5
4
3
2
4
(-40)
--5-4-2-4
+2
3
nt
(2/3)
2
(4,-4)
What is the equation of the line that is parallel to the
given line and passes through the point (2, 3)?
O x + 2y = 4
O x + 2y = 8
O
2x + y = 4
O
2x + y = 8

The number of ways to choose 0, 1, and 2 homes out of 9, respectively

we need to assume that the sample of nine homes is a random sample from the population of all homes in the United States. Based on this assumption, we can use the binomial distribution to model the number of homes in the sample that have large-screen TVs.

Let p be the probability that a randomly selected home in the United States has a large-screen TV, which is given as 0.9. Let X be the number of homes in the sample of nine that have large-screen TVs. Then X follows a binomial distribution with parameters n = 9 and p = 0.9.

where (9 choose 0), (9 choose 1), and (9 choose 2) are the number of ways to choose 0, 1, and 2 homes out of 9, respectively.

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Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{2}{3}\) x - 6 ← is in slope- intercept form

with slope m = \(\frac{2}{3}\)

Parallel lines have equal slopes , then

y = \(\frac{2}{3}\) x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = \(\frac{2}{3}\) x - 4 ← equation of parallel line

-------------------------------------------------------------------

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{\frac{2}{3} }\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = - \(\frac{27}{2}\) + c ⇒ c = 2 + \(\frac{27}{2}\) = \(\frac{31}{2}\)

y = - \(\frac{3}{2}\) x + \(\frac{31}{2}\) ← equation of perpendicular line

Answer:

48

Step-by-step explanation:

13 + 22 + 29 = 64

64/x = 4/3

x = 48

Answer:

$90

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 9%/100 = 0.09 per year,

then, solving our equation

I = 2000 × 0.09 × 0.5 = 90

I = $ 90.00

The simple interest accumulated

on a principal of $ 2,000.00

at a rate of 9% per year

for 0.5 years is $ 90.00.

Answer:

  x ≈ 0.499

Step-by-step explanation:

The value of x can be found by undoing the operations done to it.

The operations done to the variable are ...

We undo these operations in reverse order:

  7e^(2x) + 10 = 29 . . . . given

  7e^(2x) = 19 . . . . . . . . . subtract 10

  e^(2x) = 19/7 . . . . . . . . . divide by 7

  2x = ln(19/7) . . . . . . . . take the natural logarithm

  x = (ln(19/7))/2 . . . . . . divide by 2

The rounded result is ...

  x ≈ 0.499

Answer:

3 friends played golf.

Step-by-step explanation:

The length of one edge of the tabletop is 4.89 feet.

We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.

The area of square table is given by the formula -

Area of square table = side²

We will keep the value of area of square table to find the value of side which will be length of edge

24 = side²

Side = ✓24

Taking square root for the value on right side of the equation

Side = 4.89

Hence, the length of one edge of the tabletop is 4.89 feet.

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Answer:

its true, depending on the times table.

Answer:

True

Step-by-step explanation:

This statement is always true.

To find the amount of gold needed for gold plating a brick, total surface area of the brick would be needed to be calculated, assuming the brick is cuboid or cube shaped.

While dealing with cubes and cuboids, we should know how to find the surface areas and volumes of the two objects. When we either fill these or talk about all the three dimensions of an object, we talk about the volume of the said object. And, when we paint or talk about just the exterior or interior walls of an object, we talk about the surface area of the said object.

When all the six faces of a cube or a cuboid are used, we calculate surface area for all the faces and this is called the total surface area.

Let us look at the different formulas to calculate volume and total surface area of a cube and a cuboid,

Total surface area of a cube (side \(a\)) =  6 × (area of each face)  

                                                          = 6 × \(a^{2}\)  

Volume of a cube (side \(a\)) = \(a^{3}\)

Total surface area of a cuboid (length \(l\), breadth \(b\), height \(h\)) = \(2 ( lb + lh + bh)\\\)

Volume of a cuboid (length \(l\), breadth \(b\), height \(h\)) = \(lbh\)

For plating the brick with anything, gold for instance, total surface area of the brick would be calculated to determine the amount of gold needed as all the walls or faces of the brick would be plated but not the interior volume.

