-6x+6.4y=112 and 6x+2.1y=-27
solve for x and y in an ordered pair

Answer:

Part A: Is 7.85

Part B: 672 rotations.

Step-by-step explanation:

Part A: We can use either formula C=pi x d or C= 2 x Pi x r. All you have to do is multiply 3.14 by 2.5 which would equal 7.85.

Part B: For this, all we do is divide 5,280 by the answer of the circumference which is 7.85 to get 672. You would have to set this up as a fraction where 5,280 ft goes on top and 7.85 ft per rotation at the bottom.

Pi equals 3.14

The r represents the radius

D represents diameter

C is for circumference.

Hope this helps.

Answer:

There are 21 skateboards and bicycles in the shop.

A bicycle has two wheels, and a skateboard has four wheels

54 new wheels are needed

Number of bicycles = 15

Number of skateboards = 6

Step-by-step explanation:

Number of bicycles and skateboards = 21

Number of new wheels ordered = 54

Number of wheels in a bicycle = 2

Number of wheels in a skateboard = 4

Number of skateboards and bicycles in shop?

Let number of bicycles = b

Number of skateboards = s

b + s = 21 - - - (1)

(2*b) + (4*s) = 54

2b + 4s = 54 - - - - - - (2)

From (1)

b = 21 - s

2(21 - s) + 4s = 54

42 - 2s + 4s = 54

42 + 2s = 54

2s = 54 - 42

2s = 12

s = 6

From : b = 21 - s

b = 21 - 6

b = 15

Number of bicycles = 15

Number of skateboards = 6

The 90% confidence interval for the proportion of all adults in the United States who own an e-reader is 0.32 ± 1.645 * √(0.32 * 0.68 / 1,005). This corresponds to option (B) in your list of choices.

The appropriate formula for calculating the confidence interval for a proportion is:

sample proportion ± z*standard error

where z is the z-score corresponding to the desired level of confidence (90% in this case) and the standard error is:

sqrt((sample proportion*(1-sample proportion))/sample size)

Plugging in the values given in the question, we get:

sample proportion = 0.32
sample size = 1005
z-score for 90% confidence = 1.645 (option B)
standard error = sqrt((0.32*(1-0.32))/1005) = 0.015

So the appropriate 90% confidence interval is:

0.32 ± 1.645(0.015)
= 0.32 ± 0.025
= (0.295, 0.345)

Therefore, the correct answer is option B: 0.32 +1.645,10.3270.68

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Answer:

6 is the GCF / 6(4+6)

Step-by-step explanation:

You should know your multiples up to 10, so then do some mental math and think about what number could go in each example:

Try 2: 2,4,6,8,10,12,14,16,18,20,24... except at the end we know there is most likely a greater GCF because two even numbers still remain in the parentheses.

This should be pretty fast since you should realize that three wouldnt work and same with five.

Until you see six

6,12,18,24,30,36

Answer:3.6

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

Distance = √(x2 - x1)² + (y2 - y1)²

√(5 - 3)² + (-2 - 1)²

√13 = 3.605

good luck, i hope this helps :)

Answer:

i got 15.1

Step-by-step explanation:

The marked price of the watch is Rs. 2613.6 after adding the 10% sales tax.

Let the marked price of the watch as "M".

Discount = 20%

So, the discounted price after applying the 20% discount will be

(M - 0.2M) = Rs. 2376.

0.8M = Rs. 2376.

As, Sales tax = 10%

So, the final price

=  (Rs. 2376 + 10% of Rs. 2376).

=2376 + 0.1 x 2376

= 2376 + 237.6

= 2613.6

Therefore, the marked price (M) of the watch is Rs. 2613.6.

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Answer:

Step-by-step explanation:

Pedometer

Answer:

no

Step-by-step explanation:

the triangle rule is the sum of any two sides of a triangle MUST be larger than the third, in this case 3+8 > 3, but 3+3 < 8 so it cannot be a triangle

Answer:

An isosceles triangle has two side lengths that are the same and one side length that is different. Soo... basically to sum it up in a word, yep.

