) the supplement of an angle is thirty more than twice the angle. find the measure of the angle and its supplement. answer

Answer:

422 in.2

Step-by-step explanation:

Substitute the measurements of the rectangular prism into the formula SA = 2(lw) + 2 (lw) + 2(lh): 2(13)(7) + 2(6)(7) + 2(13)(6) = 422 in2.

Jeanine can create 43758 different floral arrangements using 7 flowers out of the 18 available. This was calculated using the mathematical concept of combinations.

To find the number of different selections of 7 flowers Jeanine can make out of 18, we need to use the mathematical concept of combinations. In this context, the combination formula is used, which is: C(n, k) = n! / [k!(n-k)!]

Where n is the total number, k is the number chosen, and '!' stands for factorial, which is the product of all positive integers less than or equal to the number. Thus, the number of ways Jeanine can choose 7 flowers out of 18 is calculated as follows: C(18, 7) = 18! / [7!(18-7)!] = 43758. Therefore, there are 43758 different ways Jeanine can create floral arrangements using 7 flowers out of the 18 available.

It should be noted that the color of the flowers does not influence the number of combinations if she intends to select any 7 flowers irrespective of their color.

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Answer:

462

Step-by-step explanation:

The error interval for a number x rounded to 12.3 is 12.25 ≤ x < 12.35, indicating the range that x could be before rounding to one decimal place.

If a number x, rounded to 1 decimal place, is 12.3, the error interval for x defines the range of values that x could be in order to round to 12.3. Since the value is rounded to one decimal place, we consider half of a tenth (0.05) on either side of 12.3 to find the error interval. Hence, the lower bound of the error interval would be just below 12.3 (12.25), and the upper bound would be just before it would round up to the next tenth (12.35).

The error interval for x can be written as: 12.25 ≤ x < 12.35.

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Error interval for [tex]\( x \)[/tex] rounded to 1 decimal place as 12.3 is from 12.25 to 12.35.

To find the error interval for the number [tex]\( x[/tex], rounded to 1 decimal place as 12.3, we need to consider the possible range of values that [tex]\( x \)[/tex] could have been before rounding.

1. Lower Bound: To find the lower bound, we need to consider the smallest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The smallest value that would round up to 12.3 is 12.25.

2. Upper Bound: Similarly, to find the upper bound, we need to consider the largest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The largest value that would round down to 12.3 is 12.35.

So, the error interval for [tex]\( x \)[/tex] is from 12.25 to 12.35.

Answer:

The answer should be C.

The term 'perpendicular bisector' means QS cuts PR into two equal parts at a 90-degree angle. If PR is '2x', then each half is 'x'. To solve for x, we would need data about the lengths of the line segments.

Given that QS is the perpendicular bisector of PR, it implies two things. Firstly, QS intersects PR at a 90-degree angle. Secondly, QS splits PR into two equal segments. So, if PR is represented as '2x', then PQ and QR are both 'x'.

Unfortunately, missing information prevents a specific solution for x. We'd need additional data about the lengths of these line segments to solve the equation for x. For instance, if PR = 10, then '2x = 10' which gives us 'x = 5'.

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[tex]\[\{(3 + \sqrt{5}, 3 - \sqrt{5})}\][/tex] is the one pair of real numbers [tex]\((x, y)\)[/tex] that satisfies the given equations.

Given the system of equations:

[tex]\[x + y = 6\][/tex]

[tex]\[x^3 + y^3 = 144\][/tex]

We can use the identity for the sum of cubes:

[tex]\[x^3 + y^3 = (x + y)(x^2 - xy + y^2)\][/tex]

Substitute [tex]\(x + y = 6\):[/tex]

[tex]\[x^3 + y^3 = 6(x^2 - xy + y^2)\][/tex]

Given [tex]\(x^3 + y^3 = 144\)[/tex], we substitute this into the equation:

[tex]\[144 = 6(x^2 - xy + y^2)\][/tex]

Divide both sides by 6:

[tex]\[24 = x^2 - xy + y^2\][/tex]

Next, we use the square of the sum:

[tex]\[(x + y)^2 = x^2 + 2xy + y^2\][/tex]

Substitute [tex]\(x + y = 6\):[/tex]

[tex]\[6^2 = x^2 + 2xy + y^2\][/tex]

[tex]\[36 = x^2 + 2xy + y^2\][/tex]

We already have [tex]\(x^2 - xy + y^2 = 24\)[/tex]. Let’s denote the first and second equations:

1. [tex]\(x^2 - xy + y^2 = 24\)[/tex]

