Create a system of equations of the form x ≡ c1 (mod n1) and x ≡ c2 (mod n2) that has more than one solution in \(Z_{n1n2}\)

Answer:

the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Step-by-step explanation:

Given that :

The mean value \(\mu\) = 12

The standard deviation \(\sigma\) = 3.5

Let Consider Q to be the weight of the parcel that is normally distributed .

Then;

Q \(\sim\) Norm(12,3.5)

The objective is to determine thewight  value of c under which there is a surcharge

Also, let's not that 99% of all the parcels are below the surcharge

However ;

From the Percentiles table of Standard Normal Distribution;

At 99th percentile; the value for Z = 2.33

The formula for the Z-score is:

\(Z = \dfrac{X- \mu}{\sigma}\)

\(2.33 = \dfrac{X - 12}{3.5}\)

2.33 × 3.5 = X - 12

8.155 = X - 12

- X = - 12 - 8.155

- X = -20.155

 X = 20.155

the weight  value of c under which there is a surcharge = X + 1 (0) since all the  pounds are below the surcharge

c = 20.155 + 1(0)

c = 20.155

Thus ; the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

7 raised to the power of 4 equals 2,401, and the exponent we were looking for is 4.

What is meant by power?

Power is a function that represents the number of times a base number is multiplied by itself. It is the rate at which work is done or energy is transferred, measured in watts.

What is meant by exponent?

An exponent is a mathematical notation used to indicate the number of times a quantity is multiplied by itself. It is written as a superscript and represents the power to which a number or expression is raised.

According to the given information

To find the value of the exponent that satisfies the equation 7ˣ = 2,401, we can take the logarithm of both sides of the equation with respect to base 7. This gives us:

log7(7ˣ) = log7(2,401)

x = log7(2,401)

Using a calculator, we can find that log7(2,401) is approximately 3. Therefore, the value of x that satisfies the equation 7ˣ = 2,401 is 3.

Alternatively, we could also use the fact that 2,401 is equal to 7⁴ - 2, which can be written as:

7⁴ - 2 = (7²)² - 2

= 49² - 2

= 2,401

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\(\\ \tt\hookrightarrow EI=GI\)

\(\\ \tt\hookrightarrow 16t+20=15t+21\)

\(\\ \tt\hookrightarrow 16t-15t=21-20\)

\(\\ \tt\hookrightarrow t=1\)

Answer:

C

Step-by-step explanation:

It has to be either A or C because the function is decreasing as you move left to right, this only occurs when the number inside parenthesis is less than 1.

It isn't A because if you plug in x=0, the value is 2, but on the graph it is greater than 2.

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114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120

The amount of the isotope left after 36 hours is 22.5 mg

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.

Half life is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay .

The half life of the isotope is 9hrs this means that it will take 9hrs for half of the atom nuclei of the isotope to disintegrate.

Therefore;

1/2 = 9hrs

1/4 = 18hrs

1/8 = 27 hrs

1/16 = 36 hours

This means that 1/16 of the original atom will be left after 36 hours

= 1/16 × 360

= 360/16

= 22.5 mg

therefore 22.5 mg will be left after 36 hours

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If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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His total earnings for a total sale of 7,000​ could be 1450sh

From the question, we have the following parameters that can be used in our computation:

Salary = 400

Commission = 15%

using the above as a guide, we have the following:

Total earnings = 400 + 15% * Total sales

So, we have

Total earnings = 400 + 15% * 7000

Evaluate

Total earnings = 1450

Hence, the total earnings is 1450

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Question

Simon earned 400sh weekly for goods sold and a commission of 15%

What could be his earnings for a total sale of 7,000​.

Answer:

you just see whats on the side and write it down so its 16-20

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

Answer:

5

Step-by-step explanation:

4 ×0.5+3=5...............

The​ mean, median, mode and midrange are 13, 13, 13, 17 respectively.

An average is a mean. To calculate the sum, add together all the numbers. After that, divide the total by the quantity of numbers.

The median is a midpoint. The fact that the median is in the middle of the road makes it easy to recall. Put the numbers in ascending order, lowest to largest. If there are odd numbers, find the middle one. Add the middle two numbers together and divide by two if the numbers are even.

The most frequent number in a group of numbers is called the mode.

The midpoint is discovered by arranging the numbers from smallest to largest. To determine the sum, add the two smallest and greatest numbers together. By 2, divide the total.

Given data -

The following set of​ numbers is 9​, 9​, 10​, 11​, 13​, 13​, 13​, 14​, 25

Σx = 117

To calculate the mean, we use the formula as

Mean = Σx / n

where n is the number of pieces of​ data i.e. n=9

Therefore, Mean = 117 / 9

Mean = 13

To calculate the median, we use the formula as

Median = Value of \((\frac{n+1}{2})^{th}\) th observation

when n is an odd number

So, Median = 10/2

Median = 5

Here the \(5^{th}\) observation is 13

As 13 occurs maximum number of times in the given set of numbers and it has 3 times in the given set

Therefore the mode = 13

To calculate the midrange, we use the formula as,

Midrange = (greatest number + least number) / 2

Here the greatest number is 25 and least number is 9

Therefore midrange = (25+9)/2

midrange = 34/2

midrange = 17

The​ mean, median, mode and midrange are 13, 13, 13, 17 respectively.

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Answer:

x = 30°

y = 60°

z = 96°

Step-by-step explanation:

Well the angle from the center that intercepts 120° is equal to 120° since it is a central angle.

y = 60° because oof supplementary angles.

