Lena, Alan, and Bill sent a total of 104 text messages over their cell phones during the weekend. Lena sent 8 fewer messages than Alan. Bill sent 2 times as many messages as Lena. How many messages did they each send?

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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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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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:

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:

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 ∈ {6, 7, 8, 9, 10}

Step-by-step explanation:

You want possible values of whole number x such that ...

  4 ≤ √3 +√x < 5

We can solve this inequality by first subtracting √3 from all sides:

  4 -√3 < √x < 5 -√3

Squaring these positive numbers does not change their order:

  19 -8√3 < x < 28 -10√3

  5.14 < x < 10.67

The value of x may be any whole number in the range 6–10, inclusive.

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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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 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 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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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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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

Answer: D

Step-by-step explanation:

The account value after forty (40) years is approximately $2,789,525.

We can use the formula for future value of an annuity to solve this problem:

FV = PMT * ((1 + r)^n - 1) / r

where FV is the future value, PMT is the annual deposit amount, r is the annual interest rate, and n is the number of periods (years in this case).

For the first year, the deposit amount is $3,000, so:

FV1 = 3000 * (1 + 0.0835)^40 = $65,470.22

For the subsequent years, the deposit amount increases by $300, so:

PMT = 3000 + 300 + 300 + ... = 3000 + 300 * 39 = $15,300

Using this value for PMT, we can calculate the future value for the remaining 39 years:

FV2 = 15300 * ((1 + 0.0835)^39 - 1) / 0.0835 = $2,724,054.54

Adding the two future values together, we get the total account value after forty years:

FV = FV1 + FV2 = $2,789,524.76

Therefore, the account value after forty years is approximately $2,789,525.

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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.

The operations that are performed with the exponents 2 and 3 in order to simplify the expression include the following:

x²x³ = addition.

(x²)³ = multiplication.

x³/x² = subtraction.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the addition, division, and multiplication law of exponents for powers to each of the expressions, we have the following:

x²x³ = x⁽³⁺²⁾ = x⁵ (addition).

(x²)³ = x⁶ (multiplication).

x³/x² = x⁽³⁻²⁾ = x (subtraction).

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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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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 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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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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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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Answer:

[tex]x^{2} + y^{2} = 36[/tex]

Step-by-step explanation:

The form of the equation for a circle is [tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex], where [tex](h, k)[/tex] is the center and [tex]r[/tex] is the radius. Here, (h, k) is (0,0) and r is 6, so the equation would just be [tex]x^{2} + y^{2} = 36[/tex].

Answer:

x² + y² = 36 (top right answer)

Formula for the circle:

(x - h)² + (y - k)² = r²

h = X center point  

k = Y center point

18x9=162

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

Given statement: Diversification can reduce portfolio risk even when correlations across stock returns equal zero.

Given statement is true.

Because, By diversifying, you spread your investments across various assets, which can help reduce the overall risk of your portfolio. When correlations are zero, it means that the stock returns move independently of each other, further supporting the benefit of diversification in this case.

Diversification can reduce portfolio risk by combining assets with different return patterns, but even when the correlations between the returns are zero, there is still systematic risk (market risk) that cannot be diversified away.

This is because all stocks are subject to macroeconomic factors such as inflation, interest rates, and changes in consumer confidence, which can affect the entire market.

Therefore, even if the correlations across stock returns are zero, diversification cannot completely eliminate portfolio risk.

However, it can still reduce it to a certain extent by spreading the risk across different assets.

The more uncorrelated the assets are in a portfolio, the greater the potential for risk reduction.

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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 time since the rock reached its closure temperature is approximately 579.8 years. When the rock was discovered, it had 4.375 grams of europium-151.

To find the time since the rock reached its closure temperature, we can use the following formula

t = t(1/2) * log(N0/Nt)

where t is the time elapsed, t(1/2) is the half-life, N0 is the initial amount of the isotope, and Nt is the amount of the isotope at the time it was discovered.

Substituting the given values, we get

t = 96.6 * log(5/0.625) ≈ 579.8 years

Therefore, the time since the rock reached its closure temperature is approximately 579.8 years.

To find the amount of europium-151 in the rock when it was discovered, we can use the fact that the total amount of samarium-151 and europium-151 in the rock is constant.

Since the rock originally contained 5 grams of samarium-151, it must have contained 5 - 0.625 = 4.375 grams of europium-151 when it was discovered.

Therefore, the rock had 4.375 grams of europium-151 when it was discovered.

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