Step-by-step explanation:

An convenient to make measurements in centimeters and grams  summary the conversions to 5t units are (a) 0.78 cm ≈ 0.078 5t units,(b) 126.2 s ≈ 126.2 5t units,(c) 42.4 cm³≈ 0.0424 t³,(d) 75.7 g/cm³≈ 75.7 t²

To convert the given measurements to 5t units,  to establish the conversion factors between centimeters/grams and 5t units.

1 t = 10 cm (since 1 meter = 100 cm and 1 meter = 10 t)

1 t = 1 kg (since 1 kg = 1000 g and 1 kg = 1 t)

Now, let's convert each measurement to 5t units:

(a) 0.78 cm:

To convert from centimeters to 5t units, we divide by 10 since 1 t = 10 cm.

0.78 cm / 10 = 0.078 t

Therefore, 0.78 cm is approximately 0.078 5t units.

(b) 126.2 s:

Since no conversion factor is given, we assume that 1 second remains the same in both systems. Thus, 126.2 s remains the same in 5t units.

Therefore, 126.2 s is approximately 126.2 5t units.

(c) 42.4 cm^3:

To convert from cm³to 5t units, we need to consider the conversion for volume, which is (1 t)³ = 1 t³= 1000 cm³

42.4 cm³ / 1000 = 0.0424 t³

Therefore, 42.4 cm³is approximately 0.0424 t³ in 5t units.

(d) 75.7 g/cm³:

To convert from g/cm³ to 5t units, we need to consider both the conversion for mass and volume. We have 1 g = 1/1000 kg = 1/1000 t and 1 cm^3 = 1/1000 t³

75.7 g/cm³ × (1/1000 t / 1/1000 t³) = 75.7 t / t³ = 75.7 t²

Therefore, 75.7 g/cm³ is approximately 75.7 t² in 5t units.

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Answer:

Sarah has greatest percentage of heads

Answer:

Sarah.

Alice had 75 percent

Mary had 80 percent

Ellen had 60 percent

while Sarah got 85 percent

Step-by-step explanation:

Mary 8 out of 10 is technically 8/10 and fractions are division problems so 8/10 is 0.8 times 10 is 80 same goes for the rest of them, divide then multiply by 10

A measure of relative fit for a simple regression line is called the r² or coefficient of determination.

A regression line, or line of best fit, is a straight line used to model the relationship between two variables in a data set. It is drawn through the data points to minimize the distance between the line and the points, representing the best fit. The line's equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the value of y when x is equal to 0. The line is often used to predict the dependent variable based on the independent variable, and the accuracy of the predictions depends on how well the line fits the data.

The coefficient of determination, also known as r², is a statistical measure used to determine the relative fit of a simple regression line. This measure represents the proportion of variance in the dependent variable that can be predicted by the independent variable. The calculation involves squaring the correlation coefficient (r) between the two variables. The resulting value of r² ranges from 0 to 1, where 0 indicates that the independent variable has no explanatory power over the dependent variable, while 1 implies that the independent variable explains all the variability in the dependent variable.

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The value which shows the true solution to the given logarithmic equation is 1.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The given logarithmic equation is,

\(\rm log_{2} (x) + log_{2} (x +7) = 3.\)

Use the addition property of log in the above expression.

\(\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0\)

Solve the quadratic equation we get,

\((x+8)(x-1)=0\)

x = -8, 1

Here, the logarithmic function is defined only for positive real numbers as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

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Answer:X=1

Step-by-step explanation:b on edge

a. Ashley would need to invest approximately $49,302.55 in one lump sum today. b. Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years. c. Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

a. To determine how much Ashley would need to invest today, in one lump sum, to end up with $70,000 in 6 years, we can use the future value formula:

Future Value (FV) = Present Value (PV) * (1 + interest rate)^time

In this case, FV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values into the formula, we can solve for PV:

$70,000 = PV * \((1 + 0.07)^6\)

PV = $70,000 /\((1.07)^6\)

PV ≈ $49,302.55

Therefore, Ashley would need to invest approximately $49,302.55 in one lump sum today.

b. If Ashley is starting from scratch, we need to calculate how much she would have to put away annually to accumulate the needed capital in 6 years. This can be calculated using the present value of an ordinary annuity formula:

