expression equivalent to \( {3}^{ - 3} \)

Answer:

d. 20

Step-by-step explanation:

The given question implies 5 permutation 2, i.e \(_{5}\)\(P_{2}\).

But,

\(_{n}\)\(P_{r}\) = \(\frac{n!}{(n - r)!}\)

So that for \(_{5}\)\(P_{2}\), n = 5 and r = 2.

\(_{5}\)\(P_{2}\) = \(\frac{5!}{(5 - 2)!}\)

     = \(\frac{5!}{3!}\)

    = \(\frac{5*4*3*2!}{3*2!}\)

Cancel out 3 and 2 with respect to the numerator and denominator.

\(_{5}\)\(P_{2}\) = 5 * 4

     = 20

Therefore,

\(_{5}\)\(P_{2}\) = 20

So that the correct option is D.

Answer:

D-20

Step-by-step explanation:

Answer:

b=10cm²

Step-by-step explanation:

4inx5in=20

20/2=10cm²

Let me know if this helps

Step-by-step explanation:

< 2 = 37 = <4 (vertically opposite angles)

<3 = 180-37 = 144

<1 = 144

<2 = <8 = 37 ( alternate angles)

<3 = <5 = 144 (alternate angles)

<8 = <6 = 37 (vertically opposite angles)

<5 = <7 = 144 (alternate angles)

Answer:

The measure of ∠x is 75°.

Step-by-step explanation:

From inspection of the given diagram, triangle BDH is formed by line segments BD, DH and HB.  (Shown in red on the attached diagram).

We have been given two of the three interior angles of triangle BDH:

Line segment BE is a straight line.  As the interior angles of a triangle sum to 180°, and angles on a straight line sum to 180°, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

Angle x is the exterior angle of triangle BDH where angles B and D are the two non-adjacent interior angles. Therefore, x is equal to the sum of angles B and D:

⇒ x = m∠B + m∠D

⇒ x = 36° + 39°

⇒ x = 75°

Answer:

Step-by-step explanation:

Interior angles of a triangle always add up to 180, which means that...

\(\mathrm{\angle BDH + \angle DBH + \angle DHB = 180^o}\)

From the given the diagram:-

∠BDH = 39°

∠DBH = 36°

Therefore,

\(\mathrm{39^o+36^o+\angle DHB=180^o}\)

\(\boxed{\mathrm{\angle DHB =105^o}}\)

∠x and ∠DHB form a straight line meaning they are supplementary angles (They add up to 180°).

\(\mathrm{\angle DHB+\angle x=180^o}\)

\(\mathrm{105 + \angle x=180^o}\)

\(\mathrm{\angle x = 75^o}\)

Therefore, angle x equals 75°.

____________________

Hope this helps!

If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Answer:

\(34 + ( - 21) + 15 = 28\)

Answer:

is an example of enequality

Answer:

the clean price of the bond is $999.98.

Step-by-step explanation:

First, we need to calculate the accrued interest, which is the interest that has accumulated on the bond since the last coupon payment. The bond pays a semi-annual coupon, so there are 6 months between coupon payments. Since there are 4 months to the next coupon payment, the accrued interest is:

accrued interest = coupon rate * (time since last coupon payment / time between coupon payments)

accrued interest = 0.069 * (2 / 6)

accrued interest = 0.023

Next, we can calculate the clean price of the bond by subtracting the accrued interest from the invoice price:

clean price = invoice price - accrued interest

clean price = 1022 - 0.023

clean price = 999.98

Therefore, the clean price of the bond is $999.98.

Answer:

D. 1.33

Step-by-step explanation:

\( \because \: x = tan (\theta) \\ \\ tan (\theta) = \frac{4}{3} \\ \\ tan (\theta) = 1.33 \\ \\ \implies \: x = 1.33\)

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

What is inequality?

An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.

c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).

d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.

Hence,

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

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Answer:

2.33

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want the graph of the circle defined by the equation ...

  (x-2)^2 + (y-7)^2 = 4.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Comparing this to the given equation, we see ...

  h = 2, k = 7, r² = 4

Then r = √4 = 2.

The circle will have its center at (2, 7) and will have a radius of 2. It is shown in the attached graph.

<95141404393>

Answer:

1) immigrant

2) citizen

3) native born-citizen

4) quotas

5) census

6) birth rate

Step-by-step explanation:

..

Using the combination formula, it is found that 84 different groups of 6 people are possible from the 9 remaining friends.

The order in which the friends are chosen is not important, hence the combination formula is used to solve this question.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, 6 friends are chosen from a set of 9, hence:

\(C_{9,6} = \frac{9!}{6!3!} = 84\)

84 different groups of 6 people are possible from the 9 remaining friends.

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Answer:

this wrong

Step-by-step explanation:

Answer:

\(\boxed{-20i^2 -13ij+21j^2}\)

Step-by-step explanation:

\(\sf Plug \ in \ the \ values.\)

\((5i+7j) \cdot (-4i+3j)\)

\(\sf Expand \ brackets.\)

\(5i(-4i+3j)+7j(-4i+3j)\)

\(-20i^2 +15ij+-28ij +21j^2\)

\(\sf Combine \ like \ terms.\)

\(-20i^2 -13ij+21j^2\)

The equation z = 30x represents a direct variation the two variables, z and x, are directly proportional to each other. a.

