Question 9 (10 points)
A rectangular mattress has a length that is twice it's width. The width is known to be
1 meter across, what is the area of the mattress?
O2 sq. meters
none of these
3 sq. meters
6 sq. meters

Katemust have watered at least 12 daisies (in groups of 3) and 12 lilies (in groups of 12).

To determine the minimum number of each flower Kate must have watered, we need to find the least common multiple (LCM) of 3 and 12.

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

The multiples of 12 are: 12, 24, 36, 48, 60, ...

We can see that the least common multiple of 3 and 12 is 12, as it is the smallest number that appears in both lists. Therefore, she must have watered at least 12 daisies (in groups of 3) and 12 lilies (in groups of 12).

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Answer:

The answer is x<8

Step-by-step explanation:

x/2<4

x<8

The caculated value of the length of the leg s is approximately 9.95 units.

Given that

Legs = s and 15

Hypotenuse = 18

In a right triangle, the Pythagorean theorem states that the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

That is:

s^2 + 15^2 = 18^2

Simplifying and solving for s, we get:

s^2 + 225 = 324

s^2 = 99

s = √99

s ≈ 9.95 (rounded to two decimal places)

Therefore, the length of the leg s is approximately 9.95 units.

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In scatter plot, 12 .4 million is  the number of households with cable television in year 10.

What is  scatter plot?

A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they may display the degree of connection, if any, between the values of observable quantities or events (referred to as variables).

       slope = 9 - 5/7 - 1  = 4/6  = 2/3

             N - 5 = 2/3 (T - 1 )

             N(t) = 2/3 T + 13/3

when    t = 11

        N(11) = 2/3  * 11 + 13/3

               = 35/3

               = 12.4

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The probability of exactly 3 successes in 15 trials with a probability of success on a single trial of 0.77 is approximately 0.1648.

To find the probability of exactly 3 successes in a binomial distribution with n=15 trials and a probability of success on a single trial q=0.77, we can use the formula for the probability mass function of the binomial distribution:

P(X=k) = (n choose k) * q^k * (1-q)^(n-k)

Substituting the given values into the formula, we get:

P(X=3) = (15 choose 3) * 0.77^3 * (1-0.77)^(15-3)

P(X=3) = (15!/((15-3)!3!)) * 0.77^3 * 0.23^12

P(X=3) = 0.1648.

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Answer:

[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]

An equation of the trend line in the scatter plot is equal to y = -4x/9 + 9.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 9)/(9 - 0)

Slope (m) = -4/9

At data point (0, 9) and a slope of -4/9, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 9 = -4/9(x - 0)  

y - 9 = -4x/9

y = -4x/9 + 9

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The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).

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Answer:

b. reflection and translation

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

the answer is 110-23i

Answer:[tex]\frac{21}{2} x^{2/3} - \frac{12}{5}x^{\frac{5}{3} } + C[/tex]

Step-by-step explanation:

[tex]\int {\frac{7}{x^{1/3} }-4x^{2/3} } \, dx \\\int {7x^{-1/3}} - 4x^{2/3}\, dx \\= 7*\frac{3}{2}x^{2/3} - 4*\frac{3}{5}x^{\frac{5}{3} } + C\\ =\frac{21}{2} x^{2/3} + \frac{12}{5}x^{\frac{5}{3} } + C\\\\\\ Assuming: (x^{2})^\frac{1}{3}[/tex]

Answer and Step-by-step explanation: To calculate the net income of the family after taxes, we need to first determine the amount of taxes they will pay.

The federal tax rate of 18% means that the family will pay 18 cents in taxes for every dollar of gross income they earn.

So, the amount of federal taxes the family will pay can be calculated as:

Federal taxes = Gross income x Tax rate

Federal taxes = $95,000.00 x 0.18

Federal taxes = $17,100.00

Now that we know the amount of federal taxes the family will pay, we can calculate their net income by subtracting the federal taxes from their gross income:

Net income = Gross income - Federal taxes

Net income = $95,000.00 - $17,100.00

Net income = $77,900.00

Therefore, the family's net income after paying federal taxes is $77,900.00.

Answer:

Step-by-step explanation:

2.1 so a

Answer:

To approximate the location of the square root of 14 on a number line, we can first find the two integers that √14 is between. We know that:

3^2 = 9 < 14 < 16 = 4^2

So √14 is between 3 and 4. We can divide the distance between 3 and 4 into equal parts and estimate the location of √14 based on where it falls in that interval.

