Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?

Answer:

90 planes

Step-by-step explanation:

Take the total number of planes and multiply by the  percentage of planes that took off

120 * 75%

120 * .75

90

Answer:

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Step-by-step explanation:

Quadratic function is given as [tex] f(x) = ax^2 + bx + c [/tex]

Let's find a, b and c:

Substituting (0, 6):

[tex] 6 = a(0)^2 + b(0) + c [/tex]

[tex] 6 = 0 + 0 + c [/tex]

[tex] c = 6 [/tex]

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] 16 = a(2)^2 + b(2) + 6 [/tex]

[tex] 16 = 4a + 2b + 6 [/tex]

[tex] 16 - 6 = 4a + 2b + 6 - 6 [/tex]

[tex] 10 = 4a + 2b [/tex]

[tex] 10 = 2(2a + b) [/tex]

[tex] \frac{10}{2} = \frac{2(2a + b)}{2} [/tex]

[tex] 5 = 2a + b [/tex]

[tex] 2a + b = 5 [/tex] => (Equation 1)

Substituting (3, 33), and c = 6

[tex] f(x) = ax^2 + bx + x [/tex]

[tex] 33 = a(3)^2 + b(3) + 6 [/tex]

[tex] 33 = 9a + 3b + 6 [/tex]

[tex] 33 - 6 = 9a + 3b + 6 - 6 [/tex]

[tex] 27 = 9a + 3b [/tex]

[tex] 27 = 3(3a + b) [/tex]

[tex] \frac{27}{3} = \frac{3(3a + b)}{3} [/tex]

[tex] 9 = 3a + b [/tex]

[tex] 3a + b = 9 [/tex] => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

[tex] 3a + b = 9 [/tex]

[tex] 2a + b = 5 [/tex]

[tex] a = 4 [/tex]

Replace a with 4 in equation 2.

[tex] 2a + b = 5 [/tex]

[tex] 2(4) + b = 5 [/tex]

[tex] 8 + b = 5 [/tex]

[tex] 8 + b - 8 = 5 - 8 [/tex]

[tex] b = -3 [/tex]

The quadratic function that represents the given 3 points would be as follows:

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] f(x) = (4)x^2 + (-3)x + 6 [/tex]

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Answer:

Yes, Rolle's theorem can be applied

There is only one value of c such that f'(c) = 0, and this is c = 1.5 (or 3/2 in fraction form)

Step-by-step explanation:

Yes, Rolle's theorem can be applied on this function because the function is continuous in the closed interval (it is a polynomial function) and differentiable  in the open interval, and f(a) = f(b) given that:

[tex]f(0)=-0^2+3\,(0)=0\\f(3)=-3^2+3\,(3)=-9+9=0[/tex]

Then there must be a c in the open interval for which f'(c) =0

In order to find "c", we derive the function and evaluate it at "c", making the derivative equal zero, to solve for c:

[tex]f(x)=-x^2+3\,x\\f'(x)=-2\,x+3\\f'(c)=-2\,c+3\\0=-2\,c+3\\2\,c=3\\c=\frac{3}{2} =1.5[/tex]

There is a unique answer for c, and that is c = 1.5

Rolle's theorem is applicable if [tex]f(a)=f(b)[/tex] and $f$ is differentiable in $(a,b)$

since it's polynomial function, it's always continuous and differentiable..

and you can easily check that $f(0)=f(-3)=0$

so it is applicable.

now, $f'(x)=-2x+3=0 \implies x=\frac32$

there is only once value (as you can imagine, the graph will be downward parabola)

Answer:

True

Step-by-step explanation:

The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.

Answer:

The largest possible weight of flour is 11.25  pounds.

Step-by-step explanation:

To start with, we will assume that the weight of 1 sack of sugar = x pounds

We will also assume that the weight of 1 sack of flour = y pounds

So, the weight of 2 sacks of sugar = 2 * (x) = 2x

Same thing goes for the weight of 3 sacks of flour  = 3 * (y) = 3y

Supposing that the weight of (2 sacks of sugar + 3 sacks of flour) ≤ 40 pounds

= 2x + 3y ≤ 40............ we'll call that equation 1.

Also, suppose that the weight of ( 1 sack of flour) ≤ 2 sacks of sugar + 5 pounds

= y ≤ 2x + 5........................ we'll call that equation 2

Therefore, we'll solve for the values of x and y in the two equations and we will get:

2x + 3y ≤ 40

y ≤  2x + 5

Now, substitute the value of y into equation 1

2x + 3y ≤ 40 ⇒ 2x + 3(2x +5) =40

⇒ 2x + 6x + 15= 40

⇒ 8x + 15 = 40

⇒ 8x = 25

⇒ x = 25/8

⇒ x = 3.12

x cannot be more than 3.12 pounds, so we solve for y

Putting the value of x into equation 2, we'll get

⇒ 2y + 5 = 2(3.12) + 5

⇒ y = 11.25 pounds.

So, n cannot be more than 11.25 pounds

Answer:

x = 35, y = 15°

Step-by-step explanation:

6. Since ΔRST ≅ ΔXYZ, RT = XZ because of CPCTC which means:

x + 21 = 2x - 14

-x = -35

x = 35

7. Again, since ΔRST ≅ ΔXYZ, ∠R ≅ ∠X because of CPCTC which means:

4y - 10 = 3y + 5

y = 15°

Answer:

A. 5x + 6x = 70 degrees

Step-by-step explanation:

5x + 6x = 110 degrees because the sum of two interior angles in a triangle is equal to an exterior angle.

Answer:

one solution

Step-by-step explanation:

−6+2x=3x

Subtract 2x from each side

−6+2x-2x=3x-2x

-6 = x

There is one solution

Answer:

it has 1 answer :)

Step-by-step explanation:

Answer:

Question is incomplete but use below

Step-by-step explanation:

you can do total = (price of cheese pizza) ( amount of cheese pizzas bought)+(price of pepperoni pizza) ( amount of pepperoni pizzas bought)

Answer:

28500

Step-by-step explanation:

you simply set up a equation on paper then you solve it using the method where you put numbers under each other than multiply

Answer:

28500

Step-by-step explanation:

Answer: = a = 0.0206

b = 0.0205.

Step-by-step explanation:

From the question, given that;

Order Accurate         =  328     273    242     142

Order Not Accurate  =  32       54       37       20

Let us make the Total orders given be

T.O = 328+273+242+142+32+54+37+20 = 1128.

a) Let the Prob. that the first order is from restaurant D be

= Number of order from restaurant D / Total number of orders

= 162 / 1128 = 0.1436

Probability of the second order is 0.1436.

This is because, from the question we can tell that the selections are made with replacement, that means the order is the same.

So, the probability of getting 2 orders =

= 0.1436 * 0.1436 = 0.0206

NB: The probability of getting two orders from restaurant B is 0.0206.

This is because choosing the first order does not affect the second order

(independent events).

b) Assuming that the selections are made without replacement , the probability of getting both the orders from restaurant D =

This gives the Total Probability of getting both the orders from restaurant D, without replacement to be =  0.1436*0.1428

= 0.0205.

That is to say choosing the first order affects the second order because of the events are not independent as compared to the first question.

cheers i hope tis helps

Answer:

NEGATIVE; DECREASED.

Step-by-step explanation:

A correlation coefficient of -0.76 indicates that there is a "fairly" strong negative relationship between the daily temperature and the number of people who visit the store.

This implies that, as the daily temperature increases, number of customers who come to the store decreases.

Therefore, the interpretation of the situation is:

"There is a NEGATIVE association between x and y. As the high temperature of the day increases across days, the number of customers who come to the store DECREASED.

Answer:

6:10

Step-by-step explanation:

Answer:

a. 17

Step-by-step explanation:

The pattern is add 5 then subtract 2

Answer: -4

At 1, the parabola is at (1, 3). And at 3, it's at (3, -5). The rate of change is -4, since each time it moves right 1, it goes down 4.

