Answer the equation 2.5p + 1 = 1.4p

Cinnamon tea costs $1.50 per pound, and spice tea costs $2.75 per pound.

To solve this problem, we can set up a system of equations based on the given information.

Let's denote the cost per pound of the cinnamon tea as C, and the cost per pound of the spice tea as S.

From the first mixture, we know that the total weight is 17 pounds, so we can write the equation:

12C + 5S = 28 ----(Equation 1)

From the second mixture, we know that the total weight is 20 pounds, so we can write the equation:

14C + 6S = 33 ----(Equation 2)

To solve this system of equations, we can use a method like substitution or elimination.

Let's use the elimination method to eliminate the variable C:

Multiply Equation 1 by 2 and Equation 2 by -3 to eliminate the C terms:

24C + 10S = 56 ----(Equation 3)

-42C - 18S = -99 ----(Equation 4)

Add Equation 3 and Equation 4:

-18C - 8S = -43

Solve for S:

8S = 43 - 18C

S = (43 - 18C)/8 ----(Equation 5)

Now substitute Equation 5 into Equation 1:

12C + 5((43 - 18C)/8) = 28

Multiply through by 8 to eliminate the fraction:

96C + 215 - 90C = 224

6C = 9

C = 9/6 = 1.5

Substitute the value of C back into Equation 5 to find S:

S = (43 - 18(1.5))/8 = 2.75

Therefore, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

In summary, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

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a. The distribution of X is X ~ N(68, 14).

b. The corresponding area to the right of 0.9286, which is approximately 0.1772.

c. The longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

a. The distribution of X is X ~ N(68, 14), where X represents the amount of time a person spends at Grover Hot Springs, 68 is the mean, and 14 is the standard deviation.

b. To find the probability that a randomly selected person stays longer than 81 minutes, we need to calculate the area under the normal curve to the right of 81.

Using the z-score formula: z = (x - μ) / σ, where x is the value (81), μ is the mean (68), and σ is the standard deviation (14).

Plugging in the values, we have z = (81 - 68) / 14 = 0.9286.

Using a standard normal distribution table or a calculator, we can find the corresponding area to the right of 0.9286, which is approximately 0.1772.

c. To find the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the value that corresponds to the lowest 8% of the distribution.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.4051.

Using the z-score formula, we can calculate the longest amount of time: x = μ + z [tex]\times[/tex] σ = 68 + (-1.4051) [tex]\times[/tex] 14 = 48.5654 minutes.

Therefore, the longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) is a measure of the spread of the data and represents the range between the first quartile (Q1) and the third quartile (Q3).

To find Q1 and Q3, we can use the z-score formula and the standard normal distribution table.

For Q1, we find the z-score corresponding to the 25th percentile, which is approximately -0.6745.

Using the formula Q1 = μ + z [tex]\times[/tex] σ, we have Q1 = 68 + (-0.6745) [tex]\times[/tex] 14 = 57.053.

Therefore, Q1 is approximately 57.053 minutes.

For Q3, we find the z-score corresponding to the 75th percentile, which is approximately 0.6745.

Using the formula Q3 = μ + z [tex]\times[/tex] σ, we have Q3 = 68 + (0.6745) [tex]\times[/tex] 14 = 78.426.

Therefore, Q3 is approximately 78.426 minutes.

Finally, we can calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 78.426 - 57.053 = 21.373 minutes.

Therefore, the Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = 3.

Hence the side lengths on the dilated image will be three times the side lengths on the original image.

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Answer:

Triangle????????????????? ¿

Step-by-step explanation:

since we are taking about true halves (I hope), both halves "weigh" the same, and a percentage in one has the same absolute value as in the other.

then the answer is just based on the mean value between both percentages :

x = percentage of the second half

70 = (78 + x)/2

140 = 78 + x

x = 140 - 78 = 62%

she needs at least 62% on the second half to pass the 70% minimum limit of the whole test.

Answer: The prime factorization of 15 is 3x5.

Answer:

Yes

Step-by-step explanation:

Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.

Answer:

C) -2/9

Step-by-step explanation:

[tex]\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}[/tex]

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

The mean score of Dora's bowling for this week would be = 161.

To calculate the mean score for the week the following would be carried out as follows;

The formula that is used to calculate mean = summation of the score/ number of scores recorded.

That is;

The weeks scores = 152+170+161

= 483/3

= 161

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The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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It is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

The statement "The unemployment rate in the U.S. tends to be lower than in other countries" is subjective and cannot be definitively categorized as true or false without further context and data analysis.

Unemployment rates vary across countries due to a multitude of factors, such as economic conditions, labor market policies, demographics, and government interventions. While it is true that at certain times the unemployment rate in the U.S. may be lower than in some other countries, it is not universally true in all circumstances.

Comparing unemployment rates between countries requires a comprehensive analysis of various factors and data points, including the specific time period, the methodology used for calculating unemployment, and the demographic and socio-economic characteristics of each country. Additionally, economic conditions can fluctuate over time, leading to variations in unemployment rates.

Therefore, it is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

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[tex]{\huge{\blue{\tt{Step\:by\:step\:solution}}}}[/tex]

4.1 To convert the mass of the self-raising flour to kg, we can divide the mass by 1000, since there are 1000 grams in a kilogram:

2 500 g ÷ 1000 = 2.5 kg

So the mass of the self-raising flour is 2.5 kg.

4.2 To determine the number of cups of bran flour needed to bake 400 g of rusks, we can use a proportion:

800 g of rusks requires 10 cups of bran flour

400 g of rusks requires x cups of bran flour

We can set up the proportion as:

800 g ÷ 10 cups = 400 g ÷ x cups

Cross-multiplying, we get:

800 g x cups = 10 cups x 400 g

Simplifying, we get:

x = 5 cups

So 5 cups of bran flour are needed to bake 400 g of rusks.

4.3 To write the ratio of raisins to butter in simplified form, we can divide both quantities by their greatest common factor. The greatest common factor of 200 g and 1 000 g is 200 g, so we can divide both by 200 g:

200 g ÷ 200 g = 1

1 000 g ÷ 200 g = 5

So the simplified ratio of raisins to butter is 1:5.

4.4 The rusks were placed in the oven to bake at 14:40. In words, this time is "twenty to three in the afternoon" (assuming that the time is given in a 12-hour clock format).

Answer:

-13/60

Step-by-step explanation:

trust me

The critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.

To find the critical value tₕ for a given confidence level and sample size, we can use a t-distribution table or a statistical software.

For a confidence level of 0.99, we need to determine the critical value tₕ such that the area under the t-distribution curve to the right of tₕ is equal to (1 - c) / 2. In this case, (1 - c) / 2 = (1 - 0.99) / 2 = 0.005.

Since the sample size is 22, we have n - 1 degrees of freedom, which is 22 - 1 = 21. We need to find the critical value tₕ with 21 degrees of freedom that corresponds to an area of 0.005 in the upper tail of the t-distribution.

Using a t-distribution table or a statistical software, we find that the critical value tₕ is approximately 2.831.

Therefore, the critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.

It is important to note that the critical value may vary slightly depending on the specific t-distribution table or statistical software used. However, the value obtained above is a reasonable approximation based on commonly used tables or software.

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a. The exact volume is V = π(9.5 ft)²(50 ft) = 225π ft³.

b. Rounding the answer to the nearest hundredth, the approximate volume of the silo is 706.50 ft³.

(a) The exact volume of the silo can be found using the formula for the volume of a cylinder, which is V = πr²h,

where r is the radius and h is the height.

Since the diameter is given, we can divide it by 2 to find the radius.

The radius of the silo is 19 ft / 2 = 9.5 ft.

The height of the silo is 50 ft.

Using these values, the exact volume of the silo is:

V = π(9.5 ft)²(50 ft) = 225π ft³.

The approximate volume can be found using the ALEKS calculator, which is not available in this text-based interface.

However, you can use the exact volume calculated above to manually approximate the volume to the nearest hundredth by evaluating the expression using the value of π as approximately 3.14 or 22/7.

(b) Approximate volume using the ALEKS calculator: [Please use an online calculator or a scientific calculator to approximate the value to the nearest hundredth].

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Answer:

19, 14, 38

Step-by-step explanation:

Let x, y, and z be each number respectively:

[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]

Therefore, the three numbers are 19, 14, and 38.

The profit percent made by the green grocer on the sale of the grapefruits is 50%.

To calculate the profit percent, we need to determine the profit made on the sale of the grapefruits.

The grocer buys a box of 150 grapefruits for $12, which means the cost of each grapefruit is $12/150 = $0.08.

The grocer sells each grapefruit for 12 cents, which is $0.12.

The profit made on each grapefruit is the selling price minus the cost price: $0.12 - $0.08 = $0.04.

Now, we can calculate the total profit by multiplying the profit per grapefruit by the number of grapefruits: $0.04 * 150 = $6.

To find the profit percent, we divide the profit by the cost price and multiply by 100: ($6 / $12) * 100 = 50%.

Therefore, the profit percent is 50%.

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The equations of the other line are:

BC: y = 2x

AD: y = 2x + 2

CD = -¹/₂x + 5.5

The formula for the equation of a line between two coordinates is expressed as:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Thus, for the lines we have:

BC has B(-2, 4) and C(-1, 6)

Thus:

BC: (y - 4)/(x - 2) = (6 - 4)/(-1 + 2)

BC: (y - 4)/(x - 2) =2

BC: y - 4 = 2x - 4

BC: y = 2x

AD has  A(2,2) and D(3, 4)

Thus:

AD: (y - 2)/(x - 2) = (4 - 2)/(3 - 2)

AD: y - 2 = 2x - 4

AD: y = 2x + 2

CD has C(-1, 6) and D(3, 4)

CD: (y - 6)/(x + 1) = (4 - 6)/4

CD: y - 6 = -¹/₂(x + 1)

CD = -¹/₂x + 5.5

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The equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.

To find the equation of a line perpendicular to a line with a slope of 1/13 and passing through the point (-1, 3), we need to determine the slope of the perpendicular line.

The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the given slope. The negative reciprocal of 1/13 is -13/1, or simply -13.

Now that we have the slope (-13) and a point (-1, 3) that the line passes through, we can use the point-slope form of a linear equation to find the equation of the perpendicular line.

The point-slope form is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point and m is the slope.

Substituting the values (-1, 3) and -13 into the point-slope form, we get:

y - 3 = -13(x - (-1))

Simplifying:

y - 3 = -13(x + 1)

Expanding the equation:

y - 3 = -13x - 13

To convert the equation to slope-intercept form (y = mx + b), we can isolate y:

y = -13x - 13 + 3

y = -13x - 10

Therefore, the equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.

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Answer:

n = -1/8

Step-by-step explanation:

n + 3/4 = 5/8

n = 5/8 - 3/4

n = 5/8 - 6/8

n = -1/8

So, n = -1/8

The pattern in the residual plot indicates the following about the type of model: C. The pattern is random, indicating a good fit for a linear model.

In Mathematics and Geometry, a residual plot is sometimes referred to as scatter plot and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association or correlation (relationship) between the data set.

In Mathematics, a residual value is a difference between the measured (given or observed) value from a residual plot (scatter plot) and the predicted value from a residual plot (scatter plot).

By critically observing the residual plot which shows a relationship between the residuals and carbs in grams, we can logically deduce that a linear model is the most appropriate because there isn't a clear pattern between the data points i.e a random pattern.

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Complete Question:

What does the pattern in the residual plot indicate about the type of model?

A. The pattern is random, indicating a good fit for a nonlinear model.

B. The pattern shows the points are far from the zero line, indicating a good fit for a linear model.

C. The pattern is random, indicating a good fit for a linear model.

D. The pattern shows the points are far from the zero line, indicating a good fit for a nonlinear model.

E. The pattern is random, indicating that the model is unable to be determined.

Answer:

[tex]9\frac{1}{2} cm^2[/tex]

Step-by-step explanation:

The area of the shaded region = area of triangle - area of the rectangle

Base, b of the triangle = 3 + 4 = 7 cm

Ar of triangle = base*height/2

= 7*5/2

= 35/2

[tex]=17\frac{1}{2} cm^2[/tex]

ar of rectangle = length *breadth

= 4*2

= 8 cm²

The area of the shaded region = area of triangle - area of the rectangle

[tex]=17\frac{1}{2} - 8\\\\=9\frac{1}{2} cm^2[/tex]

Answer:

16.5 cm²

Step-by-step explanation:

The shaded area is the area of the triangle minus the area of the rectangle.

A = bh/2 - LW

For the triangle,

b = 3 cm + 4 cm = 7 cm

h = 2 cm + 5 cm = 7 cm

For the rectangle,

L = 4 cm

W = 2 cm

A = bh/2 - LW

A = (7 cm)(7 cm)/2 - (4 cm)(2 cm)

A = 24.5 cm² - 8 cm²

A = 16.5 cm²

The descriptions and the cross-sectional images formed are as follows:

1. Description: a vertical plane that cuts through the top vertex perpendicular to the base

Cross-sectional image: The rectangle

2.  Description: A horizontal plane that cuts through the pyramid parallel to the base

Cross-sectional image: A triangle

3. Description: A vertical plane that cuts through the base and two opposite lateral faces.

Cross-sectional image: The square

To determine the cross-sectional images of the shapes, we will start by representing the shapes and the results obtained when the descriptions are applied to them. For the first one, running a vertical plane through the square pyramid will give us a rectangle.

Next, cutting a horizontal plane through the pyramid parallel to the base will give a triangle. Finally, running a vertical plane through the base and two lateral faces will give a square.

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Answer:  Choice 3.

The number of people purchasing coffee each day in a coffee shop

Reason:

It's not possible to have a decimal or fractional amount of people. So we select the value from the set {0,1,2,3,4,...}

On the other hand, it is possible to have a decimal temperature like 98.6 degrees, which means we rule out choice 1. Choices 2, 4, and 5 are a similar story.

Answer:

180 marbles in a 7-pound bag.

f(0) = -3

I believe, since the graph has a closed circle/point at (0,-3), f(0) should equal -3. Also, the graph 3x-3 has a domain of x>=0.

However, in terms of limits, the limit approaching x-->0 does not exist since the left and right limits do not equal one another.

Hope this helps.