Math question I need help with:

The area of the parallelogram in the figure is given as follows:

A = 39.96 in².

The area of a parallelogram is given by the multiplication of the base of the parallelogram by the height of the parallelogram, that is:

A = bh.

The parameters for this problem are given as follows:

h = 3.7 in, b = 10.8 in.

Multiplying the base of the parallelogram by the height of the parallelogram, the area is given as follows:

A = 10.8 x 3.7

A = 39.96 in².

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a) The variables are the variable unit cost of candles and the fixed cost of shipping.

b) The information given in the question include the total costs for 4 candles and 12 candles, including their shipping costs.

c) An equation representing the situation is given as

d) Allie can get 18 candles for $60.

An equation is a mathematical statement showing that two or more algebraic expressions are equal or equivalent.

Algebraic expressions combine variables, values, constants, and numbers without the equal symbol (=), but they use the mathematical operands.

The total cost for ordering 4 candles = $35

The total cost for ordering 12 candles = $49

The difference = 8 candles = $14

Unit cost of candles = $1.75 ($14 ÷ 8)

Shipping (fixed) cost for the first order = $28 ($35 - $1.75 x 4)

Shipping (fixed) cost for the second order = $28 ($49 - $1.75 x 12)

For ordering candles for $60, the number of candles Allie can get = 18 ($60 - $28) ÷ $1.75

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The inequality for the shaded region shown in the figure is; y ≥  x^2 - 1

We can see that the shaded region seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)

Then:

y ≥ ax^2 + bx + c

where ax^2 + bx + c is the general quadratic equation.

Now to find the equation for the parabola:

f(x) = ax^2 + bx + c

We also can see that the vertex of the parabola is at the point (0, -1)

This means

f(0) = -1 = a0^2 + b0 + c

     -1 = c

c = -1

Then:

f(x) = ax^2 + bx - 1

Now we can see at the graph again, to see that the zeros of the parabola are at +1 and -1

Which means that:

f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1

f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1

Then we have two equations:

a + b - 1 = 0

a - b - 1 = 0

b = 0

these equations become:

a - 1 = 0

a - 1 = 0

Then solving for a, a = 1

Then the quadratic equation is:

f(x) = 1*x^2 + 0*x - 1

f(x) = x^2 - 1

And the inequality is y ≥  x^2 - 1

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The requried measure of the hypotenuse of the given right triangle is 37.

The hypotenuse of the right angle triangle can be evaluated by Pythagoras' theorem, which states that the sum of squares of the legs of a right triangle is equal to the square of the third side.

Hypotensue² =  12²+35²
Hypotensue = √1369 = 37

Thus, the requried measure of the hypotenuse of the given right triangle is 37.

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The normal to the parabola[tex]z = x^2 + y^2[/tex] at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20).

To find the normal to the paraboloid[tex]z = x^2 + y^2[/tex] at points (3, 3, 18), we first need to find the slope of the surface at that point. The gradient vector is given by

[tex]∇f(x,y,z) = < 2x, 2y, -1 >[/tex]

So the gradient vector at points (3, 3, 18) is

∇f(3, 3, 18) = <6, 6, -1>

This gradient vector is orthogonal to the plane tangent to the surface at the point (3, 3, 18). So the surface normal at this point is parallel to the gradient vector and can be expressed as

x = 3 + 6t

y = 3 + 6t

z = 18 - t

To discover where this line converges the parabola once more, we ought to substitute the x, y, and z equations into the parabola's condition. 

[tex]z = x^2 + y^2[/tex]

So it looks like this:

[tex]18 - t = (3 + 6t)^2 + (3 + 6t)^2[/tex]

[tex]18 - t = 18t^2 + 36t + 18[/tex]

[tex]0 = 18t^2 + 37t[/tex]

t=0 or t=-37/18

The value t = 0 corresponds to the starting point (3, 3, 18), so we are interested in the second value t = -37/18. Substituting this value into the normal equation gives:

x = 3 + 6(-37/18) = -1/3

y = 3 + 6(-37/18) = -1/3

z=18-(-37/18)=360/18=20

therefore, the normal to the parabola [tex]z = x^2 + y^2[/tex] at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20). 

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Step-by-step explanation:

First, use law of SINES to find QS :

11.7 / sin 28  = QS / sin95

      shows QS = 24.83 cm

Now use law of COSINES to find QR

QR^2 = 10.2^2 + 24.83^2 - 2 ( 10.2)(24.83) cos ( 110)

   shows QR = 29.9 cm

The area of the small triangle is equal to 25 ft².

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

In Mathematics and Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:

(Scale factor of dimensions)² = Scale factor of area

Therefore, the area of the small triangle can be calculated as follows;

Area of small triangle = (12/28)² × 135

Area of small triangle = 24.80 ≈ 25 ft².

