Question 1 of 5
Drag each tile to the correct location on the table. Not all tiles will be used.
Match each quadratic function with the attributes of its graph.

Ok, so

We want to find the equation of an ellipse centered at the origin with a horizontal major axis of 8 units and a minor axis of 6 units.

For this, let's remember the form of the equation of an ellipse:

Where the center of the ellipse is located at the point (h,k).

If the ellipse is centered at the origin, then, h=0 and k=0, so the form of our equation will be:

Now, we're given that our ellipse has a horizontal major axis of 8 units and a minor axis of 6 units. Since the major and minor axis are given by the parameters 2a and 2b, then, a=4 and b=3. the greater number will divide the x² term and a>b.

So, the equation of this ellipse is:

The graph of this ellipse will be something like:

Answer:  1i=1f

Step-by-step explanation:

a. The probability that the sample proportion will be within ±0.02 of the population proportion - 0.5223

b. The probability that the sample proportion will be within 0.05 of the population proportion - 0.9232

[tex]Given, \\$P=0.2 a$ \\$n=200$ \\mean, \ $\mu \hat{p}=p$ \\$=0.20$ \\Standard deviation, $\sigma_p=\sqrt{\frac{p(1-p)}{n}}$ \\$=\sqrt{\frac{0.20(1-0.20)}{208}}$ \\$=\sqrt{\frac{0,20(0,80)}{200}}$ \\$=\sqrt{\frac{0.16}{200}}$. \\$=0.0283$ \\a) $p(|x-\mu|=\pm 0.02)=f\left(\frac{-|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma_{\hat{p}}}\right)$ \\$=1\left(\frac{-0.02}{0.0283} < = < \frac{0.02}{0.0283}\right)$ \\$=P(-0,71 < z < 0,71)$[/tex]

[tex]$$\begin{gathered}=p(z < 0,71)-p(z < -0,71) \\=0,7612-0.2389 \\=0,5223 } \\\therefore P(|x-\mu|=\pm 0.021=0,5223)\end{gathered}$$[/tex]

[tex]b)\\$$\begin{aligned}p(|x-\mu|=\pm 0.05)=p\left(\frac{|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma \hat{p}}\right) \\=p\left(\frac{-0.05}{0.0283}-z < \frac{0.05}{0.0283}\right) \\=& p(-1.77 < z < 1.77) \\=& P(z < 1.77)-p(z < -1.77) \\\therefore p(i x-\mu \mid&=\pm 0.05)=0.9232\end{aligned}$$[/tex]

A population is a complete  group of individuals, regardless of whether that group consists of a nation or a group of people with a common characteristic.

In statistics, a population is a group of individuals from which a statistical sample is taken for research. Thus, any selection of individuals grouped together on the basis of some common characteristic can be called a population. A sample may also refer to a statistically significant portion of the population rather than the entire population. Therefore, statistical analysis of a sample must report the approximate standard deviation or standard error of the results for the entire population. Only the whole population analysis has no standard error

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The volume of the cone is 36,960km³.

What is a cone?

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top called the apex.

The volume of a cone defines the space or the capacity of the cone. It is calculated using:

Vol. of a cone=1/3×π×r²h

where π=22/7

r     = raπius of the base of the cone

h= height of the cone

Thus, vol. of the cone=1/3×22/7×21²×80

                                   =  776160/21

                                    =36,960km³

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In geometry, a point is a place. It is completely empty, meaning it has no width, length, or depth. A dot indicates a point. A line is described as a collection of points that stretches in both directions indefinitely.

A point is the most fundamental geometrical object. It has a capital letter name and a dot as its symbol. A point is sizeless and just denotes position (that is, zero length, zero width, and zero height).

A point in mathematics is a precise spot on a plane. The flat, two-dimensional surface of a plane. A dot and a capital letter are typically used to identify points. Angles and forms, such the rectangle ABCD or the line segment YZ, can be named using points.

There are no measurements like length, width, or thickness for a point. The point can be determined by a star in the sky. The tip of a compass, the pointed end of a knife, and other similar objects are examples of points.

The answer is (7,9)

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We know that figure I and figure II are similar, which means that:

-The corresponding angles are equal

-The corresponding sides are at the same ratio.

The ratios between the corresponding sides are:

You have to compare the determined ratios with the given options to find the true statement.

