

Using a standard normal distribution table, we can find that the z-value that corresponds to an area of 0.01 in the upper tail is approximately 2.33.

Therefore, the critical z-value for a 98% confidence level is 2.33.

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