In exercises 5-12, write an equation in point slope form..

Answer:

The area of the top of the crate can be found by multiplying the length by the width.

        3/4 yard = 9/12 yards

        2/4 yard = 6/12 yards

    2. Now we can find the area by multiplying the length by the width:

     Area = 9/12 yards * 6/12 yards = (9/12) * (6/12) = 3/4 * 1/2 = 3/8                         yards^2

So, the area of the top of the crate is 3/8 yards^2.

The mean of the probability distribution is 3.188, the sampling distribution is 2.25 and x is an unbiased estimator.

a. To find the mean (u) of a probability distribution, we calculate the expected value as follows:

u = ∑x * p(x) = (0.5 * 0.0625) + (2.5 * 0.125) + (0.25 * 0.25) + (0.25 * 0.25) + (0.25 * 0.25) = 2.25

To find the variance (o^2) of the distribution, we calculate it as follows:

o^2 = ∑(x - u)^2 * p(x) = (0.5 - 2.25)^2 * 0.0625 + (2.5 - 2.25)^2 * 0.125 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 = 0.5625

So, o = √0.5625 = 3.188

b. The sampling distribution of the sample mean x for a random sample of n=2 measurements from this distribution is given by:

x = (x1 + x2) / n = (2.25 + 2.25) / 2 = 2.25

As n approaches infinity, the sample mean x approaches the population mean u, and the distribution of x becomes more and more concentrated around u.

c. Yes, x is an unbiased estimator of u because its expected value is equal to the population mean: E(x) = u.

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The measurements arranged from smallest to largest are 0.15 cm, 2.5 mm, 0.000035 m, and 4.5 km.

A. 1.5 cm

B. 2.5 x 10^3 mm

C. 3.5 x 10-5 m

D. 4.5 km

Convert all units to the same unit type.

A. 1.5 cm = 15 mm

B. 2.5 x 10^3 mm

C. 3.5 x 10-5 m = 0.000035 m

D. 4.5 km = 4500 m

Arrange the measurements from smallest to largest.

A. 15 mm

B. 2.5 x 10^3 mm

C. 0.000035 m

D. 4500 m

Convert the measurements back to their original units.

A. 15 mm = 0.15 cm

B. 2.5 x 10^3 mm

C. 0.000035 m = 3.5 x 10-5 m

D. 4500 m = 4.5 km

Rearrange the measurements from smallest to largest.

A. 0.15 cm

B. 2.5 x 10^3 mm

C. 3.5 x 10-5 m

D. 4.5 km

Simplify the units to the same unit type.

A. 0.15 cm

B. 2.5 mm

C. 0.000035 m

D. 4.5 km

Rearrange the measurements from smallest to largest.

A. 0.15 cm

B. 2.5 mm

C. 0.000035 m

D. 4.5 km

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The measurements arranged from smallest to largest are:

C. 3.5 x 10^-5 m

A. 1.5 cm

B. 2.5 x 10^3 mm

D. 4.5 km

To arrange the measurements from smallest to largest, it is necessary to convert all the units to the same type. The units in the measurements A, C, and D are different, so they need to be converted.

Measurement A is 1.5 cm, which can be converted to millimeters by multiplying by 10: 1.5 cm x 10 mm/cm = 15 mm.

Measurement C is 3.5 x 10^-5 m, which can be converted to millimeters by multiplying by 1000: 3.5 x 10^-5 m x 1000 mm/m = 3.5 mm.

Measurement D is 4.5 km, which can be converted to millimeters by multiplying by 10^6: 4.5 km x 10^6 mm/km = 4.5 x 10^6 mm.

Now that all the units are in millimeters, the measurements can be arranged from smallest to largest:

Measurement C (3.5 mm) is smallest, followed by Measurement A (15 mm), Measurement B (2.5 x 10^3 mm), and finally Measurement D (4.5 x 10^6 mm) is largest.

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Answer:

$40

Step-by-step explanation:

We know

Her father gave her $20 for every $50 she saved

$50 + $20 = $70

$50 + 20 + 50 + 20 = $140

$182 - $140 = $42

It is not $50 yet, so her father only give her 2 times

So, her father gives her $40

Answer:

182÷50 = 3.64, 3.64x20=72.8$

her dad gave her 72.8$

The triangles are not similar because the dimensions of GDM are larger than those of PQR.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Even though triangles GDM and PQR have the same angle measure, the triangles are not congruent / similar because they are not the same size. Triangle GDM is larger than PQR and so is not congruent to it.

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The total surface area of the composite shape is 488.7 in².

What is a composite shape?

A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently. Every day, composite shapes are around us.