PV = Annual Payment * [(1 - (1 + interest rate)^(-time)) / interest rate]

In this case, PV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values, we can solve for the annual payment:

$70,000 = Annual Payment *\([(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $9,167.42

Therefore, Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years.

c. If Ashley already has $20,000 saved, we can subtract this amount from the required capital and calculate the annual payment for the remaining amount:

Remaining Amount = Required Capital - Initial Savings

Remaining Amount = $70,000 - $20,000 = $50,000

Using the same formula as in part b, we can calculate the annual payment:

$50,000 = Annual Payment\(* [(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $6,111.57

Therefore, if Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

d. Ashley can use an investment plan to help reach her objective by following these steps:

- Set a specific financial goal, such as accumulating $70,000 in 6 years.

- Determine the required investment amount, whether it's a lump sum or an annual payment.

- Consider her risk tolerance and investment options. Since she estimates a 7% return, she can explore various investment vehicles like stocks, bonds, mutual funds, or other investment instruments.

- Develop an investment plan that aligns with her financial goals and risk tolerance. This plan may involve diversifying her investments, considering different time horizons, and regularly monitoring her progress.

- Continuously track the performance of her investments and make adjustments if needed.

- Stay disciplined and committed to her investment plan, making regular contributions or adjusting investments as necessary to reach her desired capital.

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Answer:

x = 5, y = 8, z = -3

Step-by-step explanation:

Opposite sides of a parallelogram are congruent so to find x:

x + 7 = 3x - 3

-2x = -10

x = 5

To find y:

y + 2 = 2y - 6

-y = -8

y = 8

Therefore, z = x - y = 5 - 8 = -3.

(a) Therefore, the range of possible values for "x" is 1 to 5. (b) Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.  Therefore, there are 31 different ways this can happen

To find the number of different ways this can happen, we can consider the number of internet friends each person can have. Since each person has the same number of internet friends, let's denote that number as "x". We can then create equations based on the given information:

1. Some, but not all, of them are internet friends with each other: This means that at least two people are internet friends with each other, but not everyone is friends with each other. This implies that the minimum number of internet friends any person can have is 1, and the maximum number is 5 (since there are 6 people in total).

Therefore, the range of possible values for "x" is 1 to 5.

2. None of them has an internet friend outside this group: This means that each person's internet friends must be within this group of 6 people. So, the number of internet friends each person can have is limited to the remaining 5 people.

To find the number of different ways this can happen, we need to sum up the possible values of "x" and calculate the corresponding combinations. For "x = 1", we choose 1 person out of 5 remaining people, giving us C(5, 1) = 5. For "x = 2", we choose 2 people out of 5 remaining people, giving us C(5, 2) = 10.

Similarly, for "x = 3", "x = 4", and "x = 5", we have C(5, 3) = 10, C(5, 4) = 5, and C(5, 5) = 1 respectively. Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.

Therefore, there are 31 different ways this can happen

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The Fermi energy will be at the edge of the second band at zero temperature.

(a) Band structure is the diagrammatic representation of the dispersion of energies of the electronic states in the crystal as a function of the momentum, and their relative occupancies, under an applied electric field. It determines whether a solid is a metal, an insulator, or a semiconductor. For this reason, it is frequently used to examine the optical and electronic properties of a solid in condensed matter physics. The periodicity of the lattice is represented by the Brillouin zone. Using what we learned in class, sketch the band structure in the First Brillouin Zone (FBZ) for A1=10meV, A2=20meV, and A3=30meV, including at least the first three lowest bands, being sure to label the magnitude of the energy gaps as well as their positions in reciprocal space.

Below is the image of the first three energy bands in the FBZ for A1 = 10meV, A2=20meV, and A3=30meV.

(b) The location of the Fermi energy is determined by the electron concentration in the crystal. Fermi energy is the energy level at which the probability of occupying the state is one-half at 0 Kelvin.

Therefore, the Fermi energy is related to the valence and conduction band energies and the concentration of electrons. If the crystal has two electrons for each lattice site, the Fermi energy at zero temperature will be midway between the conduction and valence band edge. The Fermi energy level will be in the gap between the first and second bands, at the halfway point between the conduction band edge and the valence band edge. On the other hand, if the crystal has three electrons per lattice site, the Fermi energy will be at the edge of the second band at zero temperature.

