Find the are of the shaded shape below it has two lines of symmetry (vertical and horizontal) that pass through its centre
Give your answer in cm^2

Answer:

Here's a set of five numbers, each of which is divisible by 3:

{ 3, 6, 9, 12, 15 }

All the numbers in this set are multiples of 3, so they are all divisible by 3.

The conditional value probability is solved and P ( J ) = 0.1105

Given data ,

P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3

We can use Bayes' theorem to find P(J):

P(J | K) = P(K | J) * P(J) / P(K)

0.35 = 0.95 * P(J) / 0.3

0.35 * 0.3 = 0.95 * P(J)

0.105 = 0.95 * P(J)

P(J) = 0.105 / 0.95

P(J) = 0.1105

Hence , the probability is P ( J ) = 0.1105

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Answer:

[tex]\mathrm{Matrix \: Form:}[/tex]
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]

[tex]\mathrm{Determinant\; of \;coefficient \;matrix = - 6}[/tex]

Step-by-step explanation:

The system of linear equations provided in the question:
[tex]\begin{aligned}3x+2y+z &= 26\\ x-4y&=-11\\ 2x+z&=13\\\\\end{aligned}[/tex]

can be represented in matrix form as

[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]

The coefficient matrix is
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]

The determinant of this matrix can be obtained by the expansion formula:
[tex]\det \begin{pmatrix}a&b&c\\ \:d&e&f\\ \:g&h&i\end{pmatrix}=a\cdot \det \begin{pmatrix}e&f\\ \:h&i\end{pmatrix}-b\cdot \det \begin{pmatrix}d&f\\ \:g&i\end{pmatrix}+c\cdot \det \begin{pmatrix}d&e\\ \:g&h\end{pmatrix}[/tex]

Therefore
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]

[tex]= 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}[/tex]

[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc[/tex]

[tex]\det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix} = \left(-4\right)\cdot \:1-0\cdot \:0 = -4[/tex]

[tex]\det \begin{pmatrix}1&0\\ 2&1\end{pmatrix} = 1\cdot \:1-0\cdot \:2 = 1[/tex]

[tex]\det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix} = 1\cdot \:0-\left(-4\right)\cdot \:2 =8[/tex]

Finally,
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\\\\\\ = 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}\\\\\\= 3\left(-4\right)-2\cdot \:1+1\cdot \:8\\\\= -12 - 2 + 8\\\\= -6[/tex]

Answer: 2 hours 15 minutes

Step-by-step explanation:

To solve this problem, we need to use the formula:

distance = speed x time

First, let's calculate the distance Jaswat covered in the first 1 1/2 hours:

distance = speed x time

distance = 6 Km/h x 1.5 h

distance = 9 Km

So, Jaswat covered 9 Km in the first 1 1/2 hours. He still had to cover 12 Km - 9 Km = 3 Km.

Now, we need to calculate the time Jaswat took to cover the remaining 3 Km at a speed of 4 Km/h:

distance = speed x time

3 Km = 4 Km/h x time

time = 3 Km / 4 Km/h

time = 0.75 hours = 45 minutes

Therefore, Jaswat took 1 1/2 hours + 45 minutes = 2 hours 15 minutes to complete the journey.

The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at;

-3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

By substitution:

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537 respectively.

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Answer:

35%

(I replaced the 1st digit by a and the second digit by b)

Answer:

B

Step-by-step explanation:

This is a linear function.

:D

The solution of the given system of equations is (1, 2.5)

From the graph attached, it van be seen that two intersecting lines represent the system of equations.

And the solution of the system of equations is a common point where these lines intersect.

The graph shows both the line are intersecting each other at (1, 2.5).

Therefore, the solution of the given system of equations will be (1, 2.5).

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Step-by-step explanation:

[tex] { ({4}^{ - 4} )}^{3} \\ = {4}^{ - 12} [/tex]

[tex] \frac{ {4}^{15} }{ {4}^{5} } \\ = {4}^{10} [/tex]

[tex] {4}^{ - 5} \times {4}^{ - 4} \\ = {4}^{ - 9} [/tex]

[tex] \frac{1}{ {4}^{ - 12} } \\ = {4}^{12} [/tex]

least to greatest

[tex]1)\: {4}^{ - 12} \\ 2) \: {4}^{ - 9} \\ 3) \: {4}^{10 } \\ 4) \: {4}^{12} [/tex]

The measure (in radians) of central angle θ in the circle below is π/3.

We have,

radius = 3 cm

Arc length = π

We can use the formula relating the arc length (s) to the central angle (θ) and radius (r) of a circle:

s = r Ф

Now,

π = 3 x Ф

Ф = π/3

Thus,

The measure (in radians) of central angle θ in the circle below is π/3.

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The appropriate statistic for testing the null hypothesis is given as  D (-2.20/0.07)

Coefficient for slope variable (Exercise time) = -2.20

Standard error of coefficient = 0.07

Therefore, the test statistic value to verify whether or not there is an apparent slope on a population regression line can be estimated as follows.

