Solve for x.
-4x+60 < 72
OR 14z +11 <-31

Answer:

B

Step-by-step explanation:

Hope this helps!

For the sample size of 20, the 95% confidence interval is (-4.87, 27.16), which is narrower than the previous interval due to the larger sample size.

In statistics, mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total number of values in the set. Mean is also commonly referred to as the arithmetic mean. It is a commonly used statistical measure in many fields including finance, economics, social sciences, and more.

Here,

To calculate the z-scores associated with each student, we first need to calculate the sample mean and standard deviation for the Distance to Work variable:

Sample mean: (0+0+5+10+15+30+32)/7 = 10.71

Sample standard deviation: √(((0-10.71)² + (0-10.71)² + (5-10.71)² + (10-10.71)² + (15-10.71)² + (30-10.71)² + (32-10.71)²)/6) = 10.72

Now we can calculate the z-scores for each student:

Student 1: (0 - 10.71) / 10.72 = -0.94

Student 2: (0 - 10.71) / 10.72 = -0.94

Student 3: (5 - 10.71) / 10.72 = -0.53

Student 4: (10 - 10.71) / 10.72 = -0.07

Student 5: (15 - 10.71) / 10.72 = 0.40

Student 6: (30 - 10.71) / 10.72 = 1.80

Student 7: (32 - 10.71) / 10.72 = 1.98

Student 8: (8 - 10.71) / 10.72 = -0.25

Student 9: (36 - 10.71) / 10.72 = 2.37

Student 10: (9 - 10.71) / 10.72 = -0.16

Student 11: (22 - 10.71) / 10.72 = 1.05

Student 12: (10 - 10.71) / 10.72 = -0.07

Student 13: (15 - 10.71) / 10.72 = 0.40

Student 14: (28 - 10.71) / 10.72 = 1.54

Student 15: (12 - 10.71) / 10.72 = 0.12

Student 16: (6 - 10.71) / 10.72 = -0.44

Student 17: (0 - 10.71) / 10.72 = -0.94

Student 18: (10 - 10.71) / 10.72 = -0.07

Student 19: (30 - 10.71) / 10.72 = 1.80

Student 20: (0 - 10.71) / 10.72 = -0.94

To identify potential outliers, we can look for z-scores that are more than 2 standard deviations away from the mean (i.e., greater than 2 or less than -2). From the list above, we can see that Students 6, 7, 9, and 19 have z-scores greater than 2, indicating that they may be potential outliers.

For the second sample of seven data points (0, 0, 5, 10, 15, 30, 32), the mean is 11.14 and the standard deviation is 12.05. Using a t-distribution with 6 degrees of freedom (n-1), the 95% confidence interval is (-7.54, 29.82).

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If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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The area of a garden is the amount of space the garden occupies

The area of the garden is (c) 375 ft^2

The given parameters are:

\(L = 15 \times W\) --- Length equals 15 times width

\(Perimeter=160\)

The perimeter of a rectangle is:

\(Perimeter= 2(L + W)\)

Substitute known values

\(160= 2(15 \times W + W)\)

Divide through by 2

\(80= 15 \times W + W\)

\(80= 15W + W\)

\(80= 16W\)

Divide through by 16

\(5= W\)

Rewrite as:

\(W =5\)

The area of a rectangle is:

\(Area = L \times W\)

Substitute \(L = 15 \times W\)

\(Area = 15 \times W \times W\)

Substitute \(W =5\)

\(Area = 15 \times 5 \times 5\)

\(Area = 375\)

Hence, the area of the garden is (c) 375 ft^2

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Answer:

Step-by-step explanation:

(t - 6)^2 = t^2 - 12t + 36

(t + 6)^2 = t^2 + 12t +36

(t - 6)^2 - (t + 6) = t^2 - 12t + 36 - (t^2 + 12t + 36)

(t - 6)^2 - (t + 6) = t^2 - 12t + 36 - t^2 - 12t - 36

(t - 6)^2 - (t + 6) = -24t    The other 4 terms cancel out.

-24t = 0   Divide by - 24

t = 0

There is one root.

The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.

To find the z-scores, we need to use the formula:

z = (x - μ) / σ

where:

z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.

Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:

z = (39 - 34) / 5

z = 5 / 5

z = 1

So, the z-score for the raw score of 39 is 1.For a raw score of 30:

z = (30 - 34) / 5

z = -4 / 5

z = -0.8

The z-score for the raw score of 30 is -0.8.

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The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically

Given the following expression

23 - √81

The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.

We know that the square root of 81 is 9, so we can simplify the expression to:

23 - √81 = 23 - 9

Evaluate the difference

23 - √81 = 14

Therefore, the value of the expression is 14.

In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.

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Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

hi,

the function is given with it's canonic form.  

canonic form is  :  f(x) = a ( x-α)² + β

α  and β are the value of the coordonnates of the vertex.

so here we  have : ƒ(x) = 2(x−1)² +3

with α = 1  and β = 3

so vertex is  V (1;3)

So yes, answer is   A.

We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

espero que sea de tu agrado la tarea que te estoy enviando

soy de peru

brillith2022

Answer:

2%

Step-by-step explanation:

The constant percent rate of change for the function g(x) is option (D) 2% is the correct answer.

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principle and the interest accumulated over the previous period.

For the given situation,

The function \(g(x) = 500(1.02)^x -------- (1)\)

Principle = $500

Number of years, T = x

The formula of amount in compound interest is

\(A=p(1+\frac{r}{n} )^{nT}\)

Interest is compounded annually, so n=1

⇒ \(A=p(1+r)^{T} ------ (2)\)

On comparing equation 1 and 2,

⇒ \(1.02=1+r\)

⇒ \(r=1.02-1\)

⇒ \(r=0.02\)

Rate of interest should be in percentage,

⇒ \(0.02(100\%)\)

⇒ \(2\%\)

Hence we can conclude that the constant percent rate of change for the function g(x) is option (D) 2% is the correct answer.

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Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Answer:

what is the question about which topic

Answer: 13

Step-by-step explanation:

I used Pythagorean theorem to solve this problem. As DC and AD is 12 and 5, you would do 12²+5²= c². 12²= 144 and 5²= 25. 144+25= 169. It doesn't end there. Do the square root of 169 ---> √169=13.

Given that ABCD is a rectangle, if a diagonal line cuts from A to C make a two equal right angled triangles, the hypotenuse which is the length of AC is 13.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Given the data in the question;

Let line AC be the hypotenuse as it cuts the rectangle into two equal right angled triangle.

From Pythagorean theorem.

c = √( a² + b² )

AC = √( AB² + BC² )

AC = √( 12² + 5² )

AC = √( 144 + 15 )

AC = √169

AC = 13

Therefore, given that ABCD is a rectangle, if a diagonal line cuts from A to C make a two equal right angled triangles, the hypotenuse which is the length of AC is 13.

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If SBI hires an independent agent and the agent's sales force after some unhappy performances, it will help him to increase the unit variable cost for the change deployed.

Also, At the same time, he gets rid of its own ' salary own ' sales force will decrease its total fixed cost.

Hence, will increase the unit variable cost and will decrease the total fix cost.

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Answer:

domain - -9 <x < 7

range - -6 < y < 4

Step-by-step explanation:

Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

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The required answers are 1) \($$A = x^2 + 28x + 192$$\) 2) 300000 3) \($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\).

area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:

\($$A = (x+12)(x+16)$$\)

Expanding this expression, we get:

\($$A = x^2 + 28x + 192$$\)

Hence, the area of the land purchased is given by the polynomial expression \($x^2 + 28x + 192$\).

The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:

\($\frac{3}{5}=\frac{x}{500000}$$\)

Simplifying this expression, we get:

\($x = \frac{3}{5}\times 500000 = 300000$$\)

Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.

We can solve the polynomial \($x^2 + 28x + 192$\) into different factors by using the quadratic formula:

\($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\)

Here, the coefficients of the polynomial are:

\($$a = 1, \quad b = 28, \quad c = 192$$\)

Substituting these values in the quadratic formula, we get:

\($x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$\)

Simplifying this expression, we get:

\($$x = -14 \pm 2\sqrt{19}$$\)

Therefore, the polynomial \($x^2 + 28x + 192$\) can be factored as:

\($$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$\)

or

\($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\)

So, we have factored the polynomial into two factors.

