Solve:
19) m∠2 = 12x-4

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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Answer:

D

Step-by-step explanation:

A P E X

The normal approximation to the binomial distribution is possible in the following case:

D. n = 30; p= 0.4

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\), as long as \(np \geq 10, n(1 - p) \geq 10\).

For option d, we have that:

Hence it is the correct option.

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Answer: V(x) = -5x^2 + 70x

Step-by-step explanation:

Let the length and width of the rectangular base be represented by x and y, respectively.

Since the perimeter of the rectangular base is 28 cm, we have:

2x + 2y = 28

x + y = 14

The height of the box is given as 5 cm.

The volume of the box is given by:

V = lwh = xy(5)

V = 5xy

We can solve for y in terms of x from the equation x + y = 14:

y = 14 - x

Substituting this into the equation for the volume, we get:

V = 5x(14 - x)

Simplifying:

V = 70x - 5x^2

Answer:

57 x 457 x 4.3 = 10 x (5.7 x 4.3) = 10 x 24.51 = 245.1

Step-by-step explanation:

If we look closely at the two equations you will see the following...

57 x 4.3 = 10 x (5.7 x 4.3)

(Since we know what 5.7 x 4.3 equals to we just substitute the value of 24.51 and get...)

57 x 4.3 = 10 x 24.51

57 x 4.3 = 245.1

Answer:

Gold coins are an example of commodity money. ... Dollar bills are an example of fiat money because their value as slips of printed paper is less than their value as money. Bank money consists of the book credit that banks extend to their depositors.

Step-by-step explanation:

Answer:12.7

Step-by-step explanation:

Answer:

it's 12.7 on delta math

Step-by-step explanation:

1-Line- A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

2- Circle- A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”

3- Cardioid- a limacon with a pointed indent occurs when a=b.

4- Limacon with a loop- a limacon with an inner loop occurs when a is less than b.

5- Limacon without a loop- A Limacon graph could be said to resemble a lima bean. It takes the form of a circle with a dented side.

6- Lemniscate - A lemniscate is a polar graph taking the shape of a propeller or figure upright, at an angle, or on its side.

7-Rose Curves- One type of curve defined by a polar equation is a rose curve. The rose curve graph is often described as flower petals arranged around the pole. The petals are all congruent to each other and can have symmetry across the polar axis or the line θ=π/2

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The number of hours it will take Santa to visit the whole children is = 10,000hours

The total number of children in UK is = 12million

That is = 12,000,000.

It took Santa 3 seconds to visit each child. That is,

1 child = 3 seconds

Therefore 12,000,000 children = x seconds

x = 12,000,000 × 3 seconds

x = 36,000,000 seconds.

But 3,600 seconds = 1 hour

36,000,000 seconds = x

x = 36,000,000/3,600

x = 10,000 hours.

Therefore, the number of hours it will take Santa to visit the whole children is = 10,000 hours.

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Answer:

It goes on for ever so it is unknown...

Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

I might be wrong but i'm pretty sure it's right

The correct match for each linear system with one of the phase plane direction fields will be:

1:B

2:C

3:D

4:A

What is plane?

In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.

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Answer:

25 in.

Step-by-step explanation:

DEC is a right triangle. <DEC is a right angle.

(DE)² + (EC)² = (DC)²

DE = ½DB = ½(48 in.) = 24 in.

(24 in.)² + (7 in.)² = (DC)²

576 in.² + 49 in.² = (DC)²

(DC)² = 625 in.²

DC = 25 in.

Answer:

45

scalene

acute

Step-by-step explanation:

Answer: The triangle classified by the sides is 59 degrees.  The triangle is classified by the angel is 1

Step-by-step explanation:

Answer

12

Step-by-step explanation:

Get equation: (n^3/16) + 8

Substitute: ((12)^3/16) + 8

Solve: 64/16 + 8

              4     + 8

               = 12

Answer: A

Step-by-step explanation:

Substitute the answers in the choices for x.

Answer:

24=5y+3y

8y=24

y=3

x+x+9y+5=90

2x+9(3)+5=90

2x=58

x=29

Step-by-step explanation:

Total amount spend by Mr. Josh is,

⇒ $7,978

We have to given that,

Mr. Josh spends $153 every week on gas to get to work.

Since, We know that,

1 year = 52.1429 weeks

Here, Mr. Josh spends $153 every week on gas to get to work.

Hence, Amount Mr. Josh spend annually to go to work is,

⇒ $153 × 52.1429

⇒ $7,978

Therefore, Total amount spend by Mr. Josh is,

⇒ $7,978

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Answer:

0=0

Step-by-step explanation:

4(a + 2) + 2 = 4 - 2(-2a - 3)

4a +  8 + 2 = 4 + 4a + 6

4a + 10 = 10 + 4a

0 = 0

Answer:

12.72792

Step-by-step explanation:

d = √2a = √2 x 9 = 12.72792

Sorry, I don't have too much time to explain the question but I hope this helps!