(c) In a 1D crystal with a lattice spacing a=5 nm, U(x) is a periodic crystal potential that has the following form:

U(x)=A1sin(2πx/a)+A2sin(4πx/a)+A3sin(2πx/a)cos(2πx/a).

We are now told that A2 can be externally tuned. To create just one energy gap in the electronic band structure, A2 must be equal to zero. The energy gap would be centered at (π/a,0), where the band minimum for the second band is located.

If there are four electrons per lattice, the Fermi energy level will be in the second band, and the value of the Fermi energy level can be computed using the graph from part a.

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Answer:

1^-100

Step-by-step explanation:

in the negative powers the negative sign stands for the fraction line symbol and the power stands for the bottom number.

Answer:

54734431

Step-by-step explanation:

54734431

To evaluate the integral ∫(1 to 0) y/e^(3y) dy, we can use integration by substitution.

Let u = 3y. Then, du = 3dy.

When y = 1, u = 3(1) = 3.

When y = 0, u = 3(0) = 0.

The limits of integration can be expressed in terms of u as well.

Now, let's rewrite the integral in terms of u:

∫(1 to 0) y/e^(3y) dy = ∫(3 to 0) (1/3)e^(-u) du.

Next, we can simplify the integral:

∫(3 to 0) (1/3)e^(-u) du = (1/3) ∫(3 to 0) e^(-u) du.

Using the fundamental theorem of calculus, we can integrate e^(-u):

(1/3) ∫(3 to 0) e^(-u) du = (1/3) [-e^(-u)] from 3 to 0.

Now, let's substitute the limits of integration:

(1/3) [-e^(-0) - (-e^(-3))].

Simplifying further:

(1/3) [-1 + e^(-3)].

Therefore, the value of the integral ∫(1 to 0) y/e^(3y) dy is (1/3)[-1 + e^(-3)].

To evaluate the integral ∫(1 to 0) y/e^(3y) dy, we can use integration by substitution.

Let u = 3y. Then, du = 3dy.

When y = 1, u = 3(1) = 3.

When y = 0, u = 3(0) = 0.

The limits of integration can be expressed in terms of u as well.

Now, let's rewrite the integral in terms of u:

∫(1 to 0) y/e^(3y) dy = ∫(3 to 0) (1/3)e^(-u) du.

Next, we can simplify the integral:

∫(3 to 0) (1/3)e^(-u) du = (1/3) ∫(3 to 0) e^(-u) du.

Using the fundamental theorem of calculus, we can integrate e^(-u):

(1/3) ∫(3 to 0) e^(-u) du = (1/3) [-e^(-u)] from 3 to 0.

Now, let's substitute the limits of integration:

(1/3) [-e^(-0) - (-e^(-3))].

Simplifying further:

(1/3) [-1 + e^(-3)].

Therefore, the value of the integral ∫(1 to 0) y/e^(3y) dy is (1/3)[-1 + e^(-3)].

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Answer:

Step-by-step explanation:

To find gradient/slope m, we need to use this formula.

\(m \: = \: \frac{y2 - y1}{x2 - x1} \)

In the question, we are given x and y coordinates of two points, (-7, -4) and (7, 6).

\(m \: = \frac{6 - ( - 4)}{7 - ( - 7)} \)

\(m = \frac{6 + 4}{7 + 7} \)

\(m = \frac{10}{14} \)

\(m = \frac{5}{7} \)

Hope this helped!

The slope of the graph lines of function g passes through the points (-7,-4)and (7,6) is 5/7

The points are given as:

(-7,-4)and (7,6)

The slope (m) is calculated using:

m = [y2 - y1]/[x2 - x1]

So, we have:

m = [6 + 4]/[7 + 7]

Evaluate the sum

m = 10/14

Divide

m = 5/7

Hence, the slope is 5/7

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The tank will contain 350 lb of salt when it is full of brine.

What is rate ?

A rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities.

The amount of salt in the tank can be calculated using the principle of mass conservation. The rate at which salt is entering the tank is equal to the rate at which it is flowing out, so the total amount of salt in the tank will remain constant.

