Find the length of the midsegment.

1. Area of the original patio: 35 ft^2

The original patio has is a rectangle with length = 7 feet and width = 5 feet. The area of a rectangle is given by the product between length and width:

[tex]A=L \cdot W[/tex]

Therefore, since in this case L=7 and W=5, the area of the original patio is

[tex]A=(7 ft)(5 ft)=35 ft^2[/tex]

2. Area of section A: 7x ft^2

Section A is also a rectangle, with length = 7 feet and width = x. Therefore, the area of this section is equal to:

[tex]A=L\cdot W=(7 feet)(x)=7x[/tex]

3. Area of section B: 5x ft^2

Section B is also a rectangle, with length = x and width = 5 feet. Therefore, the area of this section is equal to:

[tex]A=L\cdot W=(x)(5 feet)=5x[/tex]

4. Area of section C:  [tex]x^2 ft^2[/tex]

Section C is a square, with side equal to x. The area of a square is equal to the square of the length of the side:

[tex]A=L^2[/tex]

therefore, in this case, since L = x, the area of this section is

[tex]A=(x)^2 = x^2[/tex]

5. Total area of the new patio using addition: [tex]x^2 +12x+35[/tex] ft^2

The total area of the new patio is equal to the sum of the four areas calculated in the previous sections:

[tex]A=35 +7x +5x+x^2 = x^2 +12x+35[/tex] ft^2

6. Total area of the new patio using multiplication: [tex]x^2+12x+35[/tex]

The total area of the new patio is equal to the product between the length (7+x) and the width (5+x):

[tex]A=(7+x)(5+x)=35+7x+5x+x^2=x^2+12x+35[/tex] ft^2

7. Yes

As we can see by comparing the area calculated in 5. and the area calculated in 6., the two areas are equal.

8. 80 ft^2

We already have the formula for the area of the new patio:

[tex]A=x^2+12x+35[/tex]

If we substitute x=3, we find the value of the area:

[tex]A=(3)^2+12\cdot 3+35=9+36+35=80[/tex]

Answer:

2 + 3i, midpoint is (2,3)

Step-by-step explanation:

we need to find the midpoint between (-1+9i) and B=(5-3i)

To find the midpoint of two points (a+bi)  and (c+di) in a complex plane,  

we apply formula

[tex]\frac{a+c}{2} + \frac{b+d}{2} i[/tex]

A = (-1+9i) and B=(5-3i)

Midpoint for AB is

[tex]\frac{-1+5}{2} + \frac{9+(-3)}{2}i[/tex]

[tex]\frac{4}{2} + \frac{6}{2}i[/tex]

2 + 3i , so midpoint is (2,3)

38% of the bottles Ella collects are plastic and the remaining 62% are glass. Percentage is calculated by dividing the part by the whole and then multiplying by 100.

Ella has 50 bottles in total, out of which 19 are plastic. To find out what percentage of bottles are plastic, we use the formula:

Percentage = (Part/Whole) * 100

Substitute the given values into the formula we get:

Percentage of plastic bottles = (19/50) * 100 = 38%

For the percentage of glass bottles, we first need to find out how many bottles are glass. As the total number of bottles are 50 and 19 of these are plastic, we subtract 19 from 50 to find the number of glass bottles:

Total glass bottles = 50 - 19 = 31

Now we can find out what percentage of bottles are glass using our formula:

Percentage of glass bottles = (31/50) * 100 = 62%

So, 38% of the bottles Ella collects are plastic and 62% are glass.

https://brainly.com/question/30697911

#SPJ3

Answer:

[tex]\frac{a}{6}+3[/tex]

Step-by-step explanation:

We have been given an expression and we are asked to simplify our given expression.

[tex]\frac{3}{2} -\frac{1}{2}a+ \frac{2}{3} a+\frac{3}{2}[/tex]

First of all let us combine like terms.

[tex](\frac{2}{3} -\frac{1}{2})a+(\frac{3}{2}+\frac{3}{2})[/tex]

Now let us have a common denominator for the constant terms of a.

[tex](\frac{2*2}{3*2} -\frac{1*3}{2*3})a+(\frac{3}{2}+\frac{3}{2})[/tex]

[tex](\frac{4}{6} -\frac{3}{6})a+(\frac{3}{2}+\frac{3}{2})[/tex]

Now let us simplify the numerators.

[tex](\frac{4-3}{6})a+(\frac{3+3}{2})[/tex]

[tex](\frac{1}{6})a+(\frac{6}{2})[/tex]

Let us divide 6 by 2.

[tex]\frac{1}{6}a+3[/tex]

[tex]\frac{a}{6}+3[/tex]

Therefore, our expression simplifies to [tex]\frac{a}{6}+3[/tex].

To find the total you would need to multiply the 31.75 by w to get the total amount of his weekly deposits, then that would get added to the initial amount of 249.45

The equation would be 249.45 + 31.75w

249.45 +31.75w

When w = 0, the amount is 249.45. This eliminates the first two choices.

When w = 1, the amount is 31.75 greater than 249.45. This eliminates the last choice.

The remaining choice is the correct one:

... 249.45 +31.75w

It shows the account balance is initially 249.45 and increases with increasing w at the rate of 31.75 per week.

Answer:

√5

Step-by-step explanation:

We suppose the vertices are named clockwise around the top of the cube, then clockwise around the bottom (looking down from above the cube), with vertex E below vertex D. Then line AD is in plane ADEF, and line BM is in plane BCHG.

The distance between the named parallel planes is the distance between the lines. That distance is AB, which is given as √5.

_____

A diagram helps.

Answer:

option 3

Step-by-step explanation:

sin45° = 11/BC

=>1/√2 = 11/BC

=>BC = 11√2

For this case we must find the hypotenuse (H) or the BC side of the rectangular triangle shown in the figure.

We have to:

[tex]Tangent (B) = \frac {Cathet \ opposite} {Cathet \ adjacent}\\Tangent (45) = \frac {11} {BA}[/tex]

By clearing BA we have:

[tex]BA = \frac {11} {Tangent (45)}\\BA = \frac {11} {1}\\BA = 11[/tex]

The Pythagorean theorem, which states:

[tex]BC = \sqrt {(CA) ^ 2 + (BA) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {2 * 11 ^ 2}\\BC = 11 \sqrt {2}[/tex]

Answer:

[tex]BC = 11 \sqrt {2}[/tex]

Option C

Answer:

Independent events

Step-by-step explanation:

We draw a marble, and then put it back.  It was like it never happened.  Then we draw another marble.  The results of the second draw  do not depend on the results of the first draw, so they are independent.

Answer:

We should expect the population to reach 71000 in 1993.

Step-by-step explanation:

If the population will double every 54 years and the population in 1974 was 56000 people, then the function that represents this situation is

[tex]y=56000\cdot 2^{\frac{x}{54}},[/tex]

where x is time in years since 1974.

Nota that in 1974, x=0, then y=56000 and after 54 years the population will be [tex]y=56000\cdot 2^{\frac{54}{54}}=56000\cdot 2=112000.[/tex]

Therefore, you have to calculate x, when y=71000:

[tex]71000=56000\cdot 2^{\frac{x}{54}},\\ \\\dfrac{71}{56}=2^{\frac{x}{54}},\\ \\\dfrac{x}{54}=\log_2\dfrac{71}{56},\\ \\x=54\log_2\dfrac{71}{56}\approx 18.49[/tex]

Thus, we should expect the population to reach 71000 in 1993 (after full 19 years).

Answer:

The number is 12

Step-by-step explanation:

4 times a number is 8 more than 40

Write the equation

4n=40+8

4n =48

Divide each side by 4 to isolate n

4n/4 = 48/4

n = 12

Answer:

its ok to be mad just take your time

and try i bet you can do this just put in some thinking time

Step-by-step explanation:

[tex]\text{Use the Pythagorean theorem:}\\\\AB^2+BC^2=AC^2\\\\AC^2=9^2+12^2\\\\AC^2=81+144\\\\AC^2=225\to AC=\sqrt{225}\\\\AC=15\\\\sine=\dfrac{opposite}{hypotenuse}\\\\\text{We have}\ opposite=12\ \text{and}\ hypotenuse=15.\ \text{Substitute:}\\\\\sin\alpha=\dfrac{12}{15}=\dfrac{12:3}{15:3}=\dfrac{4}{5}[/tex]

Final answer:

In a right triangle with given side lengths and angles, sin α can be calculated using the opposite side and the hypotenuse. The sine function in trigonometry is essential for understanding relationships between angles and sides in triangles. The value of sin α = 3/5.

Explanation:

In this case, we have a right triangle ABC with AB = 9, BC = 12, ∠B = 90°, and ∠A = α.

To find sin α, we use the definition of sine in a right triangle: sin α = opposite/hypotenuse.

Therefore, sin α = opposite/hypotenuse = AB/AC = 9/15 = 3/5.

Answer:

Step-by-step explanation:

The specified set is fairly limited in size, so we can simply check all the choices and see which works:

For n ∈ {1, 2, 3, 4}

... 4n ∈ {4, 8, 12, 16}

Of these values, only the first three {4, 8 12} are less than 16. (16 is equal to 16, not less than 16.)

The corresponding values of n are {1, 2, 3}.

Let the Smaller Number be : S

Let the Larger Number be : L

Given : The Sum of Two Numbers is 52

⇒ S + L = 52 --------------- [1]

Given : The Smaller Number is 16 Less than Larger Number.

It Means if we Add 16 to the Smaller Number, It should be Equal to the Larger Number

⇒ S + 16 = L

⇒ S = L - 16 ------------------ [2]

Substituting Equation [2] in Equation [1], We get :

⇒ L - 16 + L = 52

⇒ 2L = 52 + 16

⇒ 2L = 68

⇒ L = 34

Substituting L = 34 in Equation [2], We get :

⇒ S = 34 - 16

⇒ S = 18

⇒ The Larger Number is 34

⇒ The Smaller Number is 18

The two numbers are 34 and 18; 34 being the larger number and 18 being the smaller number.

This is a common type of problem in algebra called a system of linear equations. We can solve it step by step.

So, the larger number is 34 and the smaller number is 18.

https://brainly.com/question/20379472

#SPJ2

[tex]3(x-3)=(3)(x)+(3)(-3)=3x-9\\\\A.\ 3x-6\qquad NOT\\\\B.\ 3x-8-1=3x-9\qquad YES\\\\C.\ x+2x-3=3x-3\qquad NOT\\\\D.\ x-3+x-3+x-3=3x-9\qquad YES[/tex]

Hi There!

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

Question #1:

A video store is selling previously owned DVDs for 40% off the regular price of $15. What is the sale price of the DVDs?

40% = 0.4

15 * 0.4 = $6 (Discount)

15 - 6 = $9 (Sale Price)

Answer: $9

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

Question #2:

Due to the increased rate of its rent, the Neat Novelties Store had to markup the cost of its helium balloons by 7%. The store’s original cost for a bunch of 8 primary-colored helium-filled balloons was $7.00. What was the selling price after markup?

7% = 0.07

7 * 0.07 = $0.49 (Increase)

7 + 0.49 = $7.49 (Price after Increase)

Answer: $7.49

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

Question #3:

Cecil Home Builders are offering 10% off the option of finishing a basement on all the new homes they are currently building in the Miller Falls Subdivision. The original cost for the finished basement option is $12,000. What is the cost to the buyer after the discount?

10% = 0.1

12,000 * 0.1 = $1,200 (Discount)

12,000 - 1,200 = $10,800 (Price after Discount)

Answer: $10,800

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

Hope This Helps :)

Answer:

x = 2

Step-by-step explanation:

[tex]11^{2x}=14641\\11^{2x}=11^4\\2x = 4\\x = 2[/tex]

Answer:

225 people.

Step-by-step explanation:

It is 225 people because if you imagine that those 250 people are all made up of groups of ten, there are 25 groups. One person in each group does not prefer David Bright's and there are 25 groups so there are 25 people in the group of 250 people that do not prefer David Bright's. 250-25=225 people.

1 27/28 ≈ 1.964 gallons/hour

You want gallons in the numerator of your unit rate, but that unit is in the denominator of the mileage rate. So, the computation must involve division by 28 mpg. Hours is already in the denominator of 55 mph, so the computation will involve multiplication by that rate.

... (55 mi/h)/(28 mi/gal) = (55 mi/h)·(1 gal/(28 mi)) = 55/28 gal/h

... = 1 27/28 gal/h

Final answer:

To calculate the gas usage per hour, divide the speed of 55 mph by the car's fuel efficiency of 28 mpg, resulting in approximately 1.9643 gallons of gas used per hour.

Explanation:

To determine the amount of gas used every hour by a car that gets 28 miles per gallon (mpg) and is travelling at 55 miles per hour (mph), we can use unit analysis as follows:

Therefore, the car uses about 1.9643 gallons of gasoline per hour when driving at a constant speed of 55 mph.

The axis of symmetry is x=-3 and the minimum or maximum y value is 5.

The vertex is the extreme point of the quadratic function. The graph is left/right symmetrical about the vertex, so the x-value defines the axis of symmetry. The y-value is the extreme, the maximum or minimum.

_____

Comment on the attachment

The graph shows two quadratic functions (red, blue), each with its vertex at (-3, 5). You can see that the line x=-3 is the axis of symmetry of each of them. You can also see that y=5 is the extreme value of the function (maximum or minimum).

The confidence interval for confidence level of [tex]1-\alpha[/tex] is

[tex]\left(\overline x-Z_{\alpha/2}\dfrac\sigma{\sqrt n},\overline x+Z_{\alpha/2}\dfrac\sigma{\sqrt n}\right)[/tex]

where [tex]\overline x[/tex] is the sample mean, [tex]Z_{\alpha/2}[/tex] is the critical value for the given confidence level, [tex]\sigma[/tex] is the standard deviation of the population, and [tex]n[/tex] is the sample size. The margin of error is the [tex]Z_{\alpha/2}\dfrac\sigma{\sqrt n}[/tex] term.

a) For a confidence level of [tex]1-\alpha=0.90[/tex], we have [tex]Z_{\alpha/2}=Z_{0.05}\approx1.64[/tex]. So in order to have a margin of error of at most 25 points, we have

[tex]1.64\dfrac{250}{\sqrt n}=25\implies n\approx268.96[/tex]

so Raina should collect a sample of at least 269 students.

b) A confidence interval with a higher confidence level would more closely approximate and reflect the population, so it stands to reason that Luke should collect a larger sample than Raina to meet his 99% confidence spec.

c) For a confidence level of [tex]1-\alpha=0.99[/tex], we have [tex]Z_{\alpha/2}=Z_{0.005}\approx2.58[/tex]. Then the margin of error would at most satisfy

[tex]2.58\dfrac{250}{\sqrt n}=25\implies n\approx665.64[/tex]

so that Luke should collect a sample of at least 666 students.

To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula: n = (z * σ) / E. For Raina's 90% confidence interval with a margin of error of 25, she should collect a sample size of 17. Luke's sample size for a 99% confidence interval should be larger than Raina's, and he should collect a minimum sample size of 26.

To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula:

n = (z * σ) / E

Where:
n = sample size
z = z-score corresponding to the desired confidence level
σ = standard deviation of the population
E = margin of error

(a) To find the sample size for Raina's 90% confidence interval with a margin of error of 25, we plug the values into the formula:

n = (1.645 * 250) / 25 = 16.45

Since sample sizes must be whole numbers, Raina should collect a sample size of 17.

(b) Luke's 99% confidence interval will require a larger sample size because the z-score for 99% confidence is larger than for 90% confidence. Therefore, without calculating the actual sample size, we can determine that Luke's sample size should be larger than Raina's.

(c) To calculate the minimum required sample size for Luke's 99% confidence interval, we use the same formula and plug in the values:

n = (2.576 * 250) / 25 = 25.76

Rounding up, Luke should collect a minimum sample size of 26.

https://brainly.com/question/34700241

#SPJ3

Answer:

39

Step-by-step explanation:

Use the Pythagorean theorem! So 15^2+36^2=x^2. So x^2=1521 or x=39

Answer:

The correct option is D.

Step-by-step explanation:

It is given that events X and Y are two independent events.

Two events are called independent events if the occurrence of one does not affect the probability other. It means

[tex]P(X\text{ and }Y)=P(X)\cdot P(Y)[/tex]

[tex]P(X\cap Y)=P(X)\cdot P(Y)[/tex]          ..... (1)

Therefore option C is correct.

We know that

[tex]P(X|Y)=\frac{P(X\cap Y)}{P(Y)}[/tex]

Using equation (1),

[tex]P(X|Y)=\frac{P(X)\cdot P(Y)}{P(Y)}[/tex]

[tex]P(X|Y)=P(X)[/tex]

Therefore option A is correct.

We know that

[tex]P(Y|X)=\frac{P(X\cap Y)}{P(X)}[/tex]

Using equation (1),

[tex]P(Y|X)=\frac{P(X)\cdot P(Y)}{P(X)}[/tex]

[tex]P(Y|X)=P(Y)[/tex]

Therefore option C is correct.

Since options A, B and C are correct, therefore we can say that correct option is D.

Final answer:

If events X and Y are INDEPENDENT, then option C) P(X and Y) = P(X) x P(Y) is correct.

Explanation:

If events X and Y are INDEPENDENT, then option C) P(X and Y) = P(X) x P(Y) is correct.

For two events to be independent, the probability of their intersection (P(X and Y)) must be equal to the product of their individual probabilities (P(X) x P(Y)).

In other words, if X and Y are independent events, the chance of both X and Y occurring is equal to the chance of X occurring multiplied by the chance of Y occurring.

Answer:

13 weeks

Step-by-step explanation:

65=5w

w=65/5

w=13

Final answer:

It will take Mark 13 weeks to save $65 for the skateboard by saving $5 each week.

Explanation:

Mark wants to buy a skateboard that costs $65. He plans to save $5 per week. To calculate how many weeks it will take him to save $65, we divide the total cost of the skateboard by the amount Mark can save per week.

Here's the calculation:

Total cost of the skateboard: $65

Therefore, it will take Mark 13 weeks to save enough money to buy the skateboard.

Look for any interval where the curve is going uphill as you read it from left to right. The interval your teacher will want is the x interval that corresponds to this upward motion.

A. -2

D. 2

"Expansion" means the magnitude of the scale factor is more than 1. Your choices for that are -2 and 2.

(0.75 and |-0.75| are less than 1.)

Answer: A. −2​  and D. 2

Step-by-step explanation:

A scale factor (k) is number which is used to scale a figure.

It is basically used to either reduce or enlarge the size of the figure

A dilation is transformation which uses scale factor to produce the images of same shape as original but of different size.

From the given options , |-2|>1 and |2|>1 where as |-0.75|=0.75<1 and |0.75|<1

Therefore the scale factors produce a expansion under a dilation of the original image are : -2 and 2.

Hence, the correct options are A. −2​  and D. 2  .

Answer:

4 1/2

Step-by-step explanation:

The point is marked at -4 1/2 on the number line. The distance from there to the origin is 4 1/2 units.

(Distances and lengths are always positive—as are values derived from them, such as perimeter or area.)

The distance from 0 to any given point P on a number line is simply the absolute value of the point's coordinate.

The distance from a point to zero on a number line is determined by the absolute value of the point's coordinate. For example, let's say Point P is situated at 5 on a number line. The distance from 0 to Point P would then simply be the absolute value of 5, which is 5 units.

Another example could be if Point P is located at -3 on the number line. In this case, the distance from 0 to Point P is the absolute value of -3, which again, equals 3 units.

So basically, the distance from 0 to any point P on a number line is just the absolute value of the coordinate of that point.

https://brainly.com/question/34827704

#SPJ3