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The solution to the given integral is: frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).

Given integral: int_0^1 (1-t^2)g(x) dt

To solve the given integral, we will make use of Beta function.

The Beta function is defined as follows:

B(p,q) = int_0^1 t^{p-1}(1-t)^{q-1} dt

Using substitution, t = sin theta, we get:

int_0^1 (1-t^2)g(x) dt = int_0^{frac{pi}{2}} (1-sin^2 theta)g(x) cos theta dtheta

= int_0^{frac{\pi}{2}} cos^2 theta g(x) d\theta

= frac{1}{2}\int_0^{\frac{\pi}{2}} (1+\cos 2\theta) g(x) d\theta

= frac{1}{2} \left(\int_0^{\frac{\pi}{2}} g(x) dtheta + int_0^{frac{pi}{2}} g(x) cos 2theta dtheta right)

Using B(p,q)$ for the second integral, we get:

int_0^1 (1-t^2)g(x) dt = frac{1}{2}left(frac{pi}{2}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x) right)

= frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).

Hence, the value of the given integral int_0^1 (1-t^2)g(x) dt is frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).

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Answer: AC=108

Step-by-step explanation:

6x=9x-27

9-6=3

27/3=9

x=9

6x9=54

9(9)=81

81-27=54

54(2)=108

AC=108

Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

<95141404393>

Answer:

4

Step-by-step explanation:

The quotient of eight and two is the same as the equation 8/2 which equals to 4.

Quotient means divide.

8 / 2 = 4

Best of Luck!

Answer:

1. A = 64 cm²

2. A = 240 yd²

3. A = 220.5 cm²

4. A = 193.4 m²

Step-by-step explanation:

1. We want to split this figure into two rectangles. We know the top figure is a rectangle because a rectangle has four right angles. For the bottom rectangle, because the sides are all perpendicular, all of the angles are also right angles.

Because they're rectangles, opposite sides are congruent. So now you can find the measures of the sides.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

2. We want to split this figure into a triangle and a rectangle.

Because the bottom figure has four right angles, we know that it's a rectangle. Therefore, its side measures are 24, 24, 8, and 8 because opposite sides of a rectangle are congruent.

For the triangle, because the sum of the triangle's base and two other segments is 24, we can use 24 - (6 + 6) = base. So the triangle base is 12.

Do this same thing to find the height of the triangle.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

3. We want to split this figure into a triangle and semicircle.

We're already given that the height is 15 and part of the base is 8, but there is no way to assume that the other part of the base is also 8. Remember, it's not to scale.

We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent, so the two radii present are both 8.

Because of Reflexive Property, the other part of the triangle base is now proven to also be 8.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

4. We want to split this figure into a rectangle and semicircle.

For the rectangle, because the sides are all perpendicular, all of the angles are also right angles. So we can prove that it is a rectangle.

Because this is a rectangle, opposite sides are congruent. So we have the sides of 15, 7, 15, and 7.

We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent.

Because of Reflexive Property, we know that the diameter of the circle is 15. The radius is half the diameter, meaning all radii are 1/2 (15), or 7.5.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

The student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

Tο find the z-scοre οf the student whο scοred 428, we can use the fοrmula:

z = (x - μ) / σ

where x is the student's scοre, μ is the mean οf the distributiοn (400 in this case), and σ is the standard deviatiοn οf the distributiοn (60 in this case).

Plugging in the values, we get:

z = (428 - 400) / 60 = 0.467

Since the z-scοre οf the student is less than 0.524, which is the z-scοre cοrrespοnding tο the tοp 30% οf the distributiοn, we can cοnclude that the student did nοt scοre in the tοp 30%.

