Points S, L, and P on this grid represent the locations of the school, the library, and the park
What is the distance, in units, from the school to the library and district from the library to the park.

Answer: B

Step-by-step explanation:

A - Nope.

B - Possibility.

C. Nope. (2.23606797)

D. Nope.

When facing questions like this, it can be easier to use the process of elimination.

Answer:

a) 3,467 gallons of water

b) 17,335 ml of insecticide = 12 bottles

c) $ 42,000

Step-by-step explanation:

1 gal. Water = 3785.412 ml

1 hectare = 10,000 m^2

2.6 hectare = 2.5 x 10.000 m^2 = 26,000 m^2

(a) 4 gal. water cover 30m^2

X gal water cover 26,000 m^2

(4 x 26,000)/30 = 3,467 gal of water

(b) 5 ml per 1 gal of water

X ml per 3,467 gal of water

(5 x 3,467) = 17,335 ml of insecticide

Bottle of insecticide = 1,500 ml of insecticide in each bottle.

17,335/1,500 = 12 bottles of insecticide

(c) 12 x $3,500 = $ 42,000

An alpha value of 0.05 means that there is a 5% chance of incorrectly rejecting the null hypothesis.

In statistics, "alpha" is used to represent the significance level in a hypothesis test. The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.

In other words, if the p-value in a hypothesis test is less than or equal to 0.05, we can reject the null hypothesis and conclude that there is a statistically significant difference between the groups or variables being tested.

An alpha value of 0.05 is commonly used in research studies, but other values such as 0.01 or 0.10 may also be used depending on the desired level of significance.

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Since, the length of one side of the pennant is 3 feet longer than the length of the other side. Therefore, the length, in feet, of the two sides of the pennant are 9 inches and 3 inches.

Hypotenuse:

The hypotenuse is the longest side of a right triangle, opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Pythagorean Theorem:

In mathematics, the Pythagorean Theorem or Pythagorean Theorem is the fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of ​​a square whose side is the hypotenuse (opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation for the lengths of sides a, b and hypotenuse c, often called the Pythagorean equation:

                                       a²+ b² = c²

According to the Question:

Now, By the Pythagorean Equation:

x²+(x - 3)² = 15²

x²+ x²-6x+9 = 225

2x²- 6x+ 9 - 225 = 0

2x²- 6x- 216 = 0

divide both sides by 2

x²- 3x- 108 =0

factor

(x- 9)(x+ 12)=0

x - 9 = 0

x = 9 inches

x- 3 = 3 inches

x and x- 3 are the legs and the hypotenuse is 15 inches

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Considering the roots of function f(x), the correct statement is given by:

D. f has exactly two zeros of [0,4].

The roots of a function are the values of x for which f(x) = 0.

In this problem, we have that:

For values of x less than 2 on the interval, the function is never negative nor zero, hence there are no roots in that interval and option D is correct.

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The slope of the table is 5 / 4 .

The slope of a line is the change in the dependent variables with respect to the change in the independent variable.

The slope of a line is rise over run.

In other words, the slope of a line is a measure of its steepness.

Therefore, let's find the slope of the table.

slope = change in y / change in x

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Using (4, 5) and (8, 10)

slope = 10 - 5 / 8 - 4

slope = 5 / 4

Therefore, the slope is 5 / 4.

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Answer:

1.25

Step-by-step explanation:

You divide five by four, and you get one and twenty-five hundredths.

Answer:

Modern uses. Roman numerals are still used today and can be found in many places. They are still used in almost all cases for the copyright date on films, television programmes, and videos - for example MCMLXXXVI for 1986.

Five monuments around the world where Roman numerals are used to depict the year in which they were built are indicated below.

The roman monuments and the dates they were built are:

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To answer this, we will find the equation of the line that passes through point C and D and check which option is in the same line, this will be the answer.

First, let's find the slope using th coordinates of the points C and D:

Now, we can use point C, for example, to right in the slope-point form:

With this equation, we can input values of x and check is we get the same y.

Alternative A and C have x = 0, so let's check it:

I got y = 3, neither alternative have y = 3, so it isn't A nor C.

B and D have x = 1, let's check it:

We got y = 4, which matches alternative D.