The given composite shape can be divided into multiple shapes, to find the area easily.

For the given question, we can see that the lower portion of the shape is a cuboid and the upper portion is half of the cylinder cut vertically.

We find the areas of the figures separately.

Area of cuboid

Length l = 6 in.

Breadth b = 10 in.

Height h = 8 in.

Area = Area of each faces =  2(lb) + 2(bh) +2(lh)

                                             = 2(6*10) + 2(10*8) + 2(6*8)

                                               = 2*60 +2* 80 + 2* 48

                                                 = 376 in²

Area of cylinder

Radius of semicircles r = 5 in.

Height of cylinder h = 6 in.

Area =  Area of semicircles + Area of half of the curved surface

        =  2 *1/2 * πr² + 1/2 * 2πrh =  πr² + πrh = 3.14 * 5² + 3.14 * 5 * 6

                                                                 = 172.7 in²

The total surface area of the composite shape = Area of cylinder + Area               of cuboid - Area of the common surface(rectangle)

                = 172.7  + 376 - (l *b) = 548.7 - ( 10*6) = 488.7 in²

Hence the total surface area of the composite shape is 488.7 in².

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Answer: 3(1p)

Step-by-step explanation:

Answer: 3+3p or 3p+3

Step-by-step explanation:First write the information given. You will need to multiply the quantity 3 by each of the terms one and p. It should look something like this 3(1+p). Multiply three to both quantities and the answer yields 3+3p or 3p+3.

Answer:

Zeroes & Multiplicity:

x = 0        :   Multiplicity = 2

x = -6/5   :   Multiplicity = 9

x = 8        :   Multiplicity = 2

Step-by-step explanation:

The equation provided is: [tex]f(x)=x^2(5x+6)^9(x-8)^2[/tex]

We're given the polynomial in factored form, which just means the polynomial is broken down into each of its factors. This is a really convenient form to have a polynomial in as we can easily find the zeroes of the polynomial.

This is due to the Zero Property of Multiplication, which essentially states zero times any number results in zero. So we just have to set each factor equal to zero, and solve, since if one of the factors is zero, then the entire thing becomes zero.

So this gives us the following equations:

[tex]x^2=0\implies x = 0\\\\(5x+6)^9=0\implies x = -\frac{6}{5}\\\\(x-8)^2=0\implies x = 8[/tex]

Now for the multiplicity, we just look at the exponent of the factor we set equal to zero. So x^2 gives us a zero of x = 0, and the exponent is 2, which is also the multiplicity of this zero.

The (5x + 6)^9 gives us a zero of x = -6/5, and the exponent is 9, which is also the multiplicity of the zero. Same thing applies for the zero at x = 8, which has a multiplicity of 2.

Answer:

[tex]\frac{7}{5}[/tex]

Step-by-step explanation:

Slope of a line =  Gradient

                        [tex]= \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]

Based on the two points provided in the question:

[tex]x_{1} = -8[/tex]

[tex]y_{1} = -3[/tex]

[tex]x_{2} = -3[/tex]

[tex]y_{2} = 4[/tex]

Slope = [tex]\frac{4 - (-3)}{-3 - (-8)}[/tex]

         = [tex]\frac{4 + 3}{-3 + 8}[/tex]

         = [tex]\frac{7}{5}[/tex]

Answer:

The son is 7 years old.

The father is 35 years old.

Step by step explantation:

Father's age-[tex]5x[/tex]

Son's age-[tex]x[/tex]

[tex]5x+x=42[/tex]

[tex]6x=42[/tex]

[tex]42[/tex]÷[tex]6=7[/tex]

[tex]7[/tex]×[tex]5[/tex][tex]=35[/tex]

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Step-by-step explanation:

Inequality Interval Notation Graph

Sajan Rai

Solve the inequalities below. Write the solution set in interval notation and graph the solution.

8x−12>158x-12>15

Solution:

Interval notation for the solution:

(-∞,5/8) U (5/8, ∞)

To graph the solution, we need to find the points that make the inequality true and shade the region that corresponds to these points. On the number line, we can start by finding x values that make the inequality equal to zero:

8x - 12 = 0

x = 12/8 = 3/2

and

15 - 8x = 0

x = 15/8 = 9/4

Next, we need to test values that are less than 3/2 and greater than 9/4 to determine the direction of the inequality. If the inequality is true for values less than 3/2, then we shade the region to the left of 3/2. If the inequality is true for values greater than 9/4, then we shade the region to the right of 9/4. In this case, since the inequality is "greater than," the shading goes to the right of 9/4 and to the left of 3/2.