Therefοre, the student will nοt be admitted tο the schοοl based οn the admissiοn criteria οf scοring in the tοp 30%.

Hence, the student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

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A possible unit vector that makes an angle of 45° with 9i + 4j is

\(v = (-9/\sqrt{(97)} )i + (0.933)j\)

Let's call the two unit vectors we're looking for as u and v.

We know that they make an angle of 45° with the vector 9i + 4j.

First, we need to find the unit vector in the direction of 9i + 4j. We can do this by dividing the vector by its magnitude:

\(|9i + 4j| = \sqrt{(9^2 + 4^2)} = \sqrt{(97)}\)

So the unit vector in the direction of 9i + 4j is:

\(u_0 = (9i + 4j) / \sqrt{(97)}\)

Now, we can use the dot product to find two unit vectors that make an angle of 45° with  \(u_0.\)

Let's call the first unit vector u.

We know that the dot product of u and \(u_0\) must be:

u . u_0 = |u| |u_0| cos(45°)

\(= (1)(1/ \sqrt{(97)} )(\sqrt{(2) /2)\)

\(= \sqrt{(2)} / (2 \sqrt{(97)} )\)

We also know that u must be a unit vector, which means its magnitude is We can use this information to solve for the components of u:

\(u . u_0 = (u_x)i + (u_y)j . (9/\sqrt{(97)} )i + (4/\sqrt{sqrt(97)} )j = \sqrt{(2) } / (2 \sqrt{(97)} )\)

Solving for the components of u, we get:

\(u_x = (9\sqrt{(2)} + 4\sqrt{(2)} ) / (2\sqrt{(97)} ) = 0.933\)

\(u_y = (4\sqrt{(2)} - 9\sqrt{(2)} ) / (2\sqrt{(97)} ) = -0.359\)

So one possible unit vector that makes an angle of 45° with 9i + 4j is:

u = 0.933i - 0.359j

To find the second unit vector, let's call it v, we know that it must be orthogonal to u (since the angle between u and v is 90°) and it must also be orthogonal to \(u_0\) (since the angle between \(u_0\) and v is also 90°).

We can use the cross product to find such a vector.

\(v = u_0 * u\)

\(v_x = (u_0)_y u_z - (u_0)_z u_y = (4/\sqrt{(97)} )(0) - (9/\sqrt{(97)} )(1) = -9/\sqrt{(97)}\)

\(v_y = (u_0)_z u_x - (u_0)_x u_z = (1/\sqrt{(97)} )(0.933) - (0/\sqrt{(97)} ) = 0.933\)

\(v_z = (u_0)_x u_y - (u_0)_y u_x = (0/\sqrt{(97)} )(-0.359) - (4/\sqrt{(97)} )(0.933) = -4/\sqrt{(97)}\)

We don't need the z-component of v, since we're working in 2-space.

So a possible unit vector that makes an angle of 45° with 9i + 4j is:

\(v = (-9/\sqrt{(97)} )i + (0.933)j\)

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Answer:

5.2 seconds

Step-by-step explanation:

Traveling straight down: 90 * 3.5 = 315 feet down

Traveling up: 30 * 2.2= 66

315-66= 249

249/48= 5.1875 seconds

5.2 seconds <- rounded

Answer:

y - x = 2

Step-by-step explanation:

Therefore , the probability that she selects none of those containing errors is 0.6798.

Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.

Here,

Number of ways of selecting 3 returns out of 59 is C(59,3).

Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).

The probability that she selects none of those containing errors is

P( No errors )=\(\frac{C(52,3)}{C(59,3)}\)=0.6798

Therefore , the probability that she selects none of those containing errors is 0.6798.

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The set A ∩ B = {3}

The intersection of sets, denoted as A ∩ B, refers to the set that contains elements that are common to both sets A and B. In this case, set A consists of the elements {1, 2, 3, 6}, and set B consists of the elements {3, 4, 5}.