So, the correct alternative is D.

An equation is a way of writing a statement with two expressions connected by an equal sign.

If the equation y = 32.95x + 12.95 is used to find the total amount charged for x coins.

The total charge for 10 coins is $342.45.

An equation is a way of writing a statement with two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an expression.

We have,

y = 32.95x + 12.95

We see that,

Shipping charge = $12.95

Total amount = y

Number of coins = x

Find x = 10

y = 32.95x + 12.95

y = 32.95 x 10 + 12.95

y = 329.5 + 12.95

y = 342.45

Thus,

If the equation y = 32.95x + 12.95 is used to find the total amount charged for x coins.

The total charge for 10 coins is $342.45.

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Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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The interest rate earned in 3 years if compounded annually to the nearest cent is $9,944.74

Principal = $7,247

Time = 3 years

Interest rate = 11 1/8%

= 11.125%

r = 11.125/100

r = 0.11125 rate per year,

A = P(1 + r/n)^(nt)

A = 7,247.00(1 + 0.11125/1)^(1)(3)

A = 7,247.00(1 + 0.11125)^(3)

A = $9,944.74

In conclusion, $9,944.74 is the interest rate earned.

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The given equation 3x^2 - y^2 + z^2 = 0 represents a surface known as an elliptic paraboloid. To sketch this surface using traces, we can fix one variable (either x, y, or z) and vary the other two to observe the resulting curve.

Let's fix x at a constant value of 0. Substituting x = 0 into the equation, we get -y^2 + z^2 = 0. This equation represents a pair of intersecting lines, forming a trace. By varying x and fixing y or z, we can obtain additional traces, which are also pairs of intersecting lines.

Thus, by considering multiple traces, we can sketch the elliptic paraboloid surface, which resembles a bowl or a saddle. The traces consist of intersecting lines that form a grid-like pattern on the surface.

Now, moving on to the second question, we are given two skew lines with parametric equations. To find the distance between these lines, we can use the closest distance formula.

First, we need to find a point on each line. By setting t = 0 in the first line's equations, we find a point (2, 3, 0). Similarly, setting s = 0 in the second line's equations gives us a point (1, 6, -2).

Next, we find the direction vectors for both lines. The direction vector for the first line is <1, 6, 2>, and for the second line is <2, 14, 5>.

Using the closest distance formula, we can calculate the distance between the two lines as follows:

distance = |(2-1, 3-6, 0+2) · (1, 6, 2) x (2, 14, 5)| / |(1, 6, 2) x (2, 14, 5)|

Simplifying this expression will give us the distance between the skew lines.

Please note that the exact calculations are omitted here, but following the steps outlined above will provide the desired distance.

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Answer:

Step-by-step explanation:

radius = diameter / 2 = 5/2 = 2.5 in

V = radius^2 x pI x height = 2.5^2 x pi x 8 = 157.1 in^3 (round to the nearest tenth)

cups = Volume of a can / Volume of a cup = 157.1 / 14.44 = 10.9 (round to the nearest tenth)

The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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Answer:

Obliviousness: Being unaware of something.

Step 1

Given;

Step 2

Thus it is increasing at;

It is decreasing at;

Answer;

Answer:

12.570 meters

Step-by-step explanation:

Answer:

b=A/h

Step-by-step explanation:

In order to solve for b, we need to isolate b. We can do this by dividing both sides by h:

A = bh

A/h=b

b=A/h

Answer: Supplementary, 3 and 2, substitution, 2.

Step-by-step explanation: just did it .

The ∠1 is congruent to ∠3 by definition of congruency.

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.

m∠1 + m∠2 = 180°  (given)

m∠2 + m∠3 = 180°  (given)

Hence:

m∠1 + m∠2  = m∠2 + m∠3  (equality property)

Subtract m∠2 from both sides to get:

m∠1  = m∠3

The ∠1 is congruent to ∠3 by definition of congruency.

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Answer:

The last one

Step-by-step explanation:

Multiply the number outside the parenthese times each term inside

Step-by-step explanation:

x+3 and 2x-5 are the same lenght, so

x+3=2x-5

x-2x=-5-3

-x=-8

x=8

Answer:

4

Step-by-step explanation:

base is not the exponent but the number being multiplied by the exponent

The estimates of tolerance intervals, we first need to calculate the mean and standard deviation of the breaking strengths of the trash bags.