The measure of z is 48 * 2 because the 48° is an inscribed angle.

z = 96°

And, the arc that angle y intercepts is also the arc the x intercepts.

That arc is 60° because 180° - 120° = 60°

x is an inscribed angle, so x = 1/2 * 60°

x = 30°

Hope this helps.

If Given f(x) = 1/2 (3 - x) ^ 2 , the value of f(15) is 72.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

The given function is:

f(x) = 1/2 (3 - x)²

To find the value of f(15), we need to substitute 15 for x in the function:

f(15) = 1/2 (3 - 15)²

Here, we subtract 15 from 3 to get -12 in the parentheses, and then we square it to get 144. We can simplify the expression further by multiplying 144 by 1/2, which gives us 72:

f(15) = 1/2 (144)

f(15) = 72

Therefore, the value of f(15) is 72.

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The percentage of students who got above 90 point is 80%

the decimal student got grade above the 90 points is 0.8

What is Decimal?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the name for the method of representing numbers in the decimal system.

Given,

Total no. of students = 30

No. of students who score above 90 points = 24

We have to find the percentage of the students who got above 90 points

So, to calculate,

                               24 / 30 x 100 = 80%

Now, we have to convert percent into decimal

so, we have,

                              80 / 100 = 0.8

Hence, 80% percent student got grade above 90 points

            And 0.8 of the student got grade above the 90 points

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These fractions are not proportional. A little tip for figuring out if a fraction is proportional to another is to simplify the larger fraction + if it simplifies to the other fractions, then it is proportional. Since 3/8 does not simplify to 2/5 or 1/3 we know it is not proportional.

Answer:

C, it is a one to one function

Step-by-step explanation:

A one to one function is when each y-value has its own x-value, which this graph does since negative numbers have negative numbers and positive numbers have positive numbers

Comment if you have any questions. Your welcome! :D

Using right triangle relations, we will get:

We assume that bot triangles are equivalent, then the angle B will be the same as the angle Z.

Now remember the relations:

If we step on angle B, we have:

Replacing that, we get:

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Answer:

160 inches

Step-by-step explanation:

47+33+47+33=160inches

The time taken by Amy to travel to the place was t = 4 hours.

A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.

In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.

Let the time taken to get back = t + 1.

Now, it took one hour less time to get there thus time = t.

Now, average speed is given as:

average speed = total distance / total time

Substituting the values:

50 km/h = d / t

d = 50t  .........(1)

40 km/h = d / (t + 1)

d = 40(t + 1)......(2)

Setting the value of d as equal we have:

50t = 40(t + 1)

50t = 40t + 40

10t = 40

t = 4

Hence, the time taken by Amy to travel to the place was t = 4 hours.

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f(x) = -1/3x + 8

Slope = -1/3

y-intercept = 8

Start at 8 then go down 1 and to the right 3. Similarly, you can go up one and to the left 3.

I included a picture of the points but you just need to connect them with a line.

The graph of the function -

\($f(x) =\frac{1}{3} x+ 8\)

is plotted below.

We have the following function -

f(x) = 1/3x + 8

We have to plot its graph on Graph paper.

The Slope - intercept form of the equation of a straight line is as follows -

y = mx + c

where -

m - slope of line

c - intercept of line on y - axis.

According to the question, we have -

\($f(x) =\frac{1}{3} x+ 8\)

Comparing it with the Slope - intercept form of the equation of a straight line, we get -

Slope = \(m=\frac{1}{3}\)

Intercept of line on y - axis = 8

Now plot the graph. it will look like the image attached with the answer.

Hence, the graph is plotted.

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Answer:

x > 5

Step-by-step explanation:

14 -14 - 3 x < -1 -14

-3 x < -15

-3 x / -3 < -15 / -3

x > 5

Answer:

can you write the word in english?

btw, a/b+ab/c= (ac+ab²)/bc

Solution:

Given:

Factorizing the function;

Hence,

To get the solution, it must satisfy the condition of the inequality given.

Hence,

Answer:

15

Step-by-step explanation:

m = 5, n = 2, and p = 4

Substituting the values in the equation p(6 – n) – m ÷ 5 ,

4(6-2) - 5/5

4(4) - 1

16 - 1

=> 15

Answer: The domain would be 1,2,3,4  

Step-by-step explanation:

Step-by-step explanation:

-2x + 11(y+x) = 2

-2x + 11y + 11x = 2

-2x + 11x +11y = 2

9x + 11y = 2

where a = 9, b= 11 and c= 2

Answer:

907.46 mm2

Step-by-step explanation:

Area of circle = (¶d^2)/4

d = 34 mm

Therefore

Area A = (3.14 x 34^2)/4

= 907.46 mm2

\(907.43 \: {yrds}^{2} \)

Step-by-step explanation:

The formula to find the area of a circle is:

\(\pi {r}^{2} \)

since pi is 3.14 then, and the radius is half of the diameter, then:

\(diameter = 34 \\ radius = \frac{34}{2} \\ radius = 17\)

Therefore;

\(area = \pi {r}^{2} \\ area = (3.14) {(17)}^{2} \\ = 3.14 \times 289 \\ = 907.46 {yrds}^{2} \)

Answer:

Step-by-step explanation:

Answer:

-49

Step-by-step explanation:

it is really hard to type using this keyboard..but am sure d answer is -49