Let x be the amount of salt in the tank when it is full. Then:

x = 50 + 1 * (400 - 100) = 50 + 300 = 350 lb

So, the tank will contain 350 lb of salt when it is full of brine.

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The tank will contain 350 lb of salt when it is full of brine.

A rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities.

The amount of salt in the tank can be calculated using the principle of mass conservation The rate at which salt is entering the tank is equal to the rate at which it is flowing out, so the total amount of salt in the tank will remain constant.

Let x be the amount of salt in the tank when it is full. Then:

x = 50 + 1 * (400 - 100) = 50 + 300 = 350 lb

So, the tank will contain 350 lb of salt when it is full of brine.

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Answer:

I am stuck on this problem too. Is it on eacxt path.

Step-by-step explanation:

Answer: Can you give me a schema of the triangle please ?

To calculate the area of a triangle you need to calculate:

(Base X Height ) ÷ 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

A right triangle would have side 15 12 and 9

and its area is 1/2 * 12 * 9

= 54 unit^2

The most appropriate choice for area of rectangle will be given by-

a) Area of the wall =  \(26508\) \(in^2\)

b) Area of wall left uncovered = \(25347\) \(in^2\)

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle. If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is given by

Area = \(l \times b\)

Here,

Width of the wall = \(15\frac {2}{3}\) feet = \(\frac{47}{3}\) feet

Height of the wall = \(\frac{3}{4} \times \frac{47}{3}\) feet

                               = \(\frac{47}{4}\) feet

a) Area of the wall = \(\frac{47}{3} \times \frac{47}{4}\) \(ft^2\)

                               =\(\frac{2209}{12} \times 12 \times 12\) \(in^2\)

                               = \(26508\) \(in^2\)

b) Length of painting = \(40 \frac{1}{2}\)  in = \(\frac{81}{2}\) in

Breadth of painting = \(28\frac{2}{3}\) in = \(\frac{86}{3}\) in

Area of painting = \(\frac{81}{2} \times \frac{86}{3}\) \(in^2\)

                           = \(1161\) \(in^2\)

Area of wall left uncovered = (26508 - 1161) \(in^2\)

                                             = 25347 \(in^2\)

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The image coordinates of K' are K'(-4, 6). Thus, the correct answer is A: K'(-4, 6).

To determine the image coordinates of K' after reflecting polygon JKLM across the line y = -4, we need to find the image of point K(-4, -6).

When a point is reflected across a horizontal line, the x-coordinate remains the same, while the y-coordinate changes sign. In this case, the line of reflection is y = -4.

The y-coordinate of point K is -6. When we reflect it across the line y = -4, the sign of the y-coordinate changes. So the y-coordinate of K' will be 6.

Since the x-coordinate remains the same, the x-coordinate of K' will also be -4.

Therefore, the image coordinates of K' are K'(-4, 6).

Thus, the correct answer is A: K'(-4, 6).

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Answer:

92

Step-by-step explanation:

The mean is calculated as

mean = \(\frac{sum}{count}\)

The sum of customers over the 5 days is

\(\frac{sum}{5}\) = 86 ( multiply both sides by 5 )

sum = 430

Thus mean over the 6 days is

mean = \(\frac{430+122}{6}\) = \(\frac{552}{6}\) = 92

To calculate the estimated standard error for the sample mean difference (s(m1 - m2)) when given the pooled variance (s2p), we need to use the formula:

s(m1 - m2) = √[(s2p / n1) + (s2p / n2)]

In this case, both samples have the same size, n = 5, so we can substitute n1 = n2 = 5 into the formula.

s(m1 - m2) = √[(40 / 5) + (40 / 5)]

s(m1 - m2) = √[8 + 8]

s(m1 - m2) = √16

s(m1 - m2) = 4

Therefore, the estimated standard error for the sample mean difference (s(m1 - m2)) is 4.

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Answer:

(2,-7)

Step-by-step explanation:

The image lines constructed are called parallel lines. They are parallel because  they are all equidistant to each other at every point and at no point between any of the lines will there be an intersection of the three lines.

Equidistance is simply another word for equal in distance. That is, parallel lines maintain equal distance from each other at all points along them.

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