which figure has both line of symmetry and rotational symmetry

The critical values are fixed values which can be obtained from the standard t crit  tables. We can find the critical value tc when the degrees of freedom and confidence level are given. The degrees of freedom is simply:

Degrees of Freedom = Number of samples – 1

Degrees of Freedom = 19 – 1

Degrees of Freedom = 18

From the t critical tables, the tc corresponding to Degrees of Freedom equal to 18 and Confidence level equal to 95% is as follows:

tc = 2.101

Therefore this means that any t value beyond 2.101, we already reject the null hypothesis.

To rewrite the equation 8x + 6x^2 - 7 = x^2 in standard form, subtract x^2 from both sides and combine like terms. The standard form of the equation is 5x^2 + 8x - 7 = 0. The values of a, b, and c are 5, 8, and -7 respectively.

The given equation is 8x + 6x^2 - 7 = x^2.

To rewrite it in standard form, we need to collect like terms. Subtracting x^2 from both sides, we get: 6x^2 + 8x - x^2 - 7 = 0.

Combining like terms, the standard form of the equation is 5x^2 + 8x - 7 = 0.

Here, a = 5, b = 8, and c = -7.

shorter piece = x

longer piece = 2x+1

3x+1 =10

3x=9

x = 9/3=3

short piece = 3 feet

 long piece = 2*3+1 = 7 feet

Answer:

I JUST HAD THIS QUESTION 1

Step-by-step explanation:

Answer: 1)  The value of truck initially would be $87000.

2)  at t = 0 , y-axis would be cut at $67000.

Step-by-step explanation:

Since we have given that

[tex]y=A_0(0.87)^x[/tex]

Here, A₀ is the initial value.

Rate of depreciation = 13%

Number of years = x

So, The value of truck initially would be $87000.

As shown in the given figure.

If the the initial value of truck = $67000

Rate will be same but the y-intercept will change.

As change in initial value does not affect the rate but the y - intercept.

Then at t = 0 , y-axis would be cut at $67000.

Answer:

Yes. This is a function.

Step-by-step explanation:

Given is a function as

[tex]y = sin 3x[/tex]

We find that for every x in the domain of real numbers there is a unique image for every x as sin 3x.

Thus this relation given satisfies the requirements of a function.

Also we find that this function is periodic with amplitude 1 and period = 2pi/3

So vertical line test if done will find that there is only one intersection for every vertical line throughout the domain

Hence this relation is definitely a function

a fraction should be number of balls over time per second

 so it should be 16/4 which is 4 balls per second

Answer: fraction 16 over 4

Step-by-step explanation:

The given graph shows the number of paintballs a machine launches, y, in x seconds.

We know that the rate of change of a line is given by :-

[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]

The ordered pairs on the line in graph are (4, 16) and (8, 32) and (12, 48) and (16, 64).

Thus, the rate per second at which the machine launches the balls is given by :-

[tex]k=\frac{32-16}{8-4}=\frac{16}{4}

The expression which represents the total number of fish in the store is 7k.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given,

Number of tank = 7

Number of fish in each tank = k

The total number of fish = number of tanks x number of fish in each tank

The total number of fish = 7 x k = 7k

Hence "The expression which represents the total number of fish in the store is 7k".

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Final answer:

The system of inequalities representing this situation is:

1500X + 1800Y ≤ 150,000.

X + Y ≤ 150.

X ≥ 0 and Y ≥ 0.

Explanation:

Let's define X as the number of air carrier loads and Y as the number of land carrier loads. Given that the mail distribution center processes up to 150,000 pieces of mail each day and the loading equipment can handle a maximum of 150 loads per day, we can write the following system of inequalities:

The total mail processed by both air and land carriers cannot exceed 150,000 pieces:

1500X + 1800Y ≤ 150,000.

The total number of loads carried by both air and land carriers cannot exceed 150 loads:

X + Y ≤ 150.

Furthermore, since there cannot be a negative number of loads, both X and Y have to be non-negative:

X ≥ 0 and Y ≥ 0.

These inequalities model the constraints for the mail distribution center's operations.

Answer: D Opposite sides of a parallelogram are congruent.

Step-by-step explanation:

The correct answer is the Opposite sides of a parallelogram are congruent.

A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.

Consider a parallelogram with diagonals that are congruent and perpendicular.

In triangles Δ AOB and Δ AOD,

OA = OA (common)

OB = OD (Since the diagonals of a parallelogram bisect each other)

∠ AOB = ∠ AOD = 90° (diagonals are perpendicular)

Therefore, Δ AOB ≅ Δ AOD (By SAS postulate)

Since, corresponding parts of congruent triangles are equal,

AB = AD

Similarly, we can prove

BC = CD and CD = DA

So, AB = BC = CD = DA.

Also, it is given that AC = BD.

