1. In a triangle∆ABC, if DE is parallel to BC, AD
DB
=
3
4
and AC = 15 cm, then the length AE is:
(a) 45 (b) 23/7 (c) 1 (d) 45/7

The solution of the system of equations is equal to (3, 4).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by  ordered pair (3, 4).

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To give the patient the 120 grams of protein per day, you must provide 1,600 ml of the tube-feeding formula.

We know that there are 6 grams of protein per 80ml of formula.

Now, we know that the patient needs 120 grams of protein, first, let's count how many times we have 6 grams in 120 grams by tanking the quotient.

120g/6g = 20

Then, to give 120 grams of protein, you need to give 20 times the 80 ml of formula, this is:

20*80ml = 1,600 ml

He should get 1,600 ml of tube-feeding formula.

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The volume of the pyramid is 576 cubic inches.

To find the volume of a square base pyramid, you can use the formula:

Volume = (1/3) x base area x height

In this case, the side of the square base is given as 12 inches, and the height is given as 12.5 inches.

First, calculate the base area of the pyramid:

Base area = side²

= 12²

= 144 square inches

Now, substitute the values into the volume formula:

Volume = (1/3) x 144 x 12.5

Volume = 576 cubic inches

Therefore, the volume of the pyramid is 576 cubic inches.

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Answer:

The range of g(x) = -2x + 33 is D. (Negative infinity, positive infinity)

Step-by-step explanation:

The function g(x) is a linear line, so all values of x are included in the domain. If all values of x in the domain works, then there are infinite amount of values for both x and y. Therefore, your answer is D.

Answer: 19 years

Step-by-step explanation:

Given

Amount invested \(\$400\)

Rate of interest \(R=6\%\)

after 1-year amount becomes

\(A=400\left (1+6\%\right)\\A=400\left (1+0.06\right)\\A=400\times 1.06\\A=\$424\)

After n years it is

\(A=400\left (1.06\right)^n\)

Sum accumulated is \(\$1200\)

\(\Rightarrow 1200=400\left(1.06\right)^n\\\Rightarrow 3=\left(1.06\right)^n\\\text{Taking log both sides}\\\Rightarrow n=\dfrac{\ln 3}{\ln 1.06}\\\\\Rightarrow n=18.85\approx 19\ \text{years}\)

The most appropriate choice for linear equation will be given by -

w = -8 is the required answer

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here

\(4(3w - 2) = 8(2w+3)\\12w - 8 = 16w+24\\16w - 12w = -8-24\\4w = -32\\w = -\frac{32}{4}\\w = -8\)

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Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

Well, it depends on their heights . If both figures have same height, then the one with greater surface area will have greater volume.

Step-by-step explanation:

Answer:

2(x+10)

Step-by-step explanation:

x + 10 + x + 10 is the same as 2 times the expression x + 10

This can be written as 2(x+10)

-Chetan K

Answer: 2(x+10)

Step-by-step explanation:

x + 10 + x + 10 is the same as 2 times the expression x + 10

This can be written as 2(x+10)

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

a. An example of a countable collection of disjoint open intervals is the collection of intervals (0, 1/n), where n is a positive integer. This collection of intervals is countable because it can be put in one-to-one correspondence with the positive integers.

In mathematics, a one-to-one correspondence between two sets is a bijective function that maps every element of one set to exactly one element of the other set, and vice versa.

b. An example of an uncountable collection of disjoint open intervals is the collection of intervals (x, x + 1/n), where x is a real number and n is a positive integer. This collection of intervals is uncountable because it can be put in one-to-one correspondence with the real numbers. To see this, note that for any real number x, we can find a positive integer n such that 1/n is smaller than x. Then, the interval (x, x + 1/n) corresponds to x.