Direct variation can be defined as a relationship between two variables where their values increase or decrease at the same rate.

In the case of the given equation, as x increases, z also increases proportionally.

Similarly, if x decreases, z will also decrease proportionally.

Direct variation can be represented as y = kx, where y and x are the variables, and k is the constant of variation.

In the given equation, we can see that z is the dependent variable, and x is the independent variable.

We can rewrite the equation as z = kx, where k = 30.

To understand how direct variation works, let's consider an example. Suppose we have an equation y = 5x, where y represents the cost of buying x apples at $5 per apple.

Here, the cost of buying apples is directly proportional to the number of apples purchased.

For instance, if we buy 10 apples, the total cost will be 10 × $5 = $50.

Similarly, if we buy 20 apples, the total cost will be 20 × $5 = $100.

Thus, we can see that the cost increases as the number of apples purchased increases, and vice versa.

The given equation z = 30x represents a direct variation is a type of relationship between two variables where their values increase or decrease proportionally.

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A 1.5 standard deviations above the mean IQ score is 122.5.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

A dependent variable is one that depends on another variable, whereas an independent variable does not depend on any other variable for its value.

Giving the z score are:

z is calculated as (raw score - mean) / standard deviation.

with a standard deviation of 15 and a mean of 100. The z-score of 1.5 is equal to the IQ score that is 1.5 standard deviations above the mean, so:

1.5 = (x - 100)/15

x = 122.5

A 1.5 standard deviations above the mean IQ score is 122.5.

The Complete Question is IQ score.

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Answer:

X=8

Step-by-step explanation:

          2x - 5 = X + 3

        -x            -x

X - 5 = 3

    +5    +5

X=8

Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

Answer:

E - Chi-Square Test of Independence

Step-by-step explanation:

- The Two-Sample Z-test is used to compare the mean of two samples in order to find out the possibility that they come from the same population.

-A linear regression t-test for slope is used to carry out hypothesis tests on the regression coefficients which are obtained in simple linear regression.

-A matched-pairs t-test is used to test whether there is a significant difference in mean between two sets of paired data.

- A two sample t-test is used to test whether the unknown population mean found in two groups are either equal or not equal.

-Chi-Square Test of Independence is a non-parametric test that is used to find out whether there is an association between categorical variables. Simply put, to find out if the categorical variables are independent or related.

From the question, the prospective home buyer is trying to investigate whether there is an association between the two variables which are the number of bathrooms contained in home and the estimated value of the home.

This means he is trying to find out if both variables are associated i.e.either independent or related. This is what Chi-Square Test of Independence does.

Answer:

A chi-square test of independence

Step-by-step explanation:

colllege board

Answer:

70%

Step-by-step explanation:

50/10 is 5 (which is 10%). 5 x 7 is 35 (or 70%)

The value of y is 48.

To find the value of y in this scenario, we need to use the fact that the angle bisector of ∠JSL splits it into two congruent angles.

Let's denote one of these congruent angles as ∠HSL and the other as ∠LSJ. Since ∠JSL is bisected, we have:

m∠JSL = m∠HSL + m∠LSJ

Given that m∠JSL = (4y - 10)° and m∠HSL = m∠LSJ = ∠HSJ = (y + 43)°, we can substitute these values into the equation:

4y - 10 = (y + 43) + (y + 43)

Simplifying the equation:

4y - 10 = 2y + 86

Subtracting 2y from both sides:

2y - 10 = 86

Adding 10 to both sides:

2y = 96

Dividing both sides by 2:

y = 48

Therefore, the value of y is 48.

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Answer:

\(\bf Slope(m)=-11\)

Step-by-step explanation:

\(\bf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}\)

\(\bf \left(x_1,\:y_1\right):\left(9,\:-9\right)\)

\(\bf \left(x_2,\:y_2\right):\left(7,\:13\right)\)

\(\bf m=\cfrac{13-\left(-9\right)}{7-9}\)

\(\bf m=-\cfrac{22}{2}\)

\(\bf m=-11\)

Therefore, the slope is -11!!

__________________

Hope this helps you!

Have a great day!

Answer:

Assuming you meant 19 1/2 then the answer would be 9.

Step-by-step explanation:

\(\large\bold{{Question :-}}\)The sum of the Squares of three consecutive number is 110. Then determine the Three Numbers.

\(\large\bold\red{\underline{Answer :-}}\)

So, First of all The Question is to find out three consecutive Numbers .

First of all let's learn a little about Consecutive Numbers. So, Consecutive Numbers are the Numbers which follows each other. For example :- 1,2,3,4 are consecutive Numbers.

Let's start with Our Question :-

So,

\(:\pink\implies\) \(\bold{{(x)^{2}}}\) + \(\bold{{(x + 1)^{2}}}\) + \(\bold{{(x + 2)^{2}}}\) = \(\bold{{110}}\)

\(:\pink\implies\) \(\bold{{(x)^{2}}}\) + \(\bold{{(x)^{2}}}\) + \(\bold{{(1)^{2}}}\