A number problem states, “–5 times a number, minus 22 gives a result of 23.” What is the number?

A cylinder with radius 1, height 1 in 1st octant of xyz-plane, center at origin, height from z=1 to z=2 and θ from 0 to π/2.

What is cylinder ?

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.

The cylindrical coordinate conditions can be expressed mathematically as:

1≤r≤2

0≤θ≤π/2

1≤z≤2

These conditions define a cylinder with radius 1 and height 1 located in the first octant of the xyz-plane. The cylinder has its center at the origin (0,0,0) and its height extends from z = 1 to z = 2. The angle θ ranges from 0 to π/2, meaning that the cylinder is restricted to the first quadrant in the xy-plane.

A cylinder with radius 1, height 1 in 1st octant of xyz-plane, center at origin, height from z=1 to z=2 and θ from 0 to π/2.

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If events A and B are independent, then P(A and B) = P(A) * P(B). Also, from Bayes' theorem we have P(A | B) = P(A and B) / P(B).

Given that P(A | B) = 0.35 and P(B) = 0.5, we can solve for P(A and B) as follows:

P(A and B) = P(A | B) * P(B) = 0.35 * 0.5 = 0.175

Since events A and B are independent, we have P(A and B) = P(A) * P(B). Solving for P(A), we get:

P(A) = P(A and B) / P(B) = 0.175 / 0.5 = 0.35

Therefore, P(A) = 0.35.

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The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is

||A - A1||₂=0 where A is 2×2 matrix.

We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]

note here that C₂= 3C₁

where Cᵢ --> iᵗʰ column

v = [ 5 ; 6 ; -1 ; -4 ; 2]

||v||² = 82 => ||v|| = √82

and A At v = 820 v

and A At = [ 82 246 ; 246 738]

AAt [1;3] = 820[1;3]

=> v1 = 1/√10(1,3)^t

Then the best rank of 1 approx

= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]

= A

Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0

Hence, the minimal Approx. ||A - A1||2 = 0 .

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Complete question:

Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

a. The standard form of the given linear programming model is as follows:

Objective function: Min Z = 8X1 + 6X2 + 0S1 + 0S2

Subject to:

2X1 + 4X2 - S1 = 8

3X1 + 2X2 - S2 = 6

X1, X2, S1, S2 ≥ 0

b. Using the linear programming simplex method to solve the standard form:

Initial tableau:

```

     BV   |   X1   X2   S1   S2   RHS

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

  Z   |   8     6    0    0    0

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

 S1   |   2     4   -1    0    8

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

 S2   |   3     2    0   -1    6

```

Entering variable: X1 (column with the most negative coefficient in the Z row).

Leaving variable: S1 (minimum ratio of the RHS to the coefficient in the X1 column).

Pivot operation: Divide the S1 row by 2.

```

     BV   |   X1   X2   S1   S2   RHS

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

  Z   |   2     6    0    0    16

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

  S1  |   1     2   -0.5  0    4

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

  S2  |   1.5   2    0.5 -1    2

```

Entering variable: X2 (column with the most negative coefficient in the Z row).

Leaving variable: S2 (minimum ratio of the RHS to the coefficient in the X2 column).

Pivot operation: Divide the S2 row by 2.

```

     BV   |   X1   X2   S1   S2   RHS

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

  Z   |   0     5    1    0    18

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

  S1  |   1     0   -1    1    2

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

  X2  |   0.75  1    0.25 -0.5  1

```

No more negative coefficients in the Z row. Optimal solution found.Solution: X1 = 2, X2 = 0.75, Z = 18. The optimal solution for the given linear programming model is X1 = 2, X2 = 0.75, with the minimum objective value Z = 18.

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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The polynomial p(x) = 16 + 2x^4 - 8x^5 can be analyzed to determine its leading term, limit as x approaches 0, and limit as x approaches infinity.

(A) The leading term of a polynomial is the term with the highest exponent. In this case, the highest exponent is 5. Therefore, the leading term of p(x) is -8x^5.

(B) To find the limit as x approaches 0, we substitute 0 for x in the polynomial expression. This gives us p(0) = 16 + 2(0)^4 - 8(0)^5 = 16 + 0 - 0 = 16. Therefore, the limit as x approaches 0 is 16.

(C) To find the limit as x approaches infinity, we examine the behavior of the leading term. The leading term -8x^5 becomes increasingly large and negative as x approaches infinity. As a result, the polynomial will also tend to negative infinity. Therefore, the limit as x approaches infinity is negative infinity. In summary, the leading term of the polynomial p(x) is -8x^5, the limit as x approaches 0 is 16, and the limit as x approaches infinity is negative infinity.

