Write a linear inequality to represent the information given. Shanley would like to give $5 gift cards and $8 teddy bears as party favors. Shanley has $144 to spend on party favors. Enter an inequality to find the number of gift cards x and teddy bears y Shanley could purchase. Give one solution to the inequality.

Answer:

a) 0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

b) 0.2946  = 29.46% probability that 30 or more will live beyond their 90th birthday

c) 0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday

d) 0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

Step-by-step explanation:

We solve this question using the normal approximation to the binomial distribution.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

In this problem, we have that:

Sample of 723, 3.7% will live past their 90th birthday.

This means that \(n = 723, p = 0.037\).

So for the approximation, we will have:

\(\mu = E(X) = np = 723*0.037 = 26.751\)

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{723*0.037*0.963} = 5.08\)

(a) 15 or more will live beyond their 90th birthday

This is, using continuity correction, \(P(X \geq 15 - 0.5) = P(X \geq 14.5)\), which is 1 subtracted by the pvalue of Z when X = 14.5. So

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

\(Z = \frac{14.5 - 26.751}{5.08}\)

\(Z = -2.41\)

\(Z = -2.41\) has a pvalue of 0.0080

1 - 0.0080 = 0.9920

0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

This is, using continuity correction, \(P(X \geq 30 - 0.5) = P(X \geq 29.5)\), which is 1 subtracted by the pvalue of Z when X = 29.5. So

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

\(Z = \frac{29.5 - 26.751}{5.08}\)

\(Z = 0.54\)

\(Z = 0.54\) has a pvalue of 0.7054

1 - 0.7054 = 0.2946

0.2946  = 29.46% probability that 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

This is, using continuity correction, \(P(25 - 0.5 \leq X \leq 35 + 0.5) = P(X 24.5 \leq X \leq 35.5)\), which is the pvalue of Z when X = 35.5 subtracted by the pvalue of Z when X = 24.5. So

X = 35.5

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

\(Z = \frac{35.5 - 26.751}{5.08}\)

\(Z = 1.72\)

\(Z = 1.72\) has a pvalue of 0.9573

X = 24.5

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

\(Z = \frac{24.5 - 26.751}{5.08}\)

\(Z = -0.44\)

\(Z = -0.44\) has a pvalue of 0.3300

0.9573 - 0.3300 = 0.6273

0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday.

(d) more than 40 will live beyond their 90th birthday

This is, using continuity correction, P(X > 40+0.5) = P(X > 40.5), which is 1 subtracted by the pvalue of Z when X = 40.5. So

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

\(Z = \frac{40.5 - 26.751}{5.08}\)

\(Z = 2.71\)

\(Z = 2.71\) has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

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

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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Answer:

B. \( \huge \red {\boxed { 64\degree}} \)

Step-by-step explanation:

\( \therefore m\angle S = m\angle R\)

\( \because m\angle R= 116\degree \)

\( \therefore m\angle S= 116\degree \)

\( m\angle S + m\angle T = 180\degree \)

(angles on the same side of transversal)

\( 116\degree + m\angle T = 180\degree \)

\( m\angle T = 180\degree - 116\degree \)

\( \huge \purple {\boxed {m\angle T = 64\degree}} \)

The number of square feet that are there for storing paint is 1/2

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

Area of the table = 3-square-foot

Number of sections = 6 sections

The number of square feet is there for storing paint is calculated as

The number of square feet = Area of the table/Number of sections

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

The number of square feet = 3-square-foot/6

Evaluate the quotient

The number of square feet = 1-square-foot/2

This gives

The number of square feet = 1/2 -square-foot

Hence, the square feet is 1/2

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Complete question

The table shows how a 3-square-foot shelf is split into 6 sections for storing art materials. How many square feet are there for storing paint?

Area (square feet)       Sections

             3                            6

             6                            12

             9                            18

To find the equation of the normal to the given curve at the point (-1,1), you can use the following steps:

Rewrite the given equation in the form "y = mx + b," where m is the slope of the curve and b is the y-intercept.

Find the slope of the curve at the point (-1,1). This can be done by taking the derivative of the equation and evaluating it at x = -1.

The slope of the normal line at the point (-1,1) is the negative reciprocal of the slope of the curve at that point. Calculate this value.

Use the point-slope formula to write the equation of the normal line in the form "y - y1 = m(x - x1)," where (x1, y1) is the point (-1,1) and m is the slope of the normal line.

Substitute the values for x1, y1, and m into the point-slope formula to obtain the final equation of the normal line.