Test statistic = Coefficient for slope variable/Standard error of coefficient = -2.20/0.07

Therefore its correct answer is D (-2.20/0.07)

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The number of real zeros for the function whose graph is shown include the following: D. 0.

In Mathematics and Geometry, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

This ultimately implies that, a polynomial graph touches the x-axis at real zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can reasonably and logically deduce that the real zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and it is non-existent on the graph above.

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Answer:

Step-by-step explanation:

so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)

The graph that shows the solution set for the given inequality is the one in option B.

Here we want to identify the graph of the inequality:

|x| ≤ 3

So, the absolute value of x is smaller or equal to 3, that means that the graph of the solution set is a segment whose endpoints are closed circles at x = -3 and x = 3.

(We use closed circles because these values are also solutions for the inequality).

With that in mind, we can see that the correct option in this case will be graph B.

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The length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).

To use the arc length formula, we need to find the derivative of the curve y = 5 - 4x:

y' = -4

Then, we can use the arc length formula:

L = ∫[a,b] √(1 + (y')^2) dx

where a and b are the limits of integration. In this case, a = -2 and b = 2.

L = ∫[-2,2] √(1 + (-4)^2) dx

= ∫[-2,2] √(17) dx

= √(17) * [x]_(-2)^(2)

= 4√(17)

So the length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).

To check this answer, we can note that the curve is a line segment with endpoints (-2, 13) and (0.75, 1), and we can calculate its length using the distance formula:

L = √((0.75 - (-2))^2 + (1 - 13)^2)

L = √(18.25 + 144)

L = √(162.25)

L = 4√(17)

This matches our previous answer, so we can be confident that the length of the curve is 4√(17).

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The sum of all the pets in the list is 11.

The average number of pets that the students own is 1.375.

It should be noted that to find the sum of all the pets in the list, we simply add up all the values:

0 + 1 + 2 + 3 + 1 + 2 + 0 + 2 = 11

Therefore, the sum of all the pets in the list is 11.

Since Cameron asked eight of his classmates, we divide the sum of pets by 8 to find the mean:

11 ÷ 8 = 1.375

Therefore, the average number of pets that the students own is 1.375.

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The measures of center can be used to summarize the number of pets that students own. Cueton asked eight of his classmates how many pets they own. The results are listed below.

0  1  2  3  1  2  0  2

What is The sum of all the pets in the list

What is the average number of pets that the students own

Answer:

Private saving (Sprivate) is equal to disposable income minus consumption:

Sprivate = Y - T - C = 15,000 - 3,000 - 9,000 = 3,000

Public saving (Spublic) is equal to government revenue minus government spending:

Spublic = T - G = 3,000 - 3,600 = -600

National saving (S) is equal to the sum of private and public saving:

S = Sprivate + Spublic = 3,000 - 600 = 2,400

Investment (I) is given by the investment function:

I = 3,900 - 100r

Equating investment to national saving gives:

I = S

3,900 - 100r = 2,400

Solving for r:

r = 15%

Therefore, the equilibrium real interest rate is 15%.

Substituting r = 15% into the investment function gives:

I = 2,400

Therefore, investment is 2,400.

Finally, to determine if the government has a budget surplus or deficit, we need to calculate the government's budget balance, which is equal to government revenue minus government spending:

Budget balance = T - G = 3,000 - 3,600 = -600

Since the budget balance is negative, the government of Flatland has a budget deficit.

Answer: e

Step-by-step explanation:

Answer:Valid

Step-by-step explanation:

The truth statements about the function f(x) = 14(0.87)^x is Growth; y = 0

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

f(x) = 14(0.87)^x

An exponential function is represented as

y = ab^x

Where

a = initial value

b = growth/decay factor

In this case, the exponential function is a decay function

This means that

The value of b is less than 1 i.e.

b = 0.87 and 0.87 < 1

Hence, the function is a decay function

Recall that

f(x) = 14(0.87)^x

So, we have

y = 0 as the the equation of the asymptote

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The next "three-umbers" in the pattern "2,0,6,-4,10,-8,..." are 14, -12, and 18.

To find the next three numbers in the pattern 2, 0, 6, -4, 10, -8, we need to analyze the pattern and identify the rule for it.

The pattern seems to be alternating between adding and subtracting the "odd-multiples" of 2.

The pattern is as follows : 2 - (2×1) = 0,

0 + (2×3) = 6,

6 - (2×5) = -4,

-4 + (2×7) = 10,

10 - (2×9) = -8,

Using this rule, we can find the next three numbers in the pattern as follows:

Add 22 because : -8 + (2×11) = 14,

Subtract 26 because : 14 - (2×13) = -12,

Add 30 , because : -12 + (2×15) = 18,

Therefore, the next three numbers in the pattern are 14, -12, and 18.

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By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).

In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."

Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

By adding the given vectors algebraically, we have the following:

[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)

[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)

[tex]\vec a + \vec b[/tex] = (3, 1).

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For the given data set of temperatures, the median temperature is 72.5 degree Fahrenheit.

In order to find the median temperature, we first need to arrange the temperatures in order from lowest to highest:

The temperatures arranged in order is : {66, 70, 72, 72, 73, 75, 79, 81}

There are 8 temperatures in total, which is an even-number, so the median will be the average of fourth and fifth day temperature.

In this case, the temperature of the fourth day is 72, and fifth day is 73,

The average will be = (72+73)/2 = 72.5,

Therefore, the median high daily temperature in the city is 72.5 degrees Fahrenheit.

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The given question is incomplete, the complete question is

The data set shown below represents the distribution of daily high temperatures in a city for 8 days.

79,73,72,70,72,66,81,75.

What is the median high daily temperature, in degrees Fahrenheit, in the city?

If Joe lowers the price he charges per pizza, he will sell more pizzas. option B

To sell more pizza, Joe must decrease the price he charges per unit. The law of demand dictates that when a product's cost decreases, its quantity demanded rises resulting in an increased sales volume.

It follows then that if Joe reduces his pizza prices more people will be inclined to purchase it creating this increase in sales . Nonetheless, whether Joe’s profit will rise or diminish depends on the extent of the rise in sales compared to the lowering of the price.

Even if there is a reduction in the price of every pizza, if the resultant sales volume is significant enough, Joe’s profit margin could still experience a positive turn.

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A ski lodge inspects 80 skis and discovers four that are faulty. The skis that are likely to be defective are 21.

It is assumed that there are 80 skis, four of which are faulty.

As a result, the total number of outcomes is 80.

Positive outcomes = 4

Let [tex]E_{1}[/tex] represent the event of selecting a faulty. As a result, the likelihood of selecting a defective ski is expressed mathematically as follows.

[tex]E_{1}[/tex] = Favorable case of defective / Total number of skis

= 4 / 80

= 1 / 20

=0.05

Skis will be discovered in 5% of cases.

So, the event of choosing a defective is 4 / 80.

If the total number of skis is 420, then the number of defective skis will be:

4 / 80 × 420

= 1/20 × 420

= 21

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Correct question:

A ski lodge inspects 80 skis and finds 4 to be defective. The lodge has 420 skis. Predict the number of skis that are likely to be defective.

a) The percent change in Jennifer's account balance each month is 2.5%.

b) Based on the future value function, A(m)= 1750(1.025)^m, the account balance is increasing because the growth factor is 1.025 and not less than 1.

A growth function is a mathematical equation that shows a constant rate in increase or growth in value of the dependent variable.

A growth function is modeled by a growth factor greater than 1 while a decay function shows a decay.

Percentage change = 2.5% (1.025 - 1)

2.5% = 2.5 ÷ 100 = 0.025

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This is a word problem involving supplementary angles. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.

Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:

x=6(180−x)−590

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

xx7xxx​=6(180−x)−590=1080−6x−590=490=7490​=70​

Therefore, the measure of the angle is 70°.

Answer: 70, 6

Step-by-step explanation:

(a)  For <F  that is the same as <D.  The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same

All of the angles are = 180   if you subtract <E, you are left with 140 to be split between <F and <D

<F= 70

(b) all of the sides are the same because all the angles are the same

so AB=6

a) The value of the investment after 4 years is $5,544.90.

b) The value of the investment after 8 years is $6,849.42.

c) The value of the investment after 12 years is $8,453.35.

The formula for calculating the value of an investment that is compounded continuously is given by:

A = [tex]Pe^{(rt)[/tex]

where A is the final value of the investment, P is the initial investment amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time period in years.

(a) To find the value of the investment after 4 years, we can substitute the given values in the formula as follows:

A = 4500[tex]e^{(0.05254)[/tex]

A = 4500[tex]e^{0.21[/tex]

A = 45001.2322

A = $5,544.90

(b) To find the value of the investment after 8 years, we can substitute the given values in the formula as follows:

A = 4500[tex]e^{(0.05258)[/tex]

A = 4500[tex]e^{0.42[/tex]

A = 45001.5221

A = $6,849.42

(c) To find the value of the investment after 12 years, we can substitute the given values in the formula as follows:

A = 4500[tex]e^{(0.052512)[/tex]

A = 4500[tex]e^{0.63[/tex]

A = 45001.8785

A = $8,453.35

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Answer:

Step-by-step explanation:

Its simple, you need to find x

4 days the same amount of time (x) gives 48 min
4x = 48

x = 48/4

x = 12

then to get the amount of minutes in 9 days it would be:

9x=days

9(12)=108

the answer would be 108 min

Answer:

108 mins

Step-by-step explanation:

48 mins/4 days = x mins/9 days

4x= 432

x=108 mins