Tracy goes on a 3 day and night school band trip. There is no cost for travel and each band member only pays half

Answer:

x = -9/20

Step-by-step explanation:

-10x-(9x+6) = 3+x

-19x - 6 = 3 + x==> -20x = 9

x = -9/20

The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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Answer:

The p-value is 0.0012.

Step-by-step explanation:

The hypothesis is:

H₀: µ = 72 vs. Hₐ: µ > 72

The information provided is:

\(n =16\\\bar x=75.8\\\sigma=5\)

Compute the test statistic value as follows:

\(z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}\)

  \(=\frac{75.8-72}{5/\sqrt{16}}\\\\=3.04\)

Compute the p-value as follows:

\(p-value=P(Z>3.04)\\\\=1-P(Z<3.04)\\\\=1-0.99882\\\\=0.00118\\\\\approx 0.0012\)

*Use a z-table.

Thus, the p-value is 0.0012.

Answer:

Neither

Step-by-step explanation:

Perpendicular lines would have negative opposite slopes (one would be -5 and the other would be 1/5, which is not the case). Parallel lines would have the same slope (one is 5 and the other is -2/5). Hope this helps!

Answer:

Step-by-step explanation:

plug the units in and multiply then you should have a answer

Answer:

He is correct!

Step-by-step explanation:

one quarter of 9 is 2.25 cause if u divide 9 by 2, you get 4.50 which is one half, so if you divide 4.50 by 2 you get 2.25 which is one quarter of 9

Answer:

y<5/3 I believe. sorry if I am wrong!

The initial sets are:

So the union between them we combinate the items:

Answer:

the answer is D.

Step-by-step explanation:

Answer: (3,2)

Step-by-step explanation:

There are 3 weeks and 2 ponchos

Therefore,  one of the rectangle braces measures 137.3 cm to the closest tenth of a centimetre.

A rectangle is a rectangle with four perpendicularly in the Euclidean plane. It is also known as an apparent equal-sided rectangle or an equiangular parallelogram. Another option for the trapezoid is a straight angle. A square has four edges that are the same length. Quadrilaterals that are rectangular have four identical sides and 4 90° edges. As a result, it is sometimes referred to as a "rectangular trapezoid".

Here,

the vertical brace serves as the hypotenuse of a right triangle, which has the bookcase's sides serving as its legs. The diagonal brace's length can be determined as follows:

length of diagonal brace

=> √(length² + height²)

When we enter the numbers from the problem, we obtain:

length of diagonal brace

= >√(115² + 76²) ≈ 137.3 cm

Using the closest tenth of a centimetre as a guide, we obtain:

diagonal brace length: 137.3 centimetres

As a result, one of the braces measures 137.3 cm to the closest tenth of a centimetre.

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The quotient

Represent the total number of slices. Let's solve it.

The total number of slices is 32.

On the other hand, a faster way to add the eight parts of each circle is to multiply 4 times 8 since there are 8 divisions inside each circle. This gives 32 also.

Answer:

x < -3

Step-by-step explanation:

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

−4x−3> 36/4

​Divide 36 by 4 to get 9.

−4x−3>9

Add 3 to both sides.

−4x>9+3

Add 9 and 3 to get 12.

−4x>12

Divide both sides by −4. Since −4 is negative, the inequality direction is changed.

x< 12/-4

​ Divide 12 by −4 to get −3.

x < -3

Answer is x < -3

4(-4x-3) > 36

Expand the brackets

-16x - 12 > 36

Rearrange the inequality to get x on its own

-16x > 36 + 12

-16x > 48

Divide both sides by -16 in order to get x on its own. When dividing both sides of the inequality by a negative number, flip the inequality sign (as this is one of the laws of inequalities)

x < 48/-16

x < -3

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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The total ticket were sold this year is 39  tickets.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

The circle graph shows last year's ticket sales with a total of 842 tickets.

Adults =4%

Students =17%

Children Under 12 =55%

Seniors =24%

This year 22 more tickets were sold to seniors.

According to given question we have

Ticket sold to the senior

=24% *842

= 202.08  tickets.

Tickets were sold this year

= 202.08/12  tickets.

=16.84  tickets.

This year 22 more tickets were sold to  seniors

=16.84  tickets+22 tickets

=38.84 ≈39  tickets

Therefore, the total ticket were sold this year is 39  tickets.

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Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:

Refer to the attachment below.