Hope that helped,

-sirswagger21

Answer:

$935.76

Step-by-step explanation:

BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?​

Step 1

We find the Present value factor of sum

The formula =

(1 + i)^n

Where

i = maturity rate = 9% = 0.09

n = number of years = 10 years

Present Value = ( 1 + 0.09)^-10

= 0.4224

Step 2

We find the present value factor of annuity

The formula is given as:

1 - (1+i)^-n / i

i = maturity rate = 9% = 0.09

n = number of years = 10 years

= 1 - (1 + 0.09)^-10 /0.09

= 1 - 0.4224 /0.09

= 0.5775 /0.09

= 6.417

Step 3

The bond's current market price is calculated as:

= PV factor of Sum × Par Value + PV factor of annuity × coupon payment

Coupon payment is calculated as:

= Coupon interest × par value

= 8% × 1000

= 80

Hence,

= 0.4224 × 1,000 + 6.417 × 80

= 422.4 + 513.36

= 935.76

In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:

[tex]\$935.76[/tex]

We find the Present value factor of sum, by the formula of:

[tex](1 + i)^n[/tex]

Where:

Substituting the values ​​in the formula as;

[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]

We find the present value factor of annuity, by the formula as:

[tex]1 - (1+i)^{-n} / i[/tex]

Where:

Substituting the values ​​in the formula as;

[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]

The bond's current market price is calculated as:

[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]

Coupon payment is calculated as:

[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]

So continue the calcule;

[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]

See more about market place at brainly.com/question/24518027

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

[tex]\boxed{108d}[/tex]

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

[tex]\frac{216}{108}=2[/tex]

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is [tex]\boxed{108d}[/tex].

Answer:

Ashley= 15

Milan= 11

Carlos= 105

Step-by-step explanation:

Let, A, M and C denotes Ashley, Milan and Carlos respectively.

A+M+C= 131 (according to the question)

Here,

C= 7A

A= M+ 4

So, M= A - 4

Now,

A+M+C = 131

or, A+ A-4+ 7A = 131 (putting the values)

or, 9A - 4 = 131 (adding like terms i.e. A + A + 7A)

or, 9A = 131 + 4

or, 9A = 135

or, A = 135 / 9

So, A = 15

C= 7A = 7×15= 105

M= A-4 = 15 - 4 = 11

Answer:

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

Step-by-step explanation:

Given that :

Mean  = 265

standard deviation = 14

The formula for calculating the z score is [tex]z = \dfrac{x -\mu}{\sigma}[/tex]

x = μ + σz

At middle of 50% i.e 0.50

The critical value for [tex]z_{\alpha/2} = z_{0.50/2}[/tex]

From standard normal table

[tex]z_{0.25}=[/tex] + 0.67  or -0.67  

So; when z = -0.67

x = μ + σz

x = 265 + 14(-0.67)

x = 265 -9.38

x = 255.62

when z = +0.67

x = μ + σz

x = 265 + 14 (0.67)

x = 265 + 9.38

x = 274.38

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

Answer:  see proof below

Step-by-step explanation:

   Statement                          Reason

1. ∠CAX ≅ ∠ BAX               1. Given

2. AC ≅ AB                        2. Given

3. AY ≅ AY                        3. Reflexive Property

4. ΔCAY ≅ ΔBAY              4. SAS Congruency Theorem

5.  CY ≅ BY                       5. CPCTC

6. ∠CYA ≅ ∠BYA              6. CPCTC

7.  ∠CXY ≅ ∠ BXY             7. Given

8. ΔCYX ≅ ΔBYX              4. AAS Congruency Theorem

9. ∠XCY ≅ ∠XBY              9. CPCTC

Step-by-step explanation:

Hope it helps u

plz mark it as brainlist

Answer:

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

Step-by-step explanation:

Given:

Weight of patient = 110 lb

Dosage = 25 mg/kg/day

Find:

Total amount receive each day

Computation:

Weight of patient = 110 lb

1 lb = 0.453592

Weight of patient = 110 (0.453592)

Weight of patient = 49.89

Weight of patient = 50 kg (Approx)

Total amount receive each day = 50 kg × 25 mg/kg/day

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

Answer:

718.75ft³

Step-by-step explanation:

Rectangular Prism=5x5x17.5=437.5

Cube=5x5x5=125

Triangular Prism=5x5x12.5x.5=156.25

437.5+125+156.25=718.75ft³

Answer: [tex]w= 52 h[/tex] .

Step-by-step explanation:

Given: Maya is interning at a law firm over the summer and is paid per hour.

Total wages = (Hourly wage) x (Number of hours worked)

If her hourly wage is $52, then the total wages(w) = 52 x (Number of hours(h))

i.e. w= 52 h

Hence, the proportional relationship between the wages she earns (w) and the number of hours (h) described by [tex]w= 52 h[/tex] .

Answer:

Step-by-step explanation:

Given the limit of a function [tex]\lim_{h \to 0} \frac{(1+h)-1}{h}[/tex], to evaluate the limit, the following steps must be taken.

Step 1: Substitute h = 0 into the function given.

[tex]= \lim_{h \to 0} \frac{(1+h)-1}{h}\\\\[/tex]

[tex]= \frac{(1+0)-1}{0}\\\\= \frac{1-1}{0} \\\\= \frac{0}{0} (indeterminate)\\[/tex]

Step 2: Apply l'hospital rule

[tex]\lim_{h \to 0} \frac{\frac{d}{dh}[(1+h)-1] } {\frac{d}{dh}(h) } \\\\= \frac{0+1-0}{1}\\ \\= \frac{1}{1} \\ \\= 1[/tex]

Hence the limit of the function [tex]\lim_{h \to 0} \frac{(1+h)-1}{h} \ is \ 1[/tex]

Answer:

Your answer is here.Enjoy dude

Answer:

12.56 unit²

Step-by-step explanation:

The form of the circle is:

Let's bring the given to the form of a circle as above:

As per the form, we got r² = 2², so the radius of circle is 2 units.

The area of circle:

Answer:

43

Step-by-step explanation:

18x+7

=18×2+7

=36×9

=45

Answer:

43

Step-by-step explanation:

x=2

18x+7

18(2)+7

36+7

43

Hope this helps ;) ❤❤❤

Answer:

The distance is 87.5 miles

Step-by-step explanation:

We can use a ratio to solve

1 in              3.5 inches

-----------  = ----------------

25 miles          x miles

Using cross products

1x = 3.5 * 25

x =87.5

The distance is 87.5 miles

━━━━━━━☆☆━━━━━━━

▹ Answer

87.5 miles

▹ Step-by-Step Explanation

[tex]\frac{1}{25} * \frac{3.5}{x} \\\\1 * 3.5 = 3.5\\25 * 3.5 = 87.5 \\\\Actual Distance = 87.5 miles[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

I believe your answer is b. the more trials you conduct, the more information you have

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger. Then the correct option is B.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Experimental probability: A probability that is established from the findings of several iterations of a test.

Theoretical probability: The proportion of positive consequences to all potential outcomes. The ratio of the favorable event to the total event.

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.

Then the correct option is B.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ2

Answer:

k=8

Step-by-step explanation:

Since y and x are in direct proportions, the equation is

y= kx, where k is a constant.

when y= 33.6, x=4.2,

33.6= k(4.2)

k= 33.6 ÷4.2

k=8

Answer:

k=8

Step-by-step explanation:

[tex]10[/tex] divisions between $389$ and $390$ so each division is $\frac{390-389}{10}=0.1$

A is 8 division from $389$, so, A is $389+8\times 0.1=389.8$

similarly, C is one division behind $389$ so it is $389-1\times 0.1=388.9$

and B is $390.3$