1. The formula to find the measure of each interior angle of a regular n-gon is (180 * (n-2))/n degrees.

2. The formula to find the measure of each individual exterior angle in any polygon is 360/n degrees.

3. The most precise name for the quadrilateral ABCD with the given vertices is a parallelogram.

The formula to find the measure of each interior angle of a regular n-gon is given by:

(180 * (n-2))/n degrees

In a regular n-gon, all interior angles are equal.

The sum of the interior angles of a polygon can be found using the formula:

(n-2) * 180 degrees, where n is the number of sides in the polygon.

Dividing the sum of the interior angles by the number of sides (n) gives us the measure of each interior angle:

(180 * (n-2))/n degrees.

2. The formula to find the measure of each individual exterior angle in any polygon is:

360/n degrees.

In any polygon, the sum of the exterior angles is equal to 360 degrees.

3. To find the measure of each individual exterior angle, we divide the sum of the exterior angles (360 degrees) by the number of sides (n) in the polygon:

360/n degrees.

The precise name for the quadrilateral ABCD is a parallelogram because:

It has opposite sides that are parallel to each other.

It has equal opposite sides.

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Answer:

Step-by-step explanation:

If Charlie buys 3 computer tables for $390, then he paid $390 / 3 = $130 for each table.

Answer: 130 dollars for each table

Step-by-step explanation: Because 3 tables is 390 dollars, we have to divide 390 and 3 to see how much 1 table costs.

390 / 3 = 130

The population of Indiana residents aged 5 years and older is around 5.7 million.

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

322000 people lacked basic math skills

5.6% of the population of Indiana residents aged 5 years and older

Let's call the population of Indiana residents aged 5 years and older "x".

The equation to estimate the population is:

322000  =  x*5.6/100

322000 = x * 0.056

Dividing both sides by 0.056:

322,000 / 0.056 = x

x = 5750000

So, the population of Indiana residents aged 5 years and older is approximately 5.7 million.

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the confidence intervals for the situation is 46%

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

the particular week that they had 50 patients the table shows the record numbers of dogs use the given data to complete the sample proportion.

Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

Hence the confidence intervals for the situation is 46%

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Answer:

c = 4

Step-by-step explanation:

if (x - a) is a factor , that is divisible by, of f(x) then f(a) = 0

then for p(x) to be divisible by (x - 1) , p(1) = 0

then

2[tex](1)^{4}[/tex] - 5(1)² + c(1) - 1 = 0

2 - 5 + c - 1 = 0

- 4 + c = 0 ( add 4 to both sides )

c = 4

First find the actual difference:

   82 - 67 = 15

Now divide that difference by the starting value (82 in this case):

    15 / 82 ≈ 0.182927

Convert that to a percent:

   0.182927 = 18.2927%

That's the percent change, a decrease of about 18.2927%

The required container of fries costs $1.20, as er the given condition

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the cost of a container of fries "x".

We know that 4 burgers cost 4 * $3.20 = $12.80.

So the total cost of burgers and fries is $12.80 + 3x = $16.40.

Subtracting the cost of the burgers from both sides:

3x = $16.40 - $12.80 = $3.60

Dividing both sides by 3:

x = $3.60 / 3 = $1.20

So each container of fries costs $1.20.

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The value of the probability is 0.167

From the question, we have the following parameters that can be used in our computation:

6   7   8

The probability of picking a 8 on the first draw and then picking a number above 7 on the second draw is:

P(6 and then >7) = P(6) x P(>7 | 6)

Given that the cards are not replaced, we have

P(6 and then >7) = 1/3 * 1/2

Evaluate

P(6 and then >7) = 0.167

Hence, the probability is 1/6

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Method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

A relation is a function if it has only One y-value for each x-value.

One method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

To do this, you can start by selecting a set of corresponding terms from each sequence and attempt to express the relationship between them using mathematical operations.

It's important to note that finding a mathematical relationship between two sequences can sometimes be difficult, and in some cases may not be possible.

In such cases, it may be helpful to analyze the sequences using other methods, such as graphical representation or statistical analysis, to gain insight into their behavior.

Hence, method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

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You would need to walk 4 miles less if you walk along the diagonal rather than the two sides.

A key concept in mathematics is the Pythagorean Theorem, which describes the relationship between the sides of a right-angled triangle. Pythagorean triples are another name for the right triangle's sides. Here, examples are used to explain the theorem's formulation and proof.

The Pythagorean theorem is mostly used to determine a triangle's angle and the length of an ambiguous side. The base, perpendicular, and hypotenuse formulas can all be derived using this theorem.

Given that, park is in the shape of a rectangle 8 miles long and 6 miles wide.

The diagonal of the park is calculated using the Pythagoras theorem.