Dividing the interval into 10 equal parts, we get:

3.0 - 3.1 - 3.2 - 3.3 - 3.4 - 3.5 - 3.6 - 3.7 - 3.8 - 3.9 - 4.0

Since √14 is closer to 3 than to 4, we can estimate its location as being closer to 3.4 than to 3.5. Therefore, a good approximation for the location of √14 on the number line is 3.7.

The answer is $359.25, which is closest to option A: $363.75.

Calculating the sum of two or more numbers is the procedure of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.

The premium for a $75,000 10-year term policy for a 25-year-old male will be $75 times the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. From the table, the premium per $1,000 face value for a 10-year term policy for a 25-year-old male is $4.79. Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male will be:

$75 × $4.79 = $359.25

Rounding to the nearest cent, the answer is $359.25, which is closest to option A: $363.75. Therefore, the answer is (a) $363.75.

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Using expression  (3 x Price per bond) + Commission, total cost of three ABC bonds would be $182.70.

What exactly are expressions?

In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated or simplified to produce a value. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple operations and functions.

Now,

The cost of three ABC bonds can be calculated as follows:

Total cost of three ABC bonds = (3 x Price per bond) + Commission

To find the price per bond, we need to use the current yield and the face value of the bond:

For bond A, current yield = 7.5, face value = 100, so price per bond = 100 x (7.5/100) = 7.50

For bond B, current yield = 8.4, face value = 100, so price per bond = 100 x (8.4/100) = 8.40

For bond C, current yield = 7.75, face value = 100, so price per bond = 100 x (7.75/100) = 7.75

So the total cost of three ABC bonds would be:

(3 x 7.50) + (3 x 8.40) + (3 x 7.75) + (3 x 10) = $104.25 + $25.20 + $23.25 + $30 = $182.70

Therefore, the correct answer is not listed.

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The number of price increases that would be needed to cause zero profit as shown on the graph, is C) 87.

The point on the graph that would show the number of price increases necessary for the company to record zero profit would be the point on the x - axis where the line crosses the x-axis. This is because this would show the 0 profit mark.

This point on the graph is shown to be 87. This means that if the company increases the price of the wood chairs they sell, 87 times, they will experience zero profit.

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In the given problem, by first  standard deviation of the four measurements, calculating the the uncertainty in the mass of the object is 0.004582g.

To find the uncertainty in the mass of the object, we need to calculate the standard deviation of the four measurements.

First, we calculate the mean of the four measurements:

mean = (2.744g + 2.756g + 2.751g + 2.758g) / 4 = 2.75225g

Next, we calculate the variance of the measurements:

variance = [(2.744g - 2.75225g)^2 + (2.756g - 2.75225g)^2 + (2.751g - 2.75225g)^2 + (2.758g - 2.75225g)^2] / 3

       = 0.000021g^2

The variance is the average of the squared deviations from the mean, divided by the number of measurements minus 1. Note that we use 3 in the denominator, not 4, because we have already used one degree of freedom to calculate the mean.

Finally, we take the square root of the variance to obtain the standard deviation:

standard deviation = sqrt(variance) = 0.004582g

Therefore, the uncertainty in the mass of the object is 0.004582g. We can report the mass as: mass = 2.75225g ± 0.004582g

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A.y-intercept: 4

axis of symmetry: x=2

x-coordinate of the vertex: 2

B.x f(x)

  0   4

  1   1

  2   0

  3     1

  4   4

C. 5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.

A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.

According to the given information:

A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.

To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).

B. We can use the vertex to make a table of values:

x f(x)

0 4

1 1

2 0

3 1

4 4

C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.

  5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

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An equivalent expression by distributing the "-" sign outside the parentheses is -5w - 5.7x + 4.7.

An equation is a mathematical statement that shows the equality of two expressions, usually containing one or more variables. Equations typically include an equal sign (=) to indicate that the expressions on either side of the sign have the same value.

Equations can take many forms, from simple equations with only one variable, such as "x + 3 = 7," to more complex equations with multiple variables and exponents, such as "2x^2 + 5xy - 3y^2 = 0."

When we distribute the "-" sign outside the parentheses, we change the sign of every term inside the parentheses. So, we can write:

-5w - (5.7x - 4.7) = -5w - 5.7x + 4.7

Therefore, an equivalent expression by distributing the "-" sign outside the parentheses is -5w - 5.7x + 4.7.

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Answer:5w - 5.7x + 4.7

Step-by-step explanation:

A sample size of 1,098  would be needed to estimate the population mean with a 90% confidence level and a margin of error of 2, assuming the estimated population standard deviation is approximately σ = 40.3.

To determine the required sample size, we can use the following formula: n = (Z * σ / E)^2 where: n is sample size, Z is the z-score, σ is the estimated population standard deviation and E is the desired margin of error.