2. [tex]\(x^2 + 2xy + y^2 = 36\)[/tex]

Subtract the first equation from the second equation:

[tex]\[(x^2 + 2xy + y^2) - (x^2 - xy + y^2) = 36 - 24\][/tex]

[tex]\[3xy = 12\][/tex]

[tex]\[xy = 4\][/tex]

Now, we have two equations:

1. [tex]\(x + y = 6\)[/tex]

2. [tex]\(xy = 4\)[/tex]

We solve these equations using the quadratic formula. Consider the quadratic equation:

[tex]\[t^2 - (x+y)t + xy = 0\][/tex]

[tex]\[t^2 - 6t + 4 = 0\][/tex]

Solve for [tex]\(t\)[/tex] using the quadratic formula [tex]\(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):[/tex]

[tex]\[t = \frac{6 \pm \sqrt{36 - 16}}{2}\][/tex]

[tex]\[t = \frac{6 \pm \sqrt{20}}{2}\][/tex]

[tex]\[t = \frac{6 \pm 2\sqrt{5}}{2}\][/tex]

[tex]\[t = 3 \pm \sqrt{5}\][/tex]

Thus, the solutions for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are:

[tex]\[x = 3 + \sqrt{5}, \quad y = 3 - \sqrt{5}\][/tex]

or

[tex]\[x = 3 - \sqrt{5}, \quad y = 3 + \sqrt{5}\][/tex]

The resulting expression of the given logarithmic function will be 4xlog2 = log14.

Given the logarithmic expression below:
[tex]2^{4x}=14[/tex]

We are to determine which of the equations would be equivalent to his original expression.

Taking the logarithm of both sides, we will have:

[tex]log2^{4x}=log14\\4xlog2=log14\\[/tex]

From the solution, we can see that the resulting expression will be 4xlog2 = log14.

Here is your answer:

All you need to do is keep the 29 and then add a hundred because of how many 9's there are.

Also, you could see that:

[tex] .29999999999 \neq \frac{29999999999}{100000000000} [/tex]

Which would also mean that:

[tex] \frac{29999999999}{100000000000} \neq \frac{29}{100} [/tex]

Therefore the answer is "29/100."

Hope this helps!

Answer:

13/46

Step-by-step explanation:

Mrs. Peter arrives 5 minutes before Mr. Peter

To find who arrives first we first need to find the speed and time they require to arrive.

Given : From Boston to Worcester

            Mr. Peter takes [tex]\rm time=30 \; minutes \; and \;speed= 60 miles /hr[/tex]

            Mrs. Peter takes [tex]\rm speed=90 miles/hr[/tex]

We will now calculate Mr. Peters speed,

[tex]\rm 60 \dfrac{miles}{h} \times \dfrac{h}{60minutes}=\dfrac{mile}{min}[/tex]

To find the distance, we will use distance formula

[tex]\rm Distance=speed\times time[/tex]

Here,given that the Mr Peters speed is [tex]\rm 60 miles /hr[/tex] and time is [tex]\rm 30 minutes[/tex]so by distance formula we will find distance of Mr. Peter

[tex]\rm Distance=\dfrac{mile}{min} \times 30 minutes[/tex]

[tex]\rm Distance= 30 miles[/tex]

Similarly, we will now calculate Mrs. Peters speed,

[tex]\rm \dfrac{90miles}{h} \times \dfrac{h}{60minutes}=1.5\times \dfrac{miles}{min}[/tex]

by the given informations we know both covers the same distance

[tex]\rm ie. \;30 miles[/tex]

we will now find distance of Mrs. Peter

[tex]\rm Distance=speed\times time\\ 30miles=1.5\dfrac{miles}{min} \times time\\ time=\dfrac{30miles}{1.5\dfrac{miles}{min}}\\\\ time=20 minutes[/tex]

Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.

[tex]\rm time=20 minutes+ 5 minutes\\ time=25 minutes[/tex]

Therefore, it is clear that Mrs.Peter arrive before Mr Peter by 5minutes.

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Answer:

596 square feet

Answer:

b I did the

Step-by-step explanation:

Answer:

Ruth was out of Portland at 35mph at 7:00 am

so at 9 am, she was 70 miles ahead of Michael

but Michael was 20 miles ahead by 3 pm.

so in 6 hours, he went past Ruth by 90 miles which is 90/6 = 15mph

Michael speed = ruth speed + 15. = 35 + 15 = 50mph

Arithmetic, because the sequence has a common difference. answer on edgenui......