The Pythagoras theorem is given as:

c² = a² +b²

c² = 8² + 6²

c² = 64 + 36

c² = 100

c = 10

If you walk along the diagonal you need to walk 10 miles.

If you walk along the two sides the distance is:

d = 8 + 6 = 14 miles

Hence, the difference between the distance is:

14 - 10 = 4 miles.

Hence, you would need to walk 4 miles less if you walk along the diagonal rather than the two sides.

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The value of x is 65°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:
Angle PQR is a right angle.

The measure of angle SQR is 25 degrees.

The measure of PQS is x degrees.

The angle addition postulates:

∠PQR = ∠SQR  + ∠PQS

90° = 25° + x

x = 90° - 25°

x = 65°

Hence, ∠PQS = 65°.

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Answer:

He would be 15 years old.

Step-by-step explanation:

If the difference is 15, and sarah is double the age, whatever age the youngest brother is, that number if multiplied by 2 or added to 15 needs to be the same answer. You could make a equation by writing those two on either side of the equation and making the unknown sum “x”. This would look like “2x=x+15”. Then to get the final product you would subtract the x on the right side from both side, ending up to be “x=15” in this scenario, that would be the final answer.

The answer is C. increasing on (0,2).

What is Strictly convex function?

A real-valued function is said to be convex if the line segment connecting any two points on its graph falls above the graph connecting the two points. A function is convex if and only if its epigraph is a convex set.

Since f"(x) > 0 for all x in (0,2), it follows that f is a strictly convex function on that interval, meaning that its second derivative is positive and its first derivative is increasing.

If f is a strictly convex function on [0,2], then f(2-x) is a strictly concave function on [0,2]. The sum of a strictly convex and a strictly concave function is also a strictly convex function.

Therefore, since f''(x) = f(x) + f(2-x), it follows that f''(x) is a strictly convex function on [0,2], which means that its first derivative is increasing.

Thus, The answer is C. increasing on (0,2).

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Answer:

The vertex of the parabola is at x = 3, and a point on the parabola can be (4, 0). Here is a Brainly link that can provide you with more information about graphing the function f(x) = (x+2) (x-4): https://brainly.com/question/31009433.

If the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled a distance is 9.5 cm.

What is the circumference of the circle?

The Circumference of a circle is basically the perimeter of the circle. It is given as (2×π×r) or (π×d).

The hand on a circular clock moves along the circumference of the circle, and the length of the circumference of a circle is given by the formula:

C = 2 * π * r

where C is the circumference, π is Pi (approximately equal to 3.14), and r is the radius of the circle.

In this case, the radius of the circle is half the length of the hand, or 12cm / 2 = 6cm.

So the circumference of the circle is:

C = 2 * π * 6 = 12 * π

Since the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled an angle of 5 * (360/12) = 150 degrees.

To find the distance traveled along the circumference, we need to multiply the circumference by the fraction of the circle traveled, which is equal to the angle in radians divided by 2π.

To convert from degrees to radians, we can use the formula:

radians = degrees * (π / 180)

So, the distance traveled by the hand is:

distance = C * (150 * (π / 180)) / (2 * π) = 12 * (150 * (π / 180)) / 2 = 9.5 cm (rounded to the nearest cm)

hence, if the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled a distance is 9.5 cm.

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The 17-foot-long ladder pulled out 3 feet farther from the wall from a distance of 8 feet, indicates, using Pythagorean Theorem that the top of the ladder moves about 2.039 feet down the wall.

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the length of the legs of the right trianglde.

Length of the ladder = 17 foot ladder

Distance of the bottom of the ladder from the wall = 8 feet

The extra distance to which the bottom of the ladder is pulled = 3 feet

The ladder resting on the wall forms a right triangle, with the length of the ladder being the hypotenuse side.

The initial vertical distance reached by the ladder on the wall, h, can be found using Pythagorean Theorem as follows;

h² = 17² - 8² = 225 = 15²

h² = 15²

The initial vertical distance up the wall the ladder reaches, h, is therefore;

h = √(15²) = 15

The ladder initially reaches 15 feet high on the wall

The ladder is then pulled 3 feet farther, from which we get;

New horizontal distance of the ladder from the wall = 8 feet + 3 feet = 11 feet

The square of the new height the ladder reaches up to on the wall, h'², can therefore be found as follows;

h'² = 17² - 11² = 168

√h'² = h' = √(168) = 2·√(42)

The new height the ladder reaches up to on the wall, h' ≈ 2·√(42) feet

The distance the ladder moves down the wall, Δh = h - h', therefore;

Δh = 15 - 2·√(42) ≈ 2.039

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Answer:

D because angle U is equal to angle W because it is diverting angle