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6) The missing angles and lengths are; x = 14, T = 14, AB = WY = 60

7) The missing angles and lengths are; X = 7, ∠A = ∠Z =31°, T = 9, YZ = AB = 28

6) We are told that;

ΔABC ≅ ΔYWZ

That means triangle ABC is congruent to triangle YWZ

Thus;

∠C ≅ ∠Z

5x - 4 = 66

5x = 70

x = 14

Similarly, AB = WY

5T - 10 = 4T + 4

5T - 4T = 10 + 4

T = 14

AB = 5(14) - 10

AB = 60 = WY

7) We are told that;

ΔABC ≅ ΔZYW

That means triangle ABC is congruent to triangle ZYW

Thus;

∠A ≅ ∠Z

5X - 4 = 3X + 10

2X = 14

X = 7

∠A = 5(7) - 4 = 31° = ∠Z

Similarly;

2T + 10 = 4T - 8

T = 18/2

T = 9

YZ = 4(9) - 8

YZ = 28 = AB

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Answer:

I think there is 140 questions

Answer:

27

Step-by-step explanation:

15+40+10+40+30=135.

135÷5 I.e the total average of the number.

135÷5=27

Answer:

27

Step-by-step explanation:

15+40+10+40+30=135

135/5

Because 5 is the number of numbers

=27

Answer:

1/100.

Step-by-step explanation:

So, we can make the following deductions from the information given in the question or problem above.

[1]. "You and your neighbor attempt to use your cordless phones at the same time."

DEDUCTION: Two people are involved, that is you and your neighbor are both involved.

[2]. "Your phones independently select one of ten channels at random to connect to the base unit. "

DEDUCTION: Both cordless phones can choose one channels each which is random. The number of channels available is ten.

Therefore, the probability that both your phone and your neighbor phone pick the same channel can be calculated or determined as follows:

The probability that both your phone and your neighbor phone pick the same channel = probability that both your phone will pick one channel out of the ten channels ×  the probability that your neighbor phone pick one channel out of the ten channels.

The probability that both your phone and your neighbor phone pick the same channel = 1/10 × 1/10 = 1/100.

Therefore, The probability that both your phone and your neighbor phone pick the same channel = 1/100.

The total compound interest is $981365.6

Compound Interest:

Compound interest is defined as interest that is earned not solely on the initial amount invested but also on any further interest.

The formula for annual compound interest is as follows:

FV = P (1+ r/m)^mt

Where:

FV - the future value of the investment, in our calculator it is the final balance

P - the initial balance (the value of the investment)

r - the annual interest rate (in decimal)

m - the number of times the interest is compounded per year (compounding frequency)

t - the numbers of years the money is invested for

Given,

Principal amount =$80,0000

Time = 11 years

Interest = 7.3%

compounding frequency = monthly

So, the compounding frequency is,

=> 1 year = 12 times

=> 7.3% = 7.3/100 = 0.073

Now apply the values on the formula,

FV = 80,0000 x (1 + (0.073/12)^(11 x 12)

FV = 80,0000 x (1.006083)^132

FV = 80,0000 x 2.226707

FV = 1781365.6

So, the interest is,

I = FV -  P

=> I = 1781365.6 - 80,0000

=> I = 981365.6

Therefore, the compound interest is 981365.6

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The probability that the teenager picked at random is male and their favorite hobby is playing video games is given as follows:

1/16.

The definition of a probability is that it is calculated as the division of the number of desired outcomes by the number of total outcomes.

The desired and the total outcomes for this problem are given as follows:

Of the 14 males, 2 have playing videogames as their favorite hobby, hence the number of desired outcomes is given as follows:

2.

Then the probability is calculated as follows:

p = 2/32

p = 1/16.

The probability was simplified as the quotient of 32 and 2 has a result of 16.