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Answer: 5 5/8

Step-by-step explanation:

6 5/8=  6*8= 48 48+5=53 53/8

8 5/8= 8*8=64 64+5=69 69/8

5 5/8= 5*8=40 40+5=45 45/8

7 5/8= 7*8=56 56+5=61 61/8

The number of Jim's model car is 48

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

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

Step-by-step explanation:

From the graph attached,

Black curve represents a function f(x) = 2ˣ

When this curve is reflected over the x-axis image of the function will be,

g(x) = -\(2^{x}\) [Red curve]

Similarly, curve represented by h(x) = \(2^{-x}\) is the blue curve [image of f(x) reflected over y-axis]

When this curve is reflected over the x-axis, image of the function will be,

h'(x) = \(-2^{-x}\) [green curve]

\(-2^{x}\) → Red

\(-2^{-x}\) → Green

\(2^{-x}\) → Blue

The value of y is given as follows:

y = -8.

When two lines are parallel, we have that they have the same slope.

Given two points, the slope is calculated as the change in y divided by the change in x.

The slope of line CD is given as follows:

m = (6 - (-2))/(10 - (-10))

m = 8/20

m = 0.4.

The slope of line EF is given as follows:

m = (y + 4)/(-4 - 6)

m = -0.1(y + 4).

As the two lines are parallel, the value of y is obtained as follows:

-0.1(y + 4) = 0.4

y + 4 = -4.

y = -8.

The x-coordinate of E is of -4.

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The side that is equivalent to side SR is side AB.

When rotating a point 180 degrees counterclockwise about the origin, our point A(x, y) becomes A'(-x, -y). Thus, all we do is make both x and y negative.

The coordinates of the original square are;

P(2, 4); Q(5, 5); R(5, 1); S(2, 1)

Now, applying the transformation rule above gives us;

P(-2, -4); Q(-5, -5); R(-5, -1); S(-2, -1)

The side that is therefore equivalent to side SR is side AB.

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Answer:

10 2/3 or 32/ 3

Step-by-step explanation:

5 - x^2 - (2 - 2x) =

= -x^2 + 2x + 3

Integral of (-x^2 + 2x + 3)dx from -1 to 3 =

= -x^3/3 + 2x^2/2 + 3x from -1 to 3

= -x^3/3 + x^2 + 3x from -1 to 3

= -27/3 + 9 + 9 - (1/3 + 1 - 3)

= -9 + 9 + 9 - 1/3 - 1 + 3

= 11 - 1/3

= 10 2/3 = 32/3

Answer:

32/3

Step-by-step explanation:

Check the pdf :)

The scale is given inches/ miles equal 1/50. This means that 1 inch is equal to 50 miles.

We can use the rule of three to find the real value.

Then

1 inch --------------------------- 50miles

2.5 inches x

Where x=(2.5inch*50miles)/1 inch

x = 125 miles

For 4.75 inches​

1 inch --------------------------- 50miles

4.75 inches--------------------- x

Where x =(4.75 inch*50miles)/1inch

x = 237.5 miles

The largest ratio, among the following ratios: 5/36, 2:9, 3 to 18, 1:3 is 1:3.

The ratio refers to the relative size of one quantity compared to another.

The ratio, which is the quotient of two quantities or values, can be expressed as a decimal, percentage, or fraction.  We can also express the ratio in its standard form (:).

Given   Sum of     Equivalent

Ratio     Ratios          Ratios

5/36        36         13.89% or 0.1389

2:9           11          18.18% or 0.1818

3 to 18     21          14.28% or 0.14.28

1:3            4           25% or 0.25

Thus, we can conclude that 1:3 is the largest ratio amont the others.

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Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Answer:

A≈118.2

Step-by-step explanation:

r= Radius= 3.5

l= Slant height= 7.25

A= πrl+πr2= π·3.5·7.25+π·3.52≈118.20242

The probability of getting someone who is a woman or a heavy drinker is,

0.546 to three decimal places.

None of the above is the correct option.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

Given:

The table lists the drinking habits of a group of college students.

If a student is chosen at random,

then the probability of getting someone who is a woman or a heavy drinker,

=P(woman) + P(heavy drinker) - P(woman and heavy drinker)

= 216/405 + 13/405 - 8/405

= 221/405

= 0.546 to three decimal places.

Therefore, the probability is 0.546.

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