How many solutions are there to the equation x1 x2 x3 x4 x5 21?

Answer:

S₃₆ = 3402

Step-by-step explanation:

there is a common difference between term in the sequence , that is

12 - 7 = 17 - 12 = 5

this indicates the sequence is arithmetic with sum to n terms

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 7 and d = 5 , then

S₃₆ = \(\frac{36}{2}\) [ (2 × 7) + (35 × 5) ]

     = 18( 14 + 175)

     = 18 × 189

     = 3402

Answer:

x = 26

Step-by-step explanation:

These angles are equal b/c of alt exterior angles

9x + 18 = 10x - 8

9x - 10x = -8 - 18

-x = -26

x = 26

Answer:

(0.63789 ; 1.38211 ) is the 98% confidence interval for the mean waste recycled per person per day for the population of texas and  Tcritical = 3.143

In a random sample of 7 residents of the state of texas ,the mean waste recycled per person per day was 1.01 pounds and standard deviation 0.29 pounds

we have to find the 98% confidence interval for the mean waste recycled per person per day for the population of texas

Mean, xbar = 1.01

Standard deviation, s = 0.29

Sample size, n = 7

Confidence interval  : xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Degree of freedom (df) = n - 1 = 7 - 1 = 6

Hence Tcritical = 3.143

Margin of Error = 3.143 * 0.29/sqrt(6)

Margin of error = 0.37211

Lower boundary = (1.01 - 0.37211) = 0.63789

Upper boundary = (1.01 + 0.37211) = 1.38211

(0.63789 ; 1.38211 )

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The mean of the time taken by a mechanic to rebuild the transmission of 2005 Chevrolet Cavalie μ = 8.4 hours The standard deviation of the time taken by a mechanic to rebuild the transmission of 2005 Chevrolet Cavalier, σ = 1.8 hours.

The sample size, n = 40 We have to find the probability that their mean rebuild time exceeds 8.7 hours. We know that the sampling distribution of the sample means is normally distributed with the following mean and standard deviation.

We have to find the probability that the sample mean rebuild time exceeds 8.7 hours or Now we need to standardize the sample mean using the formula can be found using the z-score table or a calculator. Therefore, the probability that the mean rebuild time of 40 mechanics exceeds 8.7 hours is 0.1489.

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1. Variable manufacturing overhead rate variance

The formula Actual Hours × (Actual Rate - Standard Rate) is used to calculate the variable manufacturing overhead rate variance. This variance measures the difference between the actual variable manufacturing overhead cost incurred and the standard variable manufacturing overhead cost that should have been incurred, based on the standard rate per hour.

Variable manufacturing overhead rate variance = Actual Hours × (Actual Rate - Standard Rate)

The variable manufacturing overhead rate variance provides insight into how efficiently a company is utilizing its variable manufacturing overhead resources in terms of the rate per hour. A positive variance indicates that the actual rate paid per hour for variable manufacturing overhead was higher than the standard rate, resulting in higher costs. On the other hand, a negative variance suggests that the actual rate paid per hour was lower than the standard rate, leading to cost savings.

By analyzing this variance, management can identify areas where the company may be overspending or underspending on variable manufacturing overhead and take corrective actions accordingly, such as renegotiating supplier contracts or optimizing resource allocation.

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Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

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the equation of the tangent at (0,2) to the circle with equation (x + 2)² + (y + 1)² = 13 is y = (-2/3)x + 2.

What steps I followed?

o find the equation of the tangent at the point (0,2) to the circle with equation (x + 2)² + (y + 1)² = 13, we can follow these steps:

Differentiate the equation of the circle implicitly to find the derivative of y with respect to x:

2(x + 2) + 2(y + 1)dy/dx = 0

dy/dx = - (x + 2)/(y + 1)

Evaluate the derivative at the point (0,2) to find the slope of the tangent:

dy/dx = - (0 + 2)/(2 + 1) = -2/3

Use the point-slope form of a linear equation to find the equation of the tangent:

y - 2 = (-2/3)(x - 0)

y = (-2/3)x + 2

Therefore, the equation of the tangent at (0,2) to the circle with equation (x + 2)² + (y + 1)² = 13 is y = (-2/3)x + 2.