The intersection of A and B, written as A ∩ B, represents the set of elements that appear in both sets simultaneously.

To find the intersection of sets A and B, we examine each element of set A and check if it is also present in set B. In this case, the element 3 is the only element that exists in both sets.

Therefore, the intersection of sets A and B is {3}.

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Answer:

D

Step-by-step explanation:

Answer:

D.

P′(2, -4), Q′(3, -1), R′(4, -4)

Step-by-step explanation:

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

Step-by-step explanation:

A square root function has a restricted domain because the square root operation is only defined for non-negative numbers. The square root of a negative number is not a real number, so the domain of a square root function is limited to non-negative values. This means that the input of a square root function must be greater than or equal to zero in order to obtain a real output.

On the other hand, a cube root function has a domain (-∞, ∞) because the cube root operation is defined for all real numbers. Unlike the square root, the cube root function can take both positive and negative inputs and still produce a real output. This is because raising a number to the power of 1/3 (cube root) results in a real number for any real input. Therefore, the cube root function has a domain that extends from negative infinity to positive infinity.

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The concentration of acetic acid in your dressing is approximately 0.1718 M.

To calculate the number of moles of acetic acid in the 1.00 mL of your dressing sample, we can use the equation n = cv, where n represents the number of moles, c is the concentration in molarity, and v is the volume in liters.

Given:

Titrant volume (NaOH) = 11.71 mL

Titrant concentration (NaOH) = 0.0147 M

Volume of sample (vinegar dressing) = 1.00 mL

First, let's convert the volume of the sample to liters:

1.00 mL = 1.00 x 10⁻³ L

Now we can calculate the number of moles of NaOH used in the titration:

n(NaOH) = c(NaOH) x v(NaOH)

n(NaOH) = 0.0147 M x 11.71 x 10⁻³ L

Calculating this expression gives us:

n(NaOH) = 1.71797 x 10⁻⁴ moles of NaOH

Since the balanced chemical equation between acetic acid (CH3COOH) and NaOH is 1:1, the number of moles of acetic acid is also 1.71797 x 10⁻⁴ moles.

For the final calculation, we need to determine the concentration of acetic acid in your dressing. Since the volume of the sample is 1.00 mL, we'll express the concentration in Molarity (M):

Concentration of acetic acid = (moles of acetic acid) / (volume of sample in liters)

Concentration of acetic acid = (1.71797 x 10⁻⁴ moles) / (1.00 x 10⁻³ L)

Calculating this expression gives us:

Concentration of acetic acid = 0.1718 M

Therefore, the concentration of acetic acid in your dressing is approximately 0.1718 M.

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Answer:

\(9\; \rm m\).

Step-by-step explanation:

Assume that the run of this rafter is level. Then the height of the ridge (the line with a question mark next to it in the diagram) should be perpendicular to the line marked with \(\rm 12\; m\). The three labelled lines in this diagram will form a right triangle.

Hence, the height of this ridge can be found with the Pythagorean Theorem. By the Pythagorean Theorem:

\((\text{First Leg})^2 + (\text{Second Leg})^2 = (\text{Hypotenuse})^2\).

In this particular right triangle:

\((\text{Height})^2 + (12\; \rm m)^2 = (15\; \rm m)^2\).

\((\text{Height})^2 = (15\; \rm m)^2 - (12\; \rm m)^2\).

Therefore, the height of this ridge would be \(\sqrt{81}\; \rm m = 9\; \rm m\). (Note the unit.)

Answer:

-3

Step-by-step explanation:

19-13=6+1=7-14=-7+4=-3

The integer represents the price of a share at the end of the day will be negative 3.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The price of a share of stock started the day at $19. During the day it went down $13 up $1, down $14, and up $4.

Then the integer represents the price of a share at the end of the day will be

⇒ 19 - 13 + 1 - 14 + 4

⇒ -3

The integer represents the price of a share at the end of the day will be negative 3.

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