Note that 90% confidence corresponds to a z-score of 1.645.

Plugging in the given values, we get:

n = (1.645 * 40.3 / 2)^2

n = 33.14675^2

n = 1098.70703556

n ≈ 1,098.

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Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }

Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}

The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

We can start by standardizing the values using the z-score formula:

z = (x - μ) / σ

where:

x = the wait time in minutes

μ = the population mean (average wait time of 28 minutes)

σ = the population standard deviation (5.5 minutes)

For x = 10 minutes:

z = (10 - 28) / 5.5 = -3.27

For x = 20 minutes:

z = (20 - 28) / 5.5 = -1.45

Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:

0.0735 - 0.0006 = 0.0729

Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

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Answer:

a) The distance from Springton to Watworth is 200 km. Since George travels at a constant speed of 80 km per hour without stopping, it will take him 2 1/2 hours to arrive at Watworth. Since George leaves Springton at 10:00, he will arrive at Watworth at 12:30. So plot three points: the first at (10:00, 0), the second at (11:00, 80), and the third at (12:30, 200). Draw a line connecting the three points.

b) Karen arrived at Watworth at 13:50. George arrived at Watworth at 12:30, which is 1 hour and 20 minutes earlier than Karen's arrival.

The amount of time earlier than Karen that George arrived in Watworth was 1 hour 20 minutes earlier.

The distance between Watworth and Springton according to the graph is 200 km. This means that George covered this distance in:

= 200 / 80

= 2.5 hours

He arrived at :

= 10 + 2.5 hours

= 12 : 30 am

The difference was :

= 13: 50 arrival of Karen - 12 : 30

= 1 hour 20 minutes

To draw the graph, George's distance graph should pass start from ( 10:00, 0) and then pass ( 11:00, 80) to show he drove 80km in one hour. And then it should also pass ( 12:00, 160) to show the distance covered in 2 hours of 160 km.

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Predict:

Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).

If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.

If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.

Calculate:

See the table below.

Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)

100 20 2,000 2,000 0

120 18 2,160 1,800 360

140 16 2,240 1,600 640

160 14 2,240 1,400 840

180 12 2,160 1,200 960

200 10 2,000 1,000 1,000

Analyze:

Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.

As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.

The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.

Quadratic Regression:

a) Using the provided calculator link, we obtain the following values:

a = 0.05

b = -10

c = 500

r2 = 0.9

b) The standard form of the equation that represents the data is:

f(x) = 0.05x2 - 10x + 500

c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.

d) See graph below.

Graph of quadratic equation

Evaluate:

Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these

Answer: x = -1 and x = 9

Step-by-step explanation:

Lets solve this equation step by step

1. Simplify both sides of the equation

x^2 - 8x + 16 = 25

2. Subtract 25 from both sides

x^2 - 8x + 16 - 25 = 25 - 25

3. Factor the left side of the equation

(x + 1) (x - 9) = 0

4. Set the factors equal to zero

x + 1 = 0 or x - 9 = 0

Thus your answers are x = -1 and x = 9

You can check by inputting the values into the original equation

(-1 - 4)^2 = 25 and (9 - 4)^2 = 25

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.

Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.

Here we have

DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.

Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.

Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.

From the problem,

We can set up a system of equations based on the information given:

DeShawn's purchase: 1d + 12g = 80 ---- (1)

Ndiba's purchase: 5d + 2g = 52 --- (2)

We can solve this system of equations using substitution or elimination.

Here, we will use substitution:

Solving for d in terms of g from Deshawn's equation:

1d = 80 - 12g --- (3)

Substituting into Ndiba's equation:

=> 5(80 - 12g) + 2g = 52

=> 400 - 60g + 2g = 52

=> - 58g = - 348

=>  g = 6

From (3)

1d = 80 - 12(6)

1d = 80 - 72

d = 8

Therefore,

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

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Mathematically, the quantity of wire Liam needs for the top of the 8 sculptures he is making is 5¹/₃ yards.

The quantity of wire Liam needs for the top of the sculptures that he makes is determined using mathematical operations.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The total quantity of wire used = 10²/₃ yards.

The quantity of wire needed for each base = ²/₃ yards

The quantity of wire needed for each top = ²/₃ yards

The number of sculptures Liam is making = 8

²/₃ yards + ²/₃ yards = 1¹/₃ yards

8 x 1¹/₃ yards = 10²/₃ yards

8 x ²/₃ yards = 5¹/₃ yards

5¹/₃ yards x 2 = 10²/₃ yards

Therefore, the quantity of wire needed for the top will be 5¹/₃ yards.

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