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Using similar side theorem and taking the ratios of similar sides, the value of AD is 3.6 units

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

In this problem, we can use the similar side theorem by taking ratios of similar sides.

4.5 / 5 = AD / 4

Cross multiply both sides

AD = (4.5 * 4) / 5

AD = 18/5

AD = 3.6

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The probability that exactly 2 out of 4 children will be colorblind and the other 2 will have normal color vision, assuming a probability of 1/16 for colorblindness, is approximately 0.0206 or 2.06%.

We have,

To calculate the probability, we can use the binomial probability formula:

P(2 colorblind and 2 normal) = (4 choose 2) * (1/16)² * (15/16)²

Using the formula, we can calculate:

P(2 colorblind and 2 normal) = (4! / (2! * (4-2)!)) * (1/16)² * (15/16)²

= (6) * (1/256) * (225/256)

= 1350/65536

≈ 0.0206

Therefore,

The probability that exactly 2 out of 4 children will be colorblind and the other 2 will have normal color vision, assuming a probability of 1/16 for colorblindness, is approximately 0.0206 or 2.06%.

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The complete question:

What is the probability that, if a couple with no known family history of colorblindness has 4 children, exactly 2 of them will be colorblind and the other 2 will have normal color vision, assuming that the probability of having a colorblind child is 1/16 due to a rare genetic mutation?

Answer:

The formula for ordinary interest is:

I = P * r * t

where:

I = the interest

P = the principal

r = the interest rate per year

t = the time in years

In this case, the principal is $12,500, the interest rate is 4%, and the time is 292/360 years (since there are 360 days in a year according to the problem statement). Therefore, we have:

t = 292/360 = 0.811111111

I = 12500 * 0.04 * 0.811111111 = 405.5555555

To find the maturity value, we add the interest to the principal:

M = P + I = 12500 + 405.5555555 = 12905.56

Therefore, the maturity value of the promissory note is $12,905.56 rounded to the nearest cent.

Answer:  Hence sum of interior angles of a convex 16-sided polygon would be 180∘×(16−2)=180∘×14=2520∘

Step-by-step explanation:

Answer:

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

To find the sum of the interior angles of a 16-sided polygon, you can use the formula:

In our case, n = 16.

Substitute the value of n into the formula:

The matching choice is D.

Applying the inscribed angle theorem, we have:

a. x = 55° b. x = 60°  c. x = 92°    d. x = 84°

These theorem states that:

Inscribed angle measure = 1/2(central angle) or measure of intercepted arc.

Intercepted arc measure = central angle measure.

Therefore, we have:

a. x = 180 - 35 - 90 [tangent theorem]

x = 55°

b. x = 1/2(120) [inscribed angle theorem]

x = 60°

c. x = 2(46) [inscribed angle theorem]

x = 92°

d. m(FE) = 2(42) = 84°

m(EB) = 180 - FE = 180 - 84

m(EB) = 96°

m(AB) = 180 - m(EB) = 180 - 96

m(AB) = 84°

x = m(AB) = 84° [central angle theorem]

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Starting with the given equation:

4x² - 30 = 34

Adding 30 to both sides:

4x² = 64

Dividing both sides by 4:

x² = 16

Taking the square root of both sides:

x = ±4

Therefore, the solutions to the equation are x = 4 and x = -4.

Checking each option:

A. x = -√√8 is not a solution.

B. x = 4 is a solution.

C. x = -8 is not a solution.

D. x = √√√8 is not a solution.

E. x = -4 is a solution.

F. x = 8 is not a solution.

Therefore, the solutions to the equation are x = 4 and x = -4, which are options B and E.

The calculated value of the area of the shaded region is 60.5 square meters

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

The figure

Where we have the shaded region to be the gray region

Also, we have

Shaded region = 2 triangles with base = 1/2 * 11 and height = 11

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

Area = 2 * area of 1 triangle

So, we have

Area = 2 * 1/2 * 11 * 1/2 * 11

Evaluate

Area = 60.5

Hence, the area of the shaded region is 60.5 square meters

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Answer:

Step-by-step explanation: Hello! You know the area of a right triangle shown is 24 square feet. The formula for area of a triangle is A = 1/2(b)(h).

24 can be substituted for A.

24 = 1/2(b)(h).

From here, I will need to see the triangle shown. If you post an image of the triangle with this, I might be able to come back and help you.

Good luck!

Answer:

  14 inches

Step-by-step explanation:

You want the diameter of a circle that has a circumference of 43.96 inches.

The equation for the circumference of a circle is ...

  C = πd

Then the diameter is ...

  d = C/π

  d = (43.96 in)/3.14 = 14 in

The circle's diameter is 14 inches.

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The probability that Tally is on the red team would be 1/4

Probability means a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Tally's teacher divides her class of 16 students into 4 equally sized teams: red team, yellow team, green team and the blue team.

