which graph represents the given inequality?
Y< 4x + 3

Answer:

5446cm²

Step-by-step explanation:

the surface area = the 2 isosceles triangles + the 2 sides + the base

= 2 (24/2 X 35) + 2(37 X 47) + (47 X 24)

= 5446cm²

Answer: 5,446 cm²

Step-by-step explanation:

First, we will find the area of the two triangle sides.

       A = 2 * (\(\frac{bh}{2}\))

       A = bh

       A = (35 cm)(24 cm)

       A = 840 cm²

Next, we will find the area of the three rectangular sides. We have two that are congruent and a third that is not.

       A = 2 * (LW)

       A = 2 * ((47 cm)(37 cm))

       A = 2 * 1,739 cm²

       A = 3,478 cm²

       A = LW

       A = (24 cm)(47 cm)

       A = 1,128 cm²

Lastly, we will add all of these faces together.

       840 cm² + 3,478 cm² + 1,128 cm² = 5,446 cm²

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order for a triangle to be a right triangle, it has to fit into Pythagorean's Theorem:

\(a^2+b^2=c^2\) where c is the hypotenuse.

We need to figure out which is the longest side in each of those triangles and that is the hypotenuse.

In the first set, the sqrt of 443 is 21.04, but that is not the longest side; 24 is. So the Theorem formula for that is:

\(\sqrt{443}^2+17^2=24^2\) which gives us

443 + 289 = 576, but 732 does not equal 576, so that one is not right.

In the second set, the sqrt of 725 is the longest side, so that formula is:

\(\sqrt{725}^2=14^2+23^2\) which gives us

725 = 196 + 529, and 725 does equal 725, so that one is right.

In the third set, the sqrt of 890 is the longest side, so:

\(\sqrt{890}^2=19^2+23^2\), which gives us

890 = 361 + 529, and 890 = 890, so that is a right triangle as well. That's how you know those are right, compared to the first one that is not.

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

x=20

Step-by-step explanation:

x-15=5

x=5+15

x=20

Answer:

Slope: 7/5 , Y-int: 1/5

Step-by-step explanation:

To find the slope, lets use the points (-3,-4) and (2,3)

The slope formula is (y2-y1)/(x2-x1) so we will plug in the numbers.

(3-(-4))/(2-(-3))=7/5. 7/5 is the slope (you can also do rise over run)

We find the y-int in many ways but i will show two.

We can make an equation in point-slope form. The formula is: y-y1=m(x-x1) and we use the point (-3,-4).

y-(-4)=7/5(x-(-3))

y+4=7/5x+21/5 (then move the 4 to the other side)

y=7/5x+1/5

The 1/5 is our y-int since we now have it in slope intercept form!

The other method we can use is putting it into slope intercept form first and using (-3,-4) to find the missing variable.

Slope intercept form is y=mx+b, let m be slope, b is y int, and (x,y) is our point

-4=(7/5)(-3)+b

-4=-21/5+b (move -15/7 to other side)

1/5=b !

we get the same answer I hope this helps sorry its long

Answer:

700

Step-by-step explanation:

8x + 1 = 7

y - x = 1

y = 1 + x

sub 1 + x in eqtn i

8x + 1 = 7 { 1 + x }

8x + 1 = 7 + 7x

8x - 7 = 7 - 1

x = 6

y - 6 = 1

y = 1 + 6

y = 7

So,

8x = 8 x 6 = 48

7y = 7 x 7 = 49

My present years is 48

Next year i will be 49

Multiple can be defined as a number that is the product of a given number and some other natural number. For example when we multiply 7 × 3=21 or 8×3 =24

Therefore my present age is 48 and next year will be 49

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The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

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Answer:

0.5 = 0.500

Step-by-step explanation:

Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.

0.5 = 0.500

The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

Answer:

1. Minimum: 5

Maximum: 27

Q1: 10.5

Q2: 15

Q3: 22.5

2. Minimum: 12

Maximum: 44

Q1: 18

Q2: 24.5

Q3: 32

3. Minimum: 23

Maximum: 60

Q1: 30

Q2: 49

Q3: 55.5

Step-by-step explanation:

The minimum is the lowest number in the set.

The maximum is the highest number in the set.

Q1 is the first quartile.

Q2 is the median or middle of the set.

Q3 is the third quartile.