There are three pairs of faces on a rectangular prism:

8 cm × 3 cm = 24 cm²

Since there are two of these faces, the total area is:

2 × 24 = 48 cm²

8 cm × 6 cm = 48 cm²

Since there are two of these faces, the total area is:

2 × 48 = 96 cm²

3 cm × 6 cm = 18 cm²

Since there are two of these faces, the total area is:

2 × 18 = 36 cm²

Now, add up the areas of all six faces:

Surface Area = 48 + 96 + 36 = 180 cm²

So, the surface area of the rectangular prism is 180 cm².

________________________________________________________

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Answer:

X= 110/7 or 15.7 or rounded to 16

Answer:

x=15.714285

Step-by-step explanation:

-0.35x=-3-2.5

-0.35x=-5.5

-0.35/-0.35= -5.5/0.35

X=-5.5/-0.35

X=15.714285

Answer:

2600grams or 2.6kg

Explanation:

From the question, we are told that Each packet of nuts has a mass of 325 grams, this is expressed as;

1 packet = 325grams

To get the mass of 8 packets of nut, we can write;

8 packets = x

Cross multiply both equations

1 * x= 8 * 325

x = 2600grams

Hence Mass of 8 packets is 2600grams or 2.6kg

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

Answer:

Step-by-step explanation:

Given:

Use tangent to solve for h:

Correct choice is B

Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a hexagon has 6 sides , then

sum = 180° × (6 - 2) = 180° × 4 = 720°

12

the polygon has 5 sides , so

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

y + 90 + 120 + 90 + 110 = 540

y + 410 = 540 ( subtract 410 from both sides )

y = 130

13

the polygon has 7 sides , so

sum = 180° × (7 - 2) = 180° × 5 = 900°

sum the interior angles and equate to 900

p + 90 + 141 + 130 + 136 + 123 + 140 = 900

p + 760 = 900 ( subtract 760 from both sides )

p = 140

Got it. Hope this will help.

The value of [x] = 11.67 satisfies the equation 3x + 1 = 4|9|.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following equation -

3x + 1 = 4|9|

We have -

3x + 1 = 4|9|

3x + 1 = 4 × 9

3x + 1 = 36

3x = 35

x = 11.67

Therefore, the value of [x] = 11.67 satisfies the equation 3x + 1 = 4|9|.

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The distance between point A and point B of the boat is 2220.2 feet

The boat distance from B to A is worked using SOH CAH TOA

The direction of movements describes a right angle triangle of

angle of elevation = 15 degrees

angle of elevation = 6 degrees

adjacent (point A) = 1433 feet

The distance of point B using tan, TOA let the angle be x

tan x = Opposite / Adjacent

taking the ratio of the terms and equation

tan 15 = Opposite / 1433

Opposite = tan 15 * 1433

Opposite = tan 6 * ?

Opposite = lighthouse’s beacon-light which is equal

tan 6 * ? = tan 15 * 1433

? = tan 15 * 1433 / tan 6

? = 3653.24

Distance from point B to point A

= 3653.24 - 1433

= 2220.2 feet

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A variable in mathematics is a number that can change depending on the issue. Several mathematical statements and equations use the generic letters x, y, and z. In other words, a variable is a symbol that stands for an unknowable numeric value. Say that x Plus 5 equals 10. The "x" variable is used here.

The variable "model of car driven" is qualitative because it is an attribute characteristic. Qualitative variables are those that are not numerical in nature but rather represent characteristics or categories that can be observed or measured through attributes. In this case, the model of the car driven is a type of attribute that describes the make and model of the car, such as Honda Civic, Toyota Corolla, etc.

Therefore, option B is the correct answer.

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Optiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

A qualitative variable is a type οf variable in statistics that describes a characteristic οr quality οf an οbject οr phenοmenοn. It is alsο called a categοrical variable, and it can be nοminal οr οrdinal. Nοminal variables have categοries that have nο inherent οrder, while οrdinal variables have categοries with a natural οrder οr ranking.

The variable "Mοdel οf car driven" is qualitative because it is an attribute characteristic. Qualitative variables are variables that are nοt numerical in nature but are based οn attributes οr characteristics. In this case, the mοdel οf the car driven is a categοrical variable that describes a particular characteristic οf the car, such as its make οr mοdel. This variable cannοt be measured quantitatively οr numerically, but rather it can be categοrized based οn specific attributes οr features.

Therefοre, οptiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

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Answer:

T1=-12

T2=-19

T3=-26

Step-by-step explanation:

Determine which term will have a value of -6998

-7n-5=-6998

-7n=-6998+5

-7n=-6993

-7n/-7=-6993/-7

n=999

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is