To calculate estimates of tolerance intervals using the empirical rule, we need to know the mean and standard deviation of the data. In this case, we are looking for the breaking strengths of trash bags.

The empirical rule states that for a normal distribution:
- Approximately 68.26% of the data falls within one standard deviation of the mean
- Approximately 95.44% of the data falls within two standard deviations of the mean
- Approximately 99.73% of the data falls within three standard deviations of the mean

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Answer:

the number of dreams that include people you know out of 28 is 21

Step-by-step explanation:

Here is the complete question:

It is believed that about \(\frac{3}{4}\) of our dreams  involve people that we know.

So the expression to describe the number of  dreams that feature people you know if you have "d" dreams is:

\(\frac{3}{4} d\)

Now using the above expression we can predict number of dreams that include people you know out of 28. Here 28 represents number of dreams i.e. "d". So expression becomes:

\(\frac{3}{4} (28)\)

Now simplify the above expression:

\(\frac{3}{4} (28)\) = \(\frac{3*28}{4}\) = \(\frac{84}{4}\) = \(21\)

Hence the number of dreams that include people you know out of 28 is 21

Answer:

A. Pink 0.3 Green 0.2 Yellow 0.05 Blue 0.45

Step-by-step explanation:

Adding up the total number of values:

\(6+4+1+9=20\)

Then, finding the probability of each color:

Pink: \(6/20=0.30\)

Green: \(4/20 = 0.20\)

Yellow: \(1/20=0.05\)

Blue: \(9/20=0.45\)

Answer:

The vertex is at (2, 8) and the axis of symmetry is x = 2

Step-by-step explanation:

First, let's find the zeros of the equation

Factor the equation

-2x² + 8x = -2x(x - 4) = 0

-2x = 0

x - 4 = 0

h(x) is 0 when x = 0 or 4

Now we add those zero's together and divide by 2 to find the middle (the axis of symmetry)

4 + 0 = 4

4 ÷ 2 = 2

Now plug 2 into the original equation to find the vertex

h(x) = -2(2)² + 8(2) = 8

Since h(x) equals 8 at the axis of symmetry, which is 2, our vertex is (2,8)

The correct statement concerning the vertex and axis of symmetry of

h(x) = −2x^2 + 8x is:

The vertex is at (2, 8) and the axis of symmetry is x = 2.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The correct statement concerning the vertex and axis of symmetry of

h(x) = −2x^2 + 8x is:

To find the vertex and axis of symmetry of a quadratic function in standard form (y = ax² + bx + c), we can use the formulas:

x = -b / 2a (for the x-coordinate of the vertex)

y = (c - b²) / 4a (for the y-coordinate of the vertex)

and

x = -b / 2a (for the equation of the axis of symmetry)

In this case,

a = -2, b = 8, and c = 0.

Substituting these values into the formulas above, we get:

x = -8 / 2(-2) = 2 (x-coordinate of vertex)

y = 0 - 8² / 4(-2) = 8 (y-coordinate of vertex)

x = 2 (equation of the axis of symmetry)

Therefore,

The vertex is at (2, 8) and the axis of symmetry is x = 2.

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Step-by-step explanation:

In the given triangle,

Perpendicular = d

Hypotenuse = e

Base = f

We need to find the values of sinx, tanx and cosx.

We know that,

\(\sin \theta=\dfrac{P}{H}\\\\\tan\theta=\dfrac{P}{B}\\\\\cos\theta=\dfrac{B}{H}\),

We have, P = d, H = e and base = f

So,

\(\sin \theta=\dfrac{d}{e}\\\\\tan\theta=\dfrac{d}{f}\\\\\cos\theta=\dfrac{f}{e}\)

Hence, this is the required solution.

Using the lengths given, the Trigonometry ratios of the right triangle are:

Recall:

Given the following:

Thus:

sin x = Opp/Hyp = d/e (SOH)

cos x = adj/Hypo = f/e (CAH)

tan x = Opp/Adj = d/f (TOA)

Therefore, using the lengths given, the Trigonometry ratios of the right triangle are:

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