Hope it helps!

a) The probability is 0.308538.

b) The probability is 0.066807.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

mean= 12 ounce

standard deviation = 0.2 ounce

a) The  probability the contents of a single cup will be greater than 12.1 ounces

P( x> 12.1 ounce) = P( x \(- \mu_x/ \sigma_x\) > (12.1- 12)/ 0.2)

                           = P( z< 0.1/ 0.2)

                           = P( z< 0.5)

                           = 0.308538

b) If a sample of 9 cups is selected

then, P( x> 12.1) =  P( x \(- \mu_x/( \sigma_x/ \sqrt{n} )\) > (12.1- 12)/ (0.2/ √9))

                          = 0.066807

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The probability that there is at least one car that has no working tires is given as follows:

0.0002 = 0.02%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

For each car, the parameters are given as follows:

p = 0.9, n = 4.

Hence the probability that a car has no working tires is given as follows:

P(X = 0) = (1 - 0.9)^4 = 0.0001.

Hence the probability that two cars have working tires is given as follows:

P(X = 2) = (1 - 0.0001)² = 0.9998.

The probability that at least one has no working tires is given as follows:

P(X < 2) = 1 - 0.9998 = 0.0002 = 0.02%.

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Answer: Survey

Step-by-step explanation:

Survey can be employed as a means of data collection to aid them know the amount of books student bring to into the media center during the final week. This can be achieved by the use of questioners which are handed to each and every student. The questionier must be simple and easy to understand to as to get an accurate result. Example close ended where options are provided.

We can substitute this value into the function f(x) = 1/(x + 1):

1) f(g(0)) = 1/3

2) g(f(0)) = 4.

To find the value of f(g(0)), we need to first evaluate g(0) and then substitute that result into f(x).

Given the function g(x) = 2x + 2, we can find g(0) by substituting 0 for x:

g(0) = 2(0) + 2 = 0 + 2 = 2

Now that we know g(0) = 2, we can substitute this value into the function f(x) = 1/(x + 1):

f(g(0)) = f(2)

Substituting 2 for x in f(x):

f(2) = 1/(2 + 1) = 1/3

Therefore, f(g(0)) = 1/3.

Now, let's find the value of g(f(0)).

Given the function f(x) = 1/(x + 1), we need to evaluate f(0) and then substitute that result into g(x).

f(0) = 1/(0 + 1) = 1/1 = 1

Now, using the function g(x) = 2x + 2, we substitute f(0) = 1 into g(x):

g(f(0)) = g(1)

Substituting 1 for x in g(x):

g(1) = 2(1) + 2 = 2 + 2 = 4

Therefore, g(f(0)) = 4.

In summary:

f(g(0)) = 1/3

g(f(0)) = 4

Thus, fg(0) = 1/3 and g(f(0)) = 4.

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Answer: The annual premium for a 27-year-old female purchasing a 20-Year Endowment insurance policy with a face value of $25,000 is $42.67.

Step-by-step explanation:

well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)

Answer:

6 4 5 6 7

Step-by-step explanation:

The mode would be 5. The first 2 letters of MODE are MO, which can be an abbreviation for MOST OFTEN.

Answer: C

Step-by-step explanation:

Answer:

2x+23

Step-by-step explanation:

For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.

Given information:

Cost of Guatemalan coffee = $11/lb

Cost of the other coffee = $5/lb

Desired cost of the blend = $8/lb

Total weight of the blend = 6 pounds

To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:

\((x \times 11 + (6 - x) \times 5) / 6 = 8\)

In this equation, \((x \times 11)\) represents the cost of the Guatemalan coffee in the blend, and\(((6 - x) \times 5)\) represents the cost of the other coffee in the blend.

The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.

Now, let's solve the equation for x:

(11x + 30 - 5x) / 6 = 8

6x + 30 = 48

6x = 48 - 30

6x = 18

x = 18/6

x = 3

Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.

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Answer:

A

Step-by-step explanation:

Y = ax2 +bx + c

Answer:

50.15

Step-by-step explanation:

250.75-50=200.75

200.75/5=50.15

Answer: choice B

Step-by-step explanation:

Events A and B are independent if the equation P(B)=P(B|A) or P(A∩B) = P(A) · P(B) holds true.

in this example

p(A)=1/6    {5}

p(B)=1/2   {1,3,5}

P(B|A)=1

so

P(B)≠P(B|A)

=>A and B are dependent

Answer:

the correct answer is 21

Step-by-step explanation:

5+3×3(2)-2

5+18-2

=21

Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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