Therefore the correct answer is the Opposite sides of a parallelogram are congruent.

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The graph of the line y = (1/3)x - 2 can be plotted on a graph paper by choosing some arbitrary values of x.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The given line in terms of the slope-intercept method can be written as,

y = (1/3)x - 2.

Now to plot the graph on graph paper or any digital tool we have to choose some arbitrary values of x that corresponds to some values of y.

Like at x = 0 y = -2 So, the coordinates are (0, -2).

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Answer:

C. Right isosceles

Step-by-step explanation:

In Acute scalene triangle, all angles are acute ( less than 90 degrees ) and different,

In Right scalene triangle, two angles are acute and different, while, the third angle is of 90°.

In Right isosceles triangle, two angles are acute and equal, while, the third angle is of 90°.

In Acute isosceles, all angles are acute in which any two angles are equal.

Now, given,

The two angle of the triangles are 45° and 45°,

Let x be the third angle,

⇒ x + 45° + 45° = 180°

⇒ x + 90° = 180°

⇒ x = 90°

Hence, the angles of given triangle are 45°, 45° and 90°,

By the above definitions,

It is clear that, given triangle is right isosceles.

Option C is correct.

The circumference of the circle is 31.4 cm

The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.

Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.

The formula for the circumference of a circle is expressed using the radius 'r' of the circle and the value of 'pi'. It is expressed as, Circumference of a circle formula = 2πr.

Given:

diameter= 10 cm

So,

Circumference of circle is = πd

=3.14* 10

=31.4 cm

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Answer:

A. Length of a Tour Bus                       ↔     #2.      1.1 × 10¹ meters

B. Width of an apple                             ↔      #3.     4 × 10⁰ centimeters

C. Distance from Earth to a Satellite    ↔    #6.     8 × 10² kilometers

D. Thickness of a human hair               ↔     #5.      9 × 10¹ micrometers

Step-by-step explanation:

The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.

The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10 meters = 11 meters. Thus, this is a reasonable length.

B. Width of an apple.  

The most appropriate unit to measure the width of an apple should be centimeter. It certainly is shorter than 1 meter and bigger than 1 mm.

The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4 centimeters.

C. Distance from Earth to a Satellite

The distance from Earth to a satellite should be measured in kilometers.

You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.

The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is nonseasonal (too big).

The number in the box #6 is  8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.

Thus,  8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite

D. Thickness of a human hair

Of course, kilometers, meters, centimeters and even millimeters are units too big to measure the thickness of a human hair.

One micrometer is 10⁻⁶ meters or 10⁻³ millimeters.

In the internet you can find that diameter of the human hair is in the range from 17 micrometers to 181 micrometers.

The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.

Thus, 9 × 10¹ micrometers is the most reasonable measurement for the thickness of a human hair.

A. Length of a Tour Bus                       ↔       2.      1.1 × 10¹ meters

B. Width of an apple                             ↔      3.     4 × 10⁰ centimeters

C. Distance from Earth to a Satellite   ↔     6.     8 × 10² kilometers

D. Thickness of a human hair              ↔      5.      9 × 10¹ micrometers

What is Satellite?

A satellite is a moon, planet or machine that orbits a planet or star. For example, Earth is a satellite because it orbits the sun. Likewise, the moon is a satellite because it orbits Earth.

What is expression?

An act, process, or instance of representing in a medium (such as words) : utterance freedom of expression. Something that manifests, embodies, or symbolizes something else this gift is an expression of my admiration for you.  

According to question, we have to drag the expression that is the most reasonable measurement for each object.

Length of Tour Bus is generally between 1 meter to 2 meters.

So, Reasonable measurement for Length of a Tour Bus is [tex]1.1[/tex]× [tex]10^{1}[/tex] meters

Width of an apple is generally between [tex]2[/tex] centimeters to [tex]6[/tex] centimeters

So, Reasonable measurement for Width of an apple  is  [tex]4[/tex]×[tex]10^{0}[/tex]   centimeters .

Distance from Earth to a Satellite is generally between [tex]700[/tex]  kilometers to  [tex]3600[/tex] kilometers.

So, Reasonable measurement for   Distance from Earth to a Satellite is

[tex]8[/tex]×[tex]10^{2}[/tex] kilometers.

Thickness of a human hair  is generally between  17 micrometers to 181 micrometers.

So, Reasonable measurement for Thickness of a human hair is [tex]9[/tex]×[tex]10^{1}[/tex] micrometers.

Hence, we can conclude that the following expression  is the most reasonable measurement for each object.

A. Length of a Tour Bus                        ↔     2.      1.1 × 10¹ meters

B. Width of an apple                             ↔      3.     4 × 10⁰ centimeters

C. Distance from Earth to a Satellite   ↔     6.     8 × 10² kilometers

D. Thickness of a human hair              ↔      5.      9 × 10¹ micrometers

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