The only given proportion that is true is the first one

ok

P1 = (-20, 0)

P2 = (0, 15)

slope = (15 - 0) / (0 + 20)

slope = 15/20

slope = 3/4

Equation of the line

y - 0 = 3/4(x + 20)

y = 3/4x + 3/4(20)

y = 3/4x + 15

Result y = 3/4x + 15

To solve the exercise you can use the point-slope formula, that is,

So, in this case, you have

Then,

To find:

The angular velocity of the point.

Solution:

Given the wheel moves with a velocity of 95 feet per second and the diameter is 5 feet.

So, the radius of the wheel is 5/2 feet.

The formula used to find the angular velocity of the wheel is given by:

So, by the given information is:

Thus, the angular velocity is 38 radians per second.

Number of candy's Bev has left with her is 12 .

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

No. of candy Bev has= 24

She gave 1 /3 of candy to Jamie.

No. of candy Jamie got = 1 /3 of total candy

                                       = 1 /3 * 24

                                       = 8 candy

No. of candy she remained = total no. of candy - no of candy she gave to Jamie:

                                            =24 - 8

                                            =16

No. of candy Selena got = 1 /4 of remaining candy

                                           =1 /4 ×16

                                            =4

No. of candy left = total candy - (candy Jamie got +candy Selena got)

                                             = 24-(8+4)

                                              = 12 candy

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Search for the numbers that divide all of the given set.

Notice that all three of them can be divided by two:

Therefore, 2 is the first common factor. Now, take the numbers 10, 6 and 12 and repeat the procedure. Notice that all of them are divisible by 2:

Therefore, 2 is the next common factor. Now, take the numbers 5, 3 and 6 and repeat the procedure. Notice that 3 is not divisible by 2 and 5 is not divisible by 3. Since there are no more numbers lower tan 3 that divide all of the numbers, there are no more common factors.

The common factors were 2 and 2. Multiply all the common factors to find the greatest common factor:

Therefore, 4 is the greatest common factor of 20,12 and 24.

ANSWER

EXPLANATION

We are given that the radius of the circle is 3 inches and the length of the arc that subtends the angle is 3π inches.

We can find the angle subtended by the arc by using the formula for length of an arc:

Therefore, we have that:

That is the angle subtended by the arc.

We have

So we must replace the value of y of the second equation in the first equation

So, the answer is 9x - 6 = 50. Last option.

Elements of following sets are

A = {1}

B = {-1, 1}

C = Q ∩ [0, 1]

Sets

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set. A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Given that

A = {n ∈ N : cos(nπ) greater than or equal to 0}

B = {cos(nπ) : n ∈ N}

C = {q + r : q, r ∈ Q ∩ [0, 1]}

Therefore elements of

A = {1}

as cos 2[tex]\pi[/tex], cos 4[tex]\pi[/tex], cos 6[tex]\pi[/tex], cos 8[tex]\pi[/tex] and so on is equal to 1.

B = {-1, 1}

as cos [tex]\pi[/tex] , cos 2[tex]\pi[/tex], cos 3[tex]\pi[/tex], cos 4[tex]\pi[/tex], cos 5[tex]\pi[/tex] and so on is equal to -1 and 1.

C = Q ∩ [0, 1]

as q and r both belongs to Q ∩ [0, 1] and their sum will be also equal to Q ∩ [0, 1].

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The ratio OQ/QN would not give a correct calculation of K

Here, we want to select which of the options would be a wrong calculation for k which is the scale factor

Any of the ratios that would measure k should be such a ratio that compares similar distances

The correct answer in this case is OQ/QN

The reason why it is wrong is that while OQ meaures the distance from the center of dilation to the first segment, QN should also have measured a comparable distance

Thus, ON should have been what to use if we are to compare both distances since they would have measured the distances from the center of dilation which is the origin in this case

700,000,000

+

60,000,000

+

8,000,000

+

90,000

+

20,000

+

50

+

4

____________

768,110,054

The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.

How to determine average velocity and instantaneous velocity?
Average velocity is defined as the body's overall displacement divided by its time of motion. While instantaneous velocity is defined as a body's speed at a certain instant in time, or its displacement at that instant. When the velocity is constant, average and instantaneous velocities will equalize at just one condition.
The definition of instantaneous velocity is the rate of change of position over a relatively brief time period (almost zero). Simply said, the speed of an object at that precise moment. The definition of instantaneous velocity is "The velocity of an item in motion at a certain point in time." The instantaneous velocity of an object may be equal to its standard velocity if it has uniform velocity.
Mathematically, average velocity = [s(t₂) - s(t₁)]/[t₂ - t₁]
Instantaneous velocity at time, t is = (ds/dt) at time = t

Given, the displacement for the particle is given by s = 3t² - 4t + 5
Time interval, t₁ = 5s and t₂ = 3s;
Using formula in literature, average velocity of the particle in the time interval between 3s and 5s is:
Average velocity = (s(5) - s(3))/(5 - 3) = (60 - 20)/2 = 20 ms⁻¹
Instantaneous velocity at t = 4 is ds/dt at that time-frame:
Now, v = ds/dt = 6t -4
Now, v(4) = 6(4) - 4 = 20 ms⁻¹
The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.