Therefore, the probability that Tally is on the red team will be;

P(E) = Number of favorable outcomes / total number of outcomes

P(E) = Number of teams / total number of students

P(E) = 4/16

P(E) = 1/4

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To find the actual height of the tower, we need to use the scale factor. The ratio of the scale is 1.5 inches to 10 feet, which can be simplified to 1 inch to 6.67 feet (by dividing both sides by 1.5).

Therefore, the actual height of the tower in feet would be:

24 inches × (1 inch ÷ 6.67 feet) = 3.6 feet

So the actual height of the tower is 3.6 feet.

For a sample of room temperature during winter, an upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees is equals to the 0.25.

For a sample of temperature during winter, Average temperature of room

= 70 degree

Standard deviations = 2 degrees

We have to determine upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees. According to chebyehev's theorem, [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex].

here , σ = 2 , μ = 70, kσ = 4

=> k = 2

So, the required upper bound of probability is [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex]

≤ [tex]\frac{ 1 }{2²} [/tex]

≤ [tex]\frac{ 1 }{4} [/tex]

= 0.25

Hence, required upper bound value is 0.25.

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Answer:

Yes, 86.76 is a rational number. A rational number is any number that can be expressed as a ratio of two integers (where the denominator is not zero).

86.76 can be expressed as the ratio of two integers: 8676/100, which can be simplified to 2169/25. Since 2169 and 25 are both integers, and the denominator is not zero, 86.76 is a rational number.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A rational number is any number that can be expressed as the ratio of two integers (i.e., a fraction where the numerator and denominator are both integers).

In this case, we can express 86.76 repeating as the fraction:

8676/100 = 8676 ÷ 100

Simplifying this fraction, we get:

8676/100 = 8676 ÷ 4 ÷ 25 = 2169/25

Since 2169 and 25 are both integers, we have expressed 86.76 repeating as a ratio of two integers, and therefore it is a rational number.

Using A linear equation, It ia found that:

• The equation is: L = 56 + 3d

Where D is representing the number of day crew has worked and L presenting the total length of the road. So let's solve this.

Step by step Explanation:

= L = 56 + 3d

= L = 56 + 3(36)

= L = 54 + 108

= L = 162

The population will exceed 7569 at moments beyond 7.4 years hence from 8 years (to the nearest years)​

Exponential function is a function of the form f(x) = a e^(kt)

Considering the given problem,

the initial value = a

the base factor = k

the exponents in time = t

Information given in the problem are

solving for the time wen the population will exceed 7569

7569 = 1600 x e(0.21 * t)

7569 / 1600 = e(0.21 * t)

take ㏑ of both sides

㏑ (7569 / 1600) = ㏑ e(0.21 * t)

㏑ (7569 / 1600) = 0.21t

t = ㏑ (7569 / 1600) / 0.21

t = 7.40

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The null hypothesis would be that the mean tenure for CEO's is 8 years, while the alternative hypothesis would be that the mean tenure for CEO's is less than 8 years. This would be formulated as: Null hypothesis: μ = 8 years
Alternative hypothesis: μ < 8 years

The sample mean of 5.8 years is lower than the claimed mean of 8 years, suggesting that the shareholders' claim may not be valid. To test the validity of their claim, a hypothesis test can be conducted using the sample data and assuming a normal distribution of CEO tenure in the population.

To challenge the validity of the claim made by the shareholders, you can formulate a hypothesis test using the following steps:

Step 1: State the null hypothesis (H0) and alternative hypothesis (H1)
- Null hypothesis (H0): The population mean tenure for a CEO is at least 8 years (μ ≥ 8)
- Alternative hypothesis (H1): The population mean tenure for a CEO is less than 8 years (μ < 8)

Step 2: Collect and summarize the sample data
- Sample size (n): 52 companies
- Sample mean (x): 5.8 years
- Sample standard deviation (s): 5.4 years

Step 3: Since the population standard deviation is unknown and the sample size is large (n > 30), we can assume the sampling distribution is normally distributed and use a t-test to perform the hypothesis test.

Note that we cannot directly test the validity of the shareholders' claim based on the sample data alone. The hypothesis test will help determine whether there is enough evidence to reject the null hypothesis and support the alternative hypothesis, which would then challenge the claim made by the shareholders.

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The dilated points are:

G' = (1, 1)

H' = (1, 3)

J' = (4, 1)

Option C is the correct answer.

We have,

To dilate with a scale factor of 1/3, we need to multiply the coordinates of each point by 1/3.

The new coordinates of G will be:

x-coordinate: 3 × 1/3 = 1

y-coordinate: 3 × 1/3 = 1

So, the new coordinates of G are (1, 1).

The new coordinates of H will be:

x-coordinate: 3 × 1/3 = 1

y-coordinate: 9 × 1/3 = 3

So, the new coordinates of H are (1, 3).