For example, if the given equation is 2x^2 + 2y^2 - 4x + 4y = 12, you can follow these steps:

Rewriting the equation in slope-intercept form, we get: y = -x + 2

Taking the derivative of the equation, we get: y' = -1

The slope of the normal line is the negative reciprocal of the slope of the curve, which is 1/-1 = -1

Using the point-slope formula, we get: y - 1 = -1(x + 1)

Substituting the values into the point-slope formula, we get: y - 1 = -1x - 1

Thus, the equation of the normal line at the point (-1,1) is y - 1 = -1x - 1.

The number of mice that didn't get a tumor is 9 mice out of the 25 mice.

Identify the total mice who did not have any effects or the effects did not include a tumor.

Repiratory failure: 9 mice

Based on this, it can be concluded 9 mice did not have a tumor, while 21 mice hat at least a tumor and some of them had a tumor and respiratory failure.

Note: This question is incomplete; here is the missing section:

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Answer:

5 degrees above Zero = greater than 0 = + 5

3 degrees below Zero = less than 0 = - 3

6 degrees above Zero = greater Than 0 = + 6

2 3/4 degree below Zero = less than 0 = - 2 3/4

-3 ; - 2 3/4 ; + 5 ; + 6

Step-by-step explanation:

5 degrees above Zero = greater than 0 = + 5

3 degrees below Zero = less than 0 = - 3

6 degrees above Zero = greater Than 0 = + 6

2 3/4 degree below Zero = less than 0 = - 2 3/4

The least temperature value implies the coldest while the highest implies the warmest :

Therefore.

Least temperature = - 3 ; then - 2 3/4 ; then + 5 ; then + 6

-3 ; - 2 3/4 ; + 5 ; + 6

The reasonable domain for the function is (b) x > 0

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

The function f(x) = 75x + 100

Where x is the number of hours

f(x) is the total cost.

In this case, the number of hours cannot be negative or 0

This means that the values of x in the function would be x > 0

These values of x are the domain

So, the reasonable domain for the function os (b) x > 0

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Answer:

=0.1428571428751

I hope it's helps you

The histogram is unimodal because it only has one peak point and is only loosely symmetric when flipped across such that the axes of symmetry do not entirely overlap.

The histogram is what?

A histogram is a figure made up of rectangles with widths equal to class intervals and areas proportionate to the frequency of a variable.

A histogram displaying the heights of 300 randomly chosen high school pupils is shown.

Roughly symmetric and unimodal is the form that best fits the distribution of heights.

Histograms that are unimodal have a single peak in their distribution. The graph only contains one peak point, as seen in the figure. However, both sides will not entirely overlap if we use the axis of symmetry to assess the histogram's symmetry. It is therefore roughly symmetric.

The histogram is therefore unimodal since there is only one peak point, and it is generally symmetric because when the histogram is flipped across, the axis of symmetry does not entirely cover both sides.

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Complete question:

The heights of 300 randomly chosen high school pupils are displayed in the histogram below. Which of the following best describes the pattern of the height distribution?

I

A roughly symmetric and unimodal structure; B a roughly symmetric and bimodal structure; C a roughly symmetric and multimodal structure (d) Leftward skewed (e) Rightward skewed

The probability that a comfortable chair in the store is blue is 4%

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

Proportion of blue chairs = 20%

Proportion of orange chairs = 50%

Proportion of black chairs = 30%

Comfortable Blue chairs = 20%

Comfortable non-blue chairs = 5%

The required probability is then calculated as

Probability = Proportion of blue chairs x Comfortable Blue chairs

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

Probability = 20% * 20%

Evaluate

Probability = 4%

Hence, the probability is 4%

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Answer:

W+h=         43+h=

Step-by-step explanation:

THis shows your age plus h the amount of years time. the second expression represents your mothers age plus h.

Answer:

d

Step-by-step explanation:

Simple equation when u break it down: 33 x 24=792 apartments

A building, or edifice, is an enclosed structure with a roof and walls that is standing in one location more or less permanently, such as a house or factory (although there are also portable buildings). Buildings come in a variety of sizes, shapes, and uses, and they have been modified throughout history for a wide range of reasons, including the availability of building materials, weather, land prices, ground conditions, particular uses, prestige, and aesthetic considerations.

given:

new apartments' building =33 floor

apartments on each =24 floor

33*24=792

792 apartments are in the building

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

50 ft above sea level.

Step-by-step explanation:

The exact opposite would just be 50 ft above the starting point.