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Answer:

\(\Huge \boxed{-x^2+2x}\)

Step-by-step explanation:

2 times x subtracted by x².

\(\Rightarrow 2 \cdot x-x^2\)

\(\Rightarrow 2x-x^2\)

Rearranging the expression.

\(\Rightarrow -x^2+2x\)

Answer:

2x -x^2

Step-by-step explanation:

\(2(x) - x^2\\= 2x-x^2\)

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Answer:

\(l =45\) --- length

\(w = 55\) --- width

Step-by-step explanation:

Given

\(P = 200\) --- perimeter

\(A = 2475\) --- area

Required

The dimension of the farm

Let

\(l \to length; w \to width\)

So:

\(p = 2(l+w)\) --- perimeter

\(2(l+w)=200\)

Divide by 2

\(l+w=100\)

Make l the subject

\(l = 100 - w\)

Also:

\(A= l*w\) --- area

\(l * w = 2475\)

Substitute: \(l = 100 - w\)

\((100 - w) * w = 2475\)

Open bracket

\(100w - w^2 = 2475\)

Rewrite as:

\(w^2 - 100w +2475 = 0\)

\(w^2 - 45w - 55w +2475 = 0\)

Factorize

\(w(w - 45) - 55(w -45) = 0\)

Factor out w - 45

\((w - 55)(w -45) = 0\)

Take any one of the expression and solve for w

\(w -55 = 0\)

\(w = 55\)

Recall that: \(l = 100 - w\)

\(l =100 - 55\)

\(l =45\)

Answer:

You can calculate net change by subtracting the current day's closing price for an asset from the closing price of the previous day!

Step-by-step explanation:

(What net change is) The net change theorem states that when a quantity changes, the final value equals the initial value plus the integral of the rate of change. Net change can be a positive number, a negative number, or zero.

NOT MY ANSWER OR WHATEVER I GOT IT FROM G0OGLE

Answer:

86.4m/s as 2.4^(2)=5.76

5.76x15=86.4

Find the differential of the function. y = x^2 - 7x + 9 dy = dy = (2x - 7) dx

Evaluate it at the given values of x and dx. x = 7 and dx = 0.25 dy = 1.75

To find the differential of a function, we take the derivative of the function with respect to the independent variable, and multiply it by the differential of the independent variable.

Here, we have:

y = x^2 - 7x + 9

Taking the derivative with respect to x, we get:

dy/dx = 2x - 7

So, the differential of y is:

dy = (2x - 7) dx

To evaluate dy at x = 7 and dx = 0.25, we simply substitute these values into the equation for dy:

dy = (2x - 7) dx

dy = (2(7) - 7) (0.25)

dy = (14 - 7) (0.25)

dy = 1.75

So, dy = 1.75 when x = 7 and dx = 0.25.

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Answer:  It should be the third one

Step-by-step explanation:

The amount invested in the account that pays a 5% interest is $2100 and the amount invested in the account that pays a 7.5% interest is $1400.

0.05a + 0.075b = (0.06 x $3500)

0.05a + 0.075b = $210 equation 1

a + b = $3,500 equation 2

Where:

a = amount invested in the account that paid a 5% interest

b = amount invested in the account that paid a 7.5% interest

In order to determine this value, multiply equation 2 by 0,05

0.05a + 0.05b = 175 equation 3

0.025b = 35

b = $1400

a + $1400 = $3500

a = $3500 - 1400

a = $2100

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Answer:

21.5 cm² (nearest tenth)

Step-by-step explanation:

To find the shaded region, subtract the area of the circle from the area of the square.

Square

Area of the square = 10² = 100 cm²

Circle

Given diameter of circle = 10 cm

⇒ radius = 10 ÷ 2 = 5 cm

⇒ Area of the circle = π · 5² = 25π cm²

Area of shaded region

= area of square - area of circle

= 100 - 25π

= 21.46018366...

= 21.5 cm² (nearest tenth)                                  

Thus, the Inequality effectively depicts how much somebody can spend provided his monthly savings goal is between 5% and 10%.: $55.75 < s < $111.50.

In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100.

When a number is expressed in decimal form, you can calculate its percentage by multiplying it by 100. For instance, multiplying 0.5 by 100 gives you the percentage 50%.

Given data:

Terrance's average bi-weekly net pay  = $1,115.00.

monthly budget savings - 5% to  10%.