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Answer:

2

Step-by-step explanation:

To evaluate the expression substitute t = 4 into the expression, that is

8/t = 8/4 =2

Answer:8/2=4

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

-17/4 = -4.25

and 4 is greater than that, so i think

K = -17

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

Answer:

\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)

Step-by-step explanation:

We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

↓ plugging in the given values

\(a^2 + 2^2 = 14^2\)

↓ subtracting 2² from both sides

\(a^2 = 14^2 - 2^2\)

\(a^2 = 196 - 4\)

\(a^2 = 192\)

↓ taking the square root of both sides

\(a = \sqrt{192\)

↓ simplifying the square root

\(a = \sqrt{2^6 \cdot 3\)

\(a = 2^{\, 6 / 2} \cdot \sqrt3\)

\(a = 2^3\sqrt3\)

\(a = 8\sqrt3\)

Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.

\(a = \dfrac{1}{2}x\)

↓ plugging in the a-value we solved for

\(8\sqrt3 = \dfrac{1}2x\)

↓ multiplying both sides by 2

\(\boxed{x = 16\sqrt3}\)

The number of days that this solution will probably last would be = 8 days.

To calculate the number of days the solution will last the following is taken into consideration.

The parameters given which are not in ml should be converted to ml as follows;

2 Oz of Lidocaine to ml = 2×29.6=59.2ml

½tsp of banana flavouring;

= 1/2×4.92

= 2.5ml

Therefore the total volume of the solution = 100+59.2+2.5 = 161.7ml

But 2×10 = 1 day

20ml = 1 day

161.7ml = X

Make X the subject of formula;

X = 161.7/20

= 8.1

= 8 days.

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Answer:

364.46

Step-by-step explanation:

First we need the height of the cone

so we divide the cone to two equal parts that means the adjacent 5 inches will be divided into two to give 2.5

then we use get a triangle from the cone and that's how we find our height using pythagoras theorem

hypotenuse Square = opposite Square + adjacent Square

7^2 = x^2 + 2.5^2

therefore our height is 6.53

now to get the surface area of the cone we use the formula

pi×r( r + Square root of r^2 + h^2

From the problem, 40% are red and so 60% are not red.

The formula for calculating the probability of exact number of candies :

where n = number of sample

r = number of specific samples

a = percentage of one sample

b = percentage of the other sample

The problem is looking for the probability that at least 3 of the candies in a box are red.

This is also the same as the probability that at most 3 of the candies in a box are NOT red subtracted from 1.

So we need to find the probability of having at most 3 candies are NOT red.

From the problem, n = 10 (because there are 10 candies in a box)

r = 0, 1 and 2 (these are the number of candies that are NOT red)

a = 40% or 0.4 (percentage of red candy)

b = 60% or 0.6 (percentage of not red candy)

The working equation will be :

So we need to find the probabilities of r = 0, 1 and 2.

For r = 0

As you can see, the exponent of 0.4 is 0 because we need a candy that is NOT red. So it will be 0.

For r = 1

For r = 2

Using the working equation from above.

The answer is A. 0.8327

Answer:

Step-by-step explanation:

To solve this problem, we can use the multiplication principle of counting, which states that if there are k choices for one task and m choices for a second task, then there are k x m choices for both tasks combined.

In this case, we can apply this principle to each shelf of books, as there are different numbers of books on each shelf. For the first shelf, there are 12 choices, for the second shelf there are 18 choices, for the third shelf there are 25 choices, and for the fourth shelf there are 30 choices.

To choose one book from each shelf, we need to multiply the number of choices for each shelf together, which gives us:

12 x 18 x 25 x 30 = 16,200,000

Therefore, there are 16,200,000 ways to choose three books, one from each shelf, in the library.

The total number of ways of choosing three books , one from each shelf is given by A = 162,000 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

There are 12 ways to choose a book from the first shelf, 18 ways to choose a book from the second shelf, 25 ways to choose a book from the third shelf, and 30 ways to choose a book from the fourth shelf

So , the total number of ways = 12 x 18 x 25 x 30

A = 162,000 ways

Hence , the combination is solved and there are 162,000 ways

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Answer: sample mean

Hope this helps.