The new coordinates of J will be:

x-coordinate: 12 × 1/3 = 4

y-coordinate: 3 × 1/3 = 1

So, the new coordinates of J are (4, 1).

Therefore,

The dilated points are:

G' = (1, 1)

H' = (1, 3)

J' = (4, 1)

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The probability of winning first, second, third, and fourth prizes in specific order by Bo, Colleen, Jeff, and Rohini is equals to 0.00000020.

Number of people enter in contest = 49

The number of ways to choose the first prize winner is 49.

Since the first prize winner is no longer eligible.

The number of ways to choose the second prize winner is 48.

Since the first and second prize winners are no longer eligible.

The number of ways to choose the third prize winner is 47  .

Since the first, second, and third prize winners are no longer eligible.

and the number of ways to choose the fourth prize winner is 46 .

The total number of ways to choose four prize winners out of 49 entrants is,

= 49 x 48 x 47 x 46

= 5085024

However, probability of Bo, Colleen, Jeff, and Rohini winning the first, second, third, and fourth prizes in that specific order.

The probability of this happening is,

(1/49) x (1/48) x (1/47) x (1/46)

= 1/5085024

= 0.0000001967

=  0.00000020

Therefore, probability of Bo, Colleen, Jeff, and Rohini winning first, second, third, and fourth prizes in specific order is  0.00000020.

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The probability that the Players are assigned to go in the order given can be found to be 0.833 %.

First, we need to find out the number of ways that the baseball players can be assigned to go and this is:

= 5 × 4 × 3 × 2 × 1 = 120 ways

However, there is only one way in which Player A is assigned to go 1st, Players B is assigned to go 2nd, Player C is assigned to go 3rd, Player D is assigned to go 4th, and player E is assigned to go 5th.

The probability is therefore:

= 1 / 120

= 0.833 %.

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If each bag of chips costs $1 less than a granola bar, and jack buys 2 more items than jane buys, Jack buys 15 bags of chips

Let's assume that Jack buys x bags of chips and Jane buys y granola bars. We know that they each spend $24 on snacks, so we can set up the following equation:

x*(price of one bag of chips) + y*(price of one granola bar) = $24

We also know that each bag of chips costs $1 less than a granola bar, so we can write:

(price of one bag of chips) = (price of one granola bar) - $1

Substituting this into the first equation, we get:

x*((price of one granola bar) - $1) + y*(price of one granola bar) = $24

Expanding and simplifying, we get:

x*(price of one granola bar) + y*(price of one granola bar) - x = $24

We also know that Jack buys 2 more items than Jane, so we can write:

x = y + 2

Substituting this into the previous equation, we get:

(y + 2)(price of one granola bar) + y(price of one granola bar) - (y + 2) = $24

Simplifying, we get:

2*(price of one granola bar) + y = $26

We can now solve for y:

(price of one granola bar) = ($26 - y)/2

Substituting this back into the equation for x, we get:

x = y + 2

x = (26 - y)/2 + 2

Simplifying, we get:

x = (28 - y)/2

We know that x and y must be whole numbers, so we can test different values of y until we find one that makes x a whole number. Starting with y = 2, we get:

(price of one granola bar) = ($26 - 2)/2 = $12

2*(price of one granola bar) + y = $26

2*($12) + 2 = $26

Therefore, Jack buys 15 bags of chips (x = (28 - y)/2 = (28 - 2)/2 = 15) and Jane buys 13 granola bars (y = 2).

In summary, Jack and Jane each spend $24 on snacks. Jack buys bags of chips and Jane buys granola bars. Each bag of chips costs $1 less than a granola bar, and Jack buys 2 more items than Jane buys. We can solve for the number of bags of chips Jack buys by setting up and solving equations based on these facts. We find that Jack buys 15 bags of chips.

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Using probability, we can find:

Probability of getting zero heads = 0.25

Probability of getting 1 head = 0.5

Probability of getting 2 heads = 0.25

The ability of an event to occur is known as probability. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number between 0 and 1. Probability has been introduced in mathematics to predict how likely events are to occur.

Here in the question,

2 coins are flipped at the same time.

The possible outcomes are as follows:

H H

H T

T H

T T

So, there are 4 outcomes of this event.

Now,

Probability that there are 0 heads in the event:

One event there is 0 heads = T T

Probability = 1/4

= 0.25

Now, events with one head are:

H T and T H

So,

Probability = 2/4

= 0.5

In the final event, we have 2 heads in one event = H H

So,

Probability = 1/4

= 0.25

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Answer:

24

Step-by-step explanation:

We can simplify this equality by squaring both sides.

[tex](\sqrt{x})^2 < 5^2[/tex]

[tex]x < 25[/tex]

We know that the greatest integer less than 25 is 24. Therefore, this is the greatest integer solution to the inequality.