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Explanation

Given

Therefore;

Answer:

The most appropriate choice of circle will be given by

x coordinate of the center decreases by 2

Fourth option is correct

What is circle?

Circle is a round two dimensional figure where all the points on the circle maintains a fixed distance from a point known as the center of the circle. The fixed distance of the point on the circle from the center of the circle is known as radius of the circle.

Equation of circle is (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius of the circle.

Here,

(x-2)^2 + (y - 3)^2 = 25

(x-2)^2 + (y - 3)^2 = 5^2

This is the equation of circle with center (2, 3) and radius 5 units

On shifting the circle 2 units to the left, the coordinate of center of circle changes to (0, 2)

That means x coordinate of the center decreases by 2

So fourth option is correct

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Using the Factor Theorem, the equation of the quartic polynomial in standard form is given by:

y = 4(x^4 + x³ - 13x² - x + 12).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule given as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

From the given table, the roots are given by the values of x when y = 0, hence they are given by:

[tex]x_1 = -4, x_2 = -1, x_3 = 1, x_4 = 3[/tex]

Hence the function is given by:

f(x) = a(x + 4)(x + 1)(x - 1)(x - 3)

f(x) = a(x² + 5x + 4)(x² - 4x + 3)

f(x) = a(x^4 + x³ - 13x² - x + 12).

From the table, we also have that when x = 0, y = 48, hence the leading coefficient a can be found as follows:

12a = 48

a = 48/12

a = 4.

Hence the equation is:

y = 4(x^4 + x³ - 13x² - x + 12).

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Answer:

C

Step-by-step explanation:

Just divide 48/120.

The measure of the angle in the triangle is of 85º.

In the context of this problem, the measure of the angle is found using the ruler in the given image.

Due to the position that the triangle opens, from left to right, we have to read the angles from the bottom line.

The measures are listed in intervals of 10º, however each trace represents one degree.

The angle of the illustrated triangle is positioned at the 5th trace between 80º and 90º, hence the measure of the angle in the triangle is calculated as follows:

80º + 5º = 85º.

This is because each trace represents one degree, and the angle is at the 5th trace between 80º and 90º.

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The number of bacteria after the increase is 217

Bacteria in a culture when the scientist first observed = 155

Percentage: Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.

Increase in number of bacteria post observation = 40%

Bacteria after increase:

= 155 + 40% of 155

= 155 + 0.40*155

= 155 + 62

= 217

So, bacteria after the increase is 217

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Latoya's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Latoya $5.85 per pound, and type B coffee costs $4.30 per pound.

This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $553.20.

Let, a pounds of type A coffee and b pounds of type B coffee were used.

Then,

Substituting in the first equation,

Hence, 24 pounds of type A coffee were used.

Notice that the first number is 4, that would be the missing number.

The complete expression is

Remember that the associative property just groups the numbers differently.

answer: x = 3.27

The recursive formula if the sequence is 4,7,10,13 is aₙ = 3n - 2.

This is referred to as the list of the things or items in mathematics  in which repetitions are allowed and a certain order is followed and an example of a sequence is 1,3,5,7...etc.

The formula for arithmetic sequence is aₙ = a₁ + d ( n -1) in which a is the first term while d is the common difference. a₁ is referred to as the first term while d is the common difference which is 7 - 5 = 2 or 5 - 3 = 2.

aₙ = a₁ + d ( n -1)

     = 4 + 3 ( n - 1) --- expand the bracket

     = 4 + 3n - 3   = 4 -3 + 3n

aₙ  = 3n + 1

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An outlier is a value that is outside the expected limits of the data. It Is usually more than 3 standard deviation from the mean.

In the league A, we see an outlier in the minimum value (26) and, in the league B, the maximum value (256).

The outliers can be spotted in the graph by looking at points does seem to be too far of the group of data. Also, mathematically, looking at the distance from the mean: if the difference between the value and the mean is more than 3 standard deviations, we are talking about an outlier.

Answer:

If you are talking about a triangle XYZ

<x + <y + <z = 180

73 + 90 + z =180

<z = 17