Answer:

Day 6

Step-by-step explanation:

Every 3 days 1 pound of hay is used every day 1 pound of grain is used. There are 10 pounds of grain and 8 pounds of hay. On the 6th day there are 6 pounds of hay left and 6 pounds of grain left.

The number of days after which the amount of hay and the grain will be the same is 12 days.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Hay = 8 pounds

1 pound = 3 days

From the graph,

Grain = 10 pounds

5 pounds left after 10 days

1 pound = 2 days

Now,

The number of days x after which the pounds left will be the same.

(-1/3)x + 8 = 10 - (1/2)x

(-1/3)x + (1/2)x = 10 - 8

(-2x + 3x)/6 = 2

x/6 = 2

x = 12

Thus,

After 12 days the hay and the grain left over will be the same.

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Answer:

The area remaining, correct to the nearest square meter, is approximately 436 square meters.

Step-by-step explanation:

To find the area remaining, we need to subtract the area of the flower bed and the area of the pool from the total area of the garden.

The total area of the garden is:

40m x 15m = 600 square meters

The flower bed is 1m wide and runs along two shorter sides and one long side of the garden. So the area of the flower bed is:

(40m + 2 x 1m) x (15m + 2 x 1m) - 40m x 15m

= (42m x 17m) - (40m x 15m)

= 714 - 600

= 114 square meters

Now let's calculate the area of the pool. The diameter of the pool is 8m, so the radius is 4m. The area of the pool is:

π x (4m)^2

= 16π

≈ 50.27 square meters (rounded to two decimal places)

So the area remaining is:

600 square meters - 114 square meters - 50.27 square meters

≈ 435.73 square meters

Therefore, the area remaining, correct to the nearest square meter, is approximately 436 square meters.

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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In 2010 an item cost $9.00. The price increase by 1.5% each year an exponential growth function to represent this is P(t) = \(9(1 + 1.5/100)^t.\)

A. To represent the exponential growth of the price over time, we can use the formula for compound interest:

P(t) = P₀(1 + r/100)^t,

where:

P(t) is the price at time t,

P₀ is the initial price,

r is the annual growth rate as a percentage, and

t is the number of years.

In this case, the initial price is $9.00, and the annual growth rate is 1.5%. So, the exponential growth function representing this situation is:

P(t) = 9(1 + 1.5/100)^t.

B. To find the cost in 2030, we need to calculate P(2030).

First, we need to determine the number of years between 2010 and 2030:

Number of years = 2030 - 2010 = 20 years.

Now we can substitute this value into the exponential growth function:

P(2030) = 9(1 + 1.5/100)^20.

Calculating this expression, we get:

P(2030) ≈ 9(1.015)^20 ≈ 9(1.348) ≈ 12.132.

Thus, rounding to the nearest cent, the cost in 2030 will be approximately $12.13.

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Answer:

\(\sf B. \: f(x) = 5x - 9 \: and \; g(x)=\cfrac{x+9}{5}\)

Step-by-step explanation:

f(x) = 5x - 9  and g(x) = x+9/5 are inverses of each other.

________________

The Residual is -8.4 hours and the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

A residual plot is a type of scatter plot where the horizontal axis represents the independent variable, or input variable of the data, and the vertical axis represents the residual values.

Now, looking at the given residual plot and using a calculator online, we can say that the equation of the least squares regression line is;

y^ = 180.8 + 15.2x

Now, for 2 tablespoons of sugar , we have x = 2. Thus;

y^ = 180.8 + 15.2(2)

y^ = 212.4 hours

Residual for 204 hours is;

Residual = 204 - 212.4 = -8.4 hours

Thus, the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

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Complete question is;

Does adding sugar to the water in a vase help flowers stay fresh? To find out, two statistics students went to a flower shop and randomly selected 12 carnations. When they got home, the students prepared 12 identical vases with exactly the same amount of water in each vase. They put one tablespoon of sugarin 3 vases, two tablespoons of sugar in 3 vases, and three tablespoons of sugar in 3 vases.In the remaining 3 vases, they put no sugar. After the vases were prepared, the students randomly assigned 1 carnation to each vase and observed how many hours each flower continued to look fresh.

Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.

Answer:

H= -35/4

Decimal form: -8.75

Explanation:

A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459    , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

\($$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$\)

as population variance is unknown so we used sample variance

\($$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$\)

Now

\(\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$\)

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

\($$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$\)

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