Answer:

it will be 50 feet above the sea level

The completion of the following table under different depreciation methods is as follows:

Method                           Year 1                     Year 2

Straight line                   $18,000                 $18,000

Units of production      $54,000                 $13,500

Declining balance        $37,600                $22,560

MACRS (5-year class)   $18,800                $30,080

Cost of machine = $94,000

Residual value = $4,000

Depreciable value = $90,000 ($94,000 - $4,000)

Estimated useful life = 5 years

Depreciation expense:

Straight-line method = $18,000 ($90,000/5)

Estimated units of produciton = 100,000

Unit depreciation rate = $0.90

Actual production   Depreciation

Year 1 = 60,000      $54,000 ($0.90 x 60,000)

Year 2 = 15,000      $13,500 ($0.90 x 15,000)

Declining Balance:

Year 1 = $37,600 ($94,000 x 40%)

Year 2 = $22,560 ($94,000 - $37,600) x 40%

MACRS:

Year 1 = $18,800 ($94,000 x 20%)

Year 2 = $30,080 ($94,000 x 32%)

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Answer:

10

Step-by-step explanation:

2(3)²-8

2(9)-9

18-8=10

Answer:

28

Step-by-step explanation:

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:

Sorry i dont know but thanks for The points

Step-by-step explanation:

Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Answer:

its B bud

Step-by-step explanation:

The circumference of the circle has a value of 18.86 units

From the question, we have the following parameters:

Radius, r = 3 units

The circumference of the circle can be calculated using the following circumference formula

C = 2πr

Where

π = 22/7 (a constant)

r = 3

Substitute the known values in the above equation

So, we have the following equation

C = 2 * 22/7 * 3

Evaluate the products

So, we have the following equation

C = 18.86

Hence, the circumference is 18.86 units

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Answer:

the correct choice is A. At the gas station

Step-by-step explanation:

Lucy starts at home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at the post office.

Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.

From the given data:

HP=3;

PG=4;

GH=5;

∠P=90°.

The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.

Answer:

a

Step-by-step explanation:

Answer:

wheres it at?

Step-by-step explanation:

#Everything4Zalo

Using the height and radius given, the surface area of the cylinder is 408.2m²

The surface area of a cylinder is the combined area of its curved surface (lateral surface) and its two circular bases. The formula for the surface area of a cylinder is:

A = 2πrh + 2πr²

where:

In the given question, the data are;

Substituting the value into the formula

A = 2π(5 * 8) + 2π(5)²

A = 408.2m²

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We have proven that if a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle.

Proof: Given that line ℓ is in the plane of circle ⊙ and is perpendicular to radius OX at point X, we want to prove that line ℓ is tangent to the circle.

Assume, for the sake of contradiction, that line ℓ is not tangent to circle ⊙. By definition, this means that line ℓ intersects circle ⊙ at more than one point. Let's call this point of intersection Y.

Since OX is a radius of circle ⊙ and line ℓ is perpendicular to OX at point X, it follows that angle OXℓ is a right angle.

Now, consider the triangle OXY. We know that angle OXY is also a right angle because OX is perpendicular to line ℓ at X. Therefore, angle OXY = 90 degrees.

Let's consider the angles formed at point Y. Since line ℓ intersects circle ⊙ at Y, we have two angles: angle OYX and angle OYℓ.

Now, using the fact that the sum of angles in a triangle is 180 degrees, we can write:

angle OXY + angle OYX + angle OYℓ = 180 degrees.

Substituting the known values, we have:

90 degrees + angle OYX + angle OYℓ = 180 degrees.

Simplifying this equation, we get:

angle OYX + angle OYℓ = 90 degrees.

Since angle OYℓ is a right angle (90 degrees) and angle OYX + angle OYℓ = 90 degrees, it follows that angle OYX must be 0 degrees.

But if angle OYX is 0 degrees, it means that point Y coincides with point X, which contradicts our assumption that line ℓ intersects circle ⊙ at more than one point.

Therefore, our assumption that line ℓ is not tangent to circle ⊙ is false. Hence, line ℓ must be tangent to circle ⊙.

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Answer:

Step-by-step explanation:

Use a simple Equation

Price = Number x Price

So Price = 536.

Since it was 67% off we multiple the price of the original by .67.

So

536 = .67x

Solve for x = 536/.67 = 800

The original Price is $800.

check by multiplying by the sale %.

Answer:

9 roses : 4 daisies : 13 total

Step-by-step explanation:

9 roses

4 daisies

13 total flowers

(13 - 9 = 4)

Answer:

9:4

Step-by-step explanation:

If there are 13 flowers in a vase and 9 of them are roses, all you have to do is subtract 9 from 13. 13-9 is equal to 4, so now you know there are 4 daisies. If you are looking for the ratio between roses and daisies, you just have the ratio 9:4.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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