Answer:

C. Either 46.27 miles or 17.43 miles

Answer:
x² + y² = 15

Explanation:

The formula for the equation of a circle is (x - h)² + (y - k)² = r², where the center of the circle is ordered pair (h, k) and r represents the radius (in units).

Now, we plug the given information into the circle equation and simplify.
radius = √15
center (0, 0), h = 0, k = 0

(x - 0)² + (y - 0)² = (√15)²
(x)² + (y)² = (√15)²
x² + y² = 15

The equation of the circle is x² + y² = 15

The equation of the circle with a center at (0,0) and a radius of the square root of 15 is x² + y² = 15. The standard form of the circle equation, (x - h)² + (y - k)² = r², is used with h and k set to 0 to represent the origin.

To write an equation of a circle with the center at the origin (0,0) and a radius of the square root of 15, we use the standard form of the circle equation:

(x - h)² + (y - k)² = r²

Here, (h, k) represents the center of the circle and r is the radius. Since the center of the circle in question is at the origin, h = 0 and k = 0. The given radius is the square root of 15, so we have r = √15. Substituting these values into the standard form gives us the equation:

x² + y² = ( √15 )²

Which simplifies to:

x² + y² = 15

This is the equation for the desired circle centered at the origin with radius √15.

The number of balls in 7th line would be 10.

Given is a pattern as shown in the image.

       a, a + d, a + 2d, a + 3d, ......,

We can write the pattern as -

4, 5, 6, 7, .....

This is a arithmetic progression. We can write the nth term as -

a{n} = a + (n - 1)d

a{7} = 4 + (7 - 1) x 1

a{7} = 4 + 6

a{7} = 10

Therefore, the number of balls in 7th line would be 10.

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The transformation on the graph of y = -2x²- 5 is described as 5 units downward.

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

As per the given information:

The graphs are let f(x) = y = -2x²- 5 and g(x) = y = -2x².

As per the definition, the transformation on the graph can be described as,

-5 < 0.

The graph shifts downward.

Therefore, the graph of y = -2x²- 5 is 5 units down than y = -2x².

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Final answer:

Mathematics and science are foundational to engineering, providing the tools and understanding necessary for the engineering design process. They enable engineers to create models, solve design problems, and innovate, thus influencing education and daily life through engineered products.

Explanation:

Science and mathematics are intimately related, especially in fields such as engineering. Mathematics provides the language and tools for abstract reasoning and quantitative analysis, which are fundamental in engineering. Math is used to create mathematical models that describe physical phenomena and to evaluate the merit of different possible solutions. Science, on the other hand, offers understanding of natural phenomena and constraints that inform engineering solutions. Together, math and science are essential throughout the engineering design process, from conceptualization to detailed design implementation, and in team decision-making.

In high school and college, a strong foundation in math and science courses is crucial for success in engineering education. For instance, courses like thermodynamics, circuits, and fluids—commonly referred to as engineering science courses—are grounded in these basic disciplines. The role of science and mathematics in engineering extends beyond educational prerequisites; they are operational tools that engineers use in their work every day to innovate and create products that improve our lives, such as the pocket radio, cell phones, and computers.

The connections between math, science, and engineering are dynamic and multidimensional. They enable engineers to navigate through the iterative steps of the engineering design process, which include analyzing problems, developing solutions, and optimizing products, often moving nonlinearly as real-world complexities dictate adjustments and refinements.

The answer is actually the second choice 4/25 hope this helps...

Answer:  The correct option is (2) [tex]\dfrac{4}{25}.[/tex]

Step-by-step explanation:  Given that there are 3 green, 4 yellow, 5 blue and 8 pink marbles in a bag. Fernando is going to draw a marble from the bag, replace it, and then draw another marble.

We are to find the probability that Fernando will get a green or blue marble on the first draw and a pink on the second draw.

Let, S be the sample space for the experiment of drawing a marble from  the bag.

Then, n(S) = 3 + 4 + 5 + 8 = 20.

Let E denotes the event of drawing a green or blue marble and F denote the event of drawing a pink marble.

Then, we have

n(E) = 3 + 5 = 8   and   n(F) = 8.

Since the second marble is drawn after replacing the first marble,

so the required probability of Drawing a green or blue marble on the first draw and a pink marble on the second draw is

[tex]P\\\\=P(E)\times P(F)\\\\\\=\dfrac{n(E)}{n(S)}\times \dfrac{n(F)}{n(S)}\\\\\\=\dfrac{8}{20}\times\dfrac{8}{20}\\\\\\=\dfrac{4}{25}.[/tex]  

Thus, the required probability is [tex]\dfrac{4}{25}.[/tex]

Option (2) is CORRECT.