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A)

   a

———=8       :a=64

5+3  

Steps:Multiply both sides by 8

     ———-=8  ·   8

      5+3

B)

3b/7 - 1 = 5

Add 1 in both sides

3b/7 - 1 + 1 = 5 + 1

3b/7 = 6

Multiply both sides by 7 and then divide by 3.

3b/7 . 7/3 = 6 . 7/3

b = 2.7

b = 14

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The length of the third side is \(≈15.7\)

Note:

Phitagors theorem:

\(c^{2}=a^{2}+b^{2}\)

\(c: hypotenuse\)

\(a: altitude\)

\(b: base\)

1) Using Phitagors theorem

\(c^{2}=a^{2}+b^{2}\)

\(c^{2}=14^{2}+7^{2}\)

2) Calculate

\(c^{2}=245\)

3) Take the square root of both sides of the equation

\(\sqrt {c^{2}}=\sqrt{245}\)

\(c=\sqrt{245}\)

\(c≈15.7\)

Answer:

(A) Bus 47, with a median of 16.

Step-by-step explanation:

To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since the data sets are small and discrete, we can use either the median or the mean as a measure of center.

For Bus 47, the median is the middle value, which is 16.For Bus 14, the median is also the middle value, which is 14.

Comparing the medians, we can see that Bus 47 has a higher median, which suggests that it typically has a faster travel time than Bus 14.

Therefore, the answer is (A) Bus 47, with a median of 16.

1/10 will be the result of the function j(7).

The input-output pair (-10,7) is on function h

The input-output pair 7,-10) is on function j

An inverse function is described as a function where two variables affect one another and the value of an independent variable is used to solve the function.

h and j are inverses

x=-10 so h(x)=7

h(-10)=7

H is inverse of j

h(x)=j-1(x)

7=j-1(x)

j(7)=x

Hence j(7)=-10

F(x) = 2x

y = 2x

The inverse function is calculated as:-

x = 2y

y = x / 2

F'(x) = x / 2

Given that Functions hand j are inverses. For x = -10, the value of h(x), or h (-10) = 7, is 7.

As, h(x) is 7

The input-output pair (-10,7) is on function h

The input-output pair (7,-10) is on function j

Using the supplied data, the value of the function j(7) will be 1/10.

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Answer:

D

Step-by-step explanation:

in this case, because it is being dilated by a factor of 2 this means that figure A´B´C´ will be double the size of its pre-image ABC.

each side will now be its double which means:

side A´C´= 10

side B´C´= 6

and side A´B´= 8

since the figure is only increasing its sides the angles of the right triangle remain the same.

<A= 37 degrees

The length of A'B' is, 8 units and the measure of angle A' is, 37 degree.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

ΔABC is dilated by a factor of 2 to produce ΔA'B'C'.

Now, When the triangle undergoes dilation, the length of its sides gets multiplied by 2 (dilation factor) but the angles remain the same ( since, the shape has to remain same).

Thus, The length of A'B' is,

= 4 x 2

= 8

And, the measure of angle A' is, 37 degree.

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Every pair of real numbers in B can be mapped to by f(x) for some pair (a,b) in A, which means the function is onto. As the function is one-to-one and onto, it is a bijection.

(a) The function f(x)=x-1 from A=B=Z is one-to-one, not onto and not a bijection.

The given function f(x) subtracts 1 from each element of the set A. Since each element of A has only one unique predecessor in A, the function is one-to-one. However, there exists no element in B that can be mapped to by f(x) for any negative integer in A, which means the function is not onto. As the function is not onto, it is not a bijection.

(b) The function f(x)=|x| from A=R and B={x:x∈R,x≥0} is not one-to-one, not onto, and not a bijection.

The absolute value function f(x) maps every element of A to a non-negative value in B. Since both positive and negative numbers in A are mapped to the same non-negative value in B, the function is not one-to-one. Additionally, there are no negative values in B that can be mapped to from A, which means the function is not onto. As the function is not one-to-one and not onto, it is not a bijection.

(c) The function f((a,b))=a from A=R×R and B=R is not one-to-one, onto, and not a bijection.

The function f((a,b))=a maps each element of A to its first component. Since different pairs in A can have the same first component, the function is not one-to-one. However, every real number in B can be mapped to by f(x) for some element (a,b) in A, which means the function is onto. As the function is not one-to-one and onto, it is not a bijection.

(d) The function f((a,b))=(a+b,a−b) from A=B=R×R is one-to-one, onto, and a bijection.

The function f((a,b))=(a+b,a−b) maps each element of A to a unique element in B. Since each pair (a,b) in A corresponds to a unique pair of values in B, the function is one-to-one. Additionally, every pair of real numbers in B can be mapped to by f(x) for some pair (a,b) in A, which means the function is onto. As the function is one-to-one and onto, it is a bijection.

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P(A and B) = P(A) × P(B) is the formula used to assess if two events are independent (B).

P(A) is the chance that event A will occur.

The chance that event B will occur is marked as P(B).

If the chance of both occurrences happening at the same time, P (A and B), equals the product of the individual probabilities of each event, P(A) x P(B), the events are called independent.

If, on the other hand, the chance of both occurrences occurring simultaneously is less than the product of the individual probabilities of each event, the events are deemed dependent.

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Answer:

$46.272

Step-by-step explanation:

Answer:

Step-by-step explanation:

The bumblebee flutters its wings more times in 1 minute, as it flutters its wings 7,800 times in one minute, whereas the hummingbird flaps its wings 80 times in one second, which translates to 4,800 times in one minute.

To understand this calculation in more detail, we can use unit conversions and multiplication. Since the hummingbird's wing flaps are given in seconds and the bumblebee's wing flutters are given in minutes,

we convert the hummingbird's wing flaps from seconds to minutes by multiplying by 60. We then compare the total number of wing flaps for each animal and find that the bumblebee flutters its wings more times in one minute than the hummingbird flaps its wings.

This is due to the bumblebee's higher frequency of wing movement, which enables it to achieve more wing flutters in a given amount of time.

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The concentration of the drug after the 3rd dose is given by the formula C3 = d(1+e^(-0.2T)+e^(-0.4T) + e^(-0.6T))

The given differential equation is

dC / dt = -kC

where C is the concentration of the drug, and k is a constant representing the rate of decay of the drug.

The concentration of the drug immediately after the nth dose is given by

Cn = d(1+e^(-0.2T) + e^(-0.4T)+...+e^(-0.2(n-1)T))

where d is the dose given, and T is the time between doses.

To find the concentration after the 3rd dose, we can use the above formula with n = 3

C3 = d(1 + e^(-0.2T) + e^(-0.4T) + e^(-0.6T))

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The approximate ratio of the diameter of the Sun to the diameter of Mars is 200. This means that the diameter of the Sun is approximately 200 times larger than the diameter of Mars.

The approximate ratio of the diameter of the Sun to the diameter of Mars can be found by dividing the diameter of the Sun by the diameter of Mars.

Given that the diameter of the Sun is about 1.4x10^6 km and the diameter of Mars is about 7000 km, we can calculate the ratio as follows:

1.4x10^6 km ÷ 7000 km

To divide these values, we can simplify the equation by canceling out the common factor of 1000:

(1.4x10^6 ÷ 1000) km ÷ (7000 ÷ 1000) km

Simplifying further, we have:

1.4x10^3 km ÷ 7 km

Dividing these values gives us:

200 km

Therefore, the approximate ratio of the diameter of the Sun to the diameter of Mars is 200. This means that the diameter of the Sun is approximately 200 times larger than the diameter of Mars.

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The 95% confidence interval for the difference in mean heights of professional football and basketball players is (-0.517, -0.023) feet.

To find a 95% confidence interval for the difference in mean heights between professional football and basketball players, we can use the formula for the confidence interval:

CI = (X1 - X2) ± t * sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

X1 and X2 are the sample means (6.18 feet for football players and 6.45 feet for basketball players).

s1 and s2 are the sample standard deviations (0.37 feet for football players and 0.31 feet for basketball players).

n1 and n2 are the sample sizes (45 for football players and 40 for basketball players).

t is the critical value for a 95% confidence level.

First, we need to calculate the critical value t. Since the sample sizes are relatively large, we can use the Z-distribution instead of the t-distribution. For a 95% confidence level, the critical value is approximately 1.96.

Now we can calculate the confidence interval:

CI = (6.18 - 6.45) ± 1.96 * sqrt((0.37^2 / 45) + (0.31^2 / 40))

CI = -0.27 ± 1.96 * sqrt(0.0082 + 0.007675)

CI = -0.27 ± 1.96 * sqrt(0.015875)

CI = -0.27 ± 1.96 * 0.126

CI = -0.27 ± 0.247

CI = (-0.517, -0.023)

The 95% confidence interval for the difference in mean heights of professional football and basketball players is (-0.517, -0.023) feet.

Since the confidence interval includes negative values, it suggests that the average height of football players tends to be shorter than the average height of basketball players. However, it's important to note that this conclusion is based on the sample data and there is still some uncertainty due to sampling variability.

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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Salik and Maya are discussing a project that examines the relationship between the number of siblings someone has and their household income. Maya predicts that those with more siblings will have a higher household income. Salik questions whether the number of siblings is a categorical variable since it is a whole number. Our response can be : "In order to conduct this project, we need to choose two quantitative variables, which are variables that can be measured and expressed as numbers. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value."

The number of siblings is a quantitative variable because it can be expressed as a whole number. Household income is also a quantitative variable because it can be measured and expressed as a numerical value. Categorical variables are variables that can be divided into distinct categories or groups, such as gender, race, or occupation. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value.

To examine the relationship between the number of siblings and household income, Maya and Salik could use statistics to analyze their data. They could calculate descriptive statistics such as the mean and standard deviation for each variable, as well as the correlation coefficient to determine the strength and direction of the relationship between the two variables. They could also use probability theory to make predictions about the likelihood of certain outcomes, such as the probability that someone with more siblings will have a higher household income.

The complete question is:

Our classmates, Maya and Salik, are talking about the variables they want to study and how they plan to collect their samples. Here is part of their conversation. Respond in the places that say “your response.”

Double-check that both of their variables are quantitative.

Maya: I want to look at the relationship between the number of siblings someone has and the household income. I predict that those with more siblings have a higher household income.

Salik: We need two quantitative variables for this project. Wouldn’t number of siblings be categorical since it is whole numbers?

Your response:.........

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Answer:

1175/954 there your answer

Answer:

Step-by-step explanation:

here you go mate'

step 1

6+(-6)  equation

step 2

6+(– 6)  simplify the signs

6-6

step 3

6-6  subtract

answer

0

mind if i get brainliest

Therefοre , the sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be  40 < 42.

Tο accοmplish the οbjective, οne may use unitary methοd widely used cοnvenience, already existing variables, οr all significant cοmpοnents frοm the initial Bishοp custοmizable questiοn. If sο, there's will be a secοnd οppοrtunity tο interact with the item. Otherwise, every essential cοmpοnent that cοntributes tο the prοοf οutcοme οf an expressiοn will be lοst.

Here,

This statement can be cοnverted intο an inequality, and the expressiοn οn the left side οf the inequality can be made simpler by using the sequence οf οperatiοns:

=> 9 * 2² = 9 × 4 = 36

40 is four more than 36.

The phrase thus reads:

=> 40 < 7 × 6

which is equivalent to:

=> 40 < 42

Since this is correct, the inequality is as follows:

=> 40 < 42

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Complete question:

Convert the sentence into a mathematical expression and solve.

Four more than the product of 9 and 2 squared is less than the product of 7 and 6.

Answer:

12/40

Step-by-step explanation:

12/40=3/10

It is safe to say that it is nearly impossible for devices to be produced at zero production costs.

It is highly unlikely that any devices will be produced if the production cost is R0,00 (assuming R refers to South African Rand). There are various factors involved in the production of devices, including the cost of materials and labor, research and development, marketing, and distribution costs.

Even if we disregard the cost of materials and labor, there are still other production expenses that cannot be escaped, like facility costs, machinery, and intellectual property rights. Furthermore, marketing and distribution costs add considerable expenses.

Therefore, it is safe to say that it is nearly impossible for devices to be produced at zero production costs. Even if a device could somehow be developed without incurring any initial costs, other costs incurred during the device's production, such as power costs, facility rent, and salaries, would have to be covered. Therefore the reality is that there is always a cost involved in producing any device, and that cost must be factored in for any real-world production.

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The expressions that are equivalent to 5% of 60 are  5/100 * 60, 0.05 * 60 and 1/20 * 60

The expression is given as:

5% of 60

Express as fraction and decimal

5% of 60 = 5/100 * 60

5% of 60 = 0.05 * 60

This gives

5% of 60 = 1/20 * 60

Hence, the expressions that are equivalent to 5% of 60 are  5/100 * 60, 0.05 * 60 and 1/20 * 60

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