Let s be the savings:

Then,

5% of 1,115.00.  < s < 10% of 1,115.00.  (both not included)

5 *1,115.00 / 100  < s < 10*1,115.00/100

55.75 < s < 111.50

Thus, the Inequality effectively depicts how much somebody can spend provided his monthly savings goal is between 5% and 10%.: $55.75 < s < $111.50.

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Approximately 166 mice must be weighed to achieve a 99% confidence interval for the population mean weight gain with a margin of error of 0.4 grams.

To estimate the mean weight gain of mice with a 99% confidence interval and a margin of error of 0.4 grams, we need to determine the required sample size using the given information about the population standard deviation.
Identify the relevant information:
- Standard deviation (σ) = 2 grams
- Margin of error (E) = 0.4 grams
- Confidence level = 99%
Find the critical value (z-score) for the given confidence level:
For a 99% confidence interval, the critical value (z-score) is approximately 2.576.

This value can be found using a z-table or a calculator with a built-in function for finding critical values.
Use the formula for determining the sample size (n) with a known standard deviation:
\(n = (z * \sigma/ E)^2\)
where z is the critical value, σ is the standard deviation, and E is the margin of error.
Plug in the values and calculate the required sample size:
\(n = (2.576 * 2 / 0.4)^2\)
\(n = (5.152 / 0.4)^2\)
\(n = 12.88^2\)
n ≈ 166.

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You will need to weigh approximately 166 mice to achieve a 99% confidence interval for the population mean weight with a margin of error of 0.4 grams.

In order to find the sample size required for a 99% confidence interval with a margin of error of 0.4 grams, we'll need to use the following formula:

n = (Z * σ / E)^2\(n = (Z * del / E)^2\)

where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level (in this case, 99%)
- σ is the known standard deviation (2 grams)
- E is the desired margin of error (0.4 grams)

For a 99% confidence interval, the Z-score is approximately 2.576 (you can find this value in a standard Z-score table).

Now, we'll plug the values into formula:

\(n = (2.576 * 2 / 0.4)^2\\n = (5.152 / 0.4)^2\)
\(n = 12.88^2\)
n ≈ 166

You will need to weigh approximately 166 mice to achieve a 99% confidence interval for the population mean weight with a margin of error of 0.4 grams.

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Answer:

The price of one DVD is 4 and price of one CD is 5

Step-by-step explanation:

2DVDs and 2CDs = 18

3DVDs and 2CDs = 22

DVDs can be x and CDs can be y:

2x + 2y = 18

3x + 2y = 22

Subtract to get:

-x = -4

x = 4

So the price of one DVD is 4

Plug that into one of the original equations:

2x + 2y = 18

2(4) + 2y = 18

8 + 2y = 18

2y = 10

y = 5

So the price of one CD is 5

The closer the correlation coefficient is to -1,The correlation coefficient that indicates the strongest relationship between two variables is -0.97.

The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship. The closer the correlation coefficient is to -1 or 1, the stronger the relationship between the variables.

Among the given options, the correlation coefficient of -0.97 indicates the strongest relationship. This value indicates a strong negative linear relationship between the variables, meaning that as one variable increases, the other variable tends to decrease in a consistent and predictable manner. The closer the correlation coefficient is to -1, the stronger and more consistent the negative relationship between the variables.

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We need to find how much water Ella needs to make the different concentrations of syrups. The solution will be for 1.5%, we need 32.83 lbs of water.

The percentage in the concentration tells us how much in the mixture is sugar.

So for example, in the 50% syrup, we have a 50% of sugar, meaning that half of it is sugar, and we have 0.5 lbs of sugar, so we need to add the same amount of water, 0.5 lbs of water.

For the 1.5% syrup, this will be:

= (0.5 - 0.5 × 0.015) / 0.015

= 32.83 lbs

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Complete question

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case.  1.5% syrup?

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

the hexadecimal number 3AB8 (base 16) is equivalent to 0011 1010 1011 1000 in binary (base 2).

The above solution comprises more than 100 words.

The hexadecimal number 3AB8 can be converted to binary in the following way.

Step 1: Write the given hexadecimal number3AB8

Step 2: Convert each hexadecimal digit to its binary equivalent using the following table.

Hexadecimal Binary

0 00001

00012

00103

00114 01005 01016 01107 01118 10009 100110 101011 101112 110013 110114 111015 1111

Step 3: Combine the binary equivalent of each hexadecimal digit together.3AB8 = 0011 1010 1011 1000,

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Given:

\(\sin (x)=-\dfrac{1}{2}\)

\(\cos (y)=-\dfrac{1}{3}\)

x is an angle in quadrant III, and y is an angle in quadrant II.

To find:

The value of sin(x+y).

Solution:

We know that, only sin and cosec are positive in II quadrant. Only tan and cot are positive in III quadrant.

x is an angle in quadrant III,

\(\cos x=-\sqrt{1-\sin^2 x}\)

\(\cos x=-\sqrt{1-(-\dfrac{1}{2})^2}\)

\(\cos x=-\sqrt{1-\dfrac{1}{4}}\)

\(\cos x=-\sqrt{\dfrac{4-1}{4}}\)

\(\cos x=-\dfrac{\sqrt{3}}{2}\)

y is an angle in quadrant II.

\(\sin y=\sqrt{1-\cos^2x}\)

\(\sin y=\sqrt{1-(-\dfrac{1}{3})^2}\)

\(\sin y=\sqrt{1-\dfrac{1}{9}}\)

\(\sin y=\sqrt{\dfrac{9-1}{9}}\)

\(\sin y=\sqrt{\dfrac{8}{9}}\)

\(\sin y=\dfrac{2\sqrt{2}}{3}\)

Now,

\(\sin(x+y)=\sin x\cos y+\cos x\sin y\)

\(\sin(x+y)=(-\dfrac{1}{2})\times (-\dfrac{1}{3})+(-\dfrac{\sqrt{3}}{2})\times (\dfrac{2\sqrt{2}}{3})\)

\(\sin(x+y)=\dfrac{1}{6}-\dfrac{2\sqrt{6}}{6}\)

\(\sin(x+y)=\dfrac{1-2\sqrt{6}}{6}\)

Therefore, the correct option is B.

Answer:

Choice B

Step-by-step explanation:

Answer:

19-3*x=88

Step-by-step explanation:

(x is the variable not the times!) (this symbol: * means times)

answer :

x  = - 23

explanation :

19 - 3x  = 88

Break it down :

"19 less than": Means we are going to subtract 19 from a number.

"3 times a number":  Pick a variable to represent the number and multiply

                                    that by 3. ex:   3x

Solve : 19 - 3x  = 88

          - 19           - 19         ( subtract - 19 from both sides,              

                                                    to get " -3x = 69 " )

                    -3x = 69                    

                   / -3    / -3               ( divide both sides by -3,

                                                 to get your answer, x = -23 )

                  x =  - 23

The order of processes that support the central dogma are:1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

The central dogma of molecular biology describes the flow of genetic information within a biological system. The method by which DNA instructions are translated into useful products is known as the "Central Dogma." Francis Crick, who discovered the structure of DNA, first put up the idea in 1958.

The order of processes that support the central dogma are:

1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

In summary, the central dogma can be described as follows: DNA is replicated to make more DNA, DNA is transcribed into RNA, and RNA is translated into proteins.

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Answer:

29

Step-by-step explanation:

count the rectangles one by one :)

Answer:

If the value of Mike's car decreased by 30%, we can calculate the new value of the car as follows:

New value = Original value - (Percentage decrease × Original value)

Percentage decrease = 30%

Original value = 12000

New value = 12000 - (0.30 × 12000)

New value = 12000 - 3600

New value = 8400

Therefore, at the end of the decrease, the value of Mike's car was 8400.

In the given stem-and-leaf plot, we can conclude that there are at least 5 outliers

The number of outliers in the given stem-and-leaf plot can be determined by identifying values that are significantly higher or lower than the majority of the data.

To find the number of outliers in the stem-and-leaf plot, we need to analyze the data distribution and identify values that deviate significantly from the rest of the scores.

Looking at the stem-and-leaf plot, we observe that the majority of the scores are concentrated between 20 and 90. The numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10 represent the tens digit of the scores, while the leaves represent the ones digit.

Upon examining the plot, we notice that there are a few values that stand out from the rest. These values are 00, 01677, 6899, 233569999, and 01268. Outliers are typically defined as values that fall outside the "typical" range of the data, and these values appear to deviate significantly from the majority of the scores.

To determine the exact number of outliers, we need to apply specific criteria. One common method is to use the 1.5 × IQR (interquartile range) rule. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the data. Any values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR are considered outliers.

In this case, we don't have the exact raw data to calculate the quartiles and IQR. However, based on visual inspection of the stem-and-leaf plot, we can still identify the values mentioned earlier as outliers due to their significant deviation from the majority of the scores.

Therefore, in the given stem-and-leaf plot, we can conclude that there are at least 5 outliers

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Answer:

(6, 2)

Step-by-step explanation:

I did this over 10 times it's so easy it is like a breeze

Answer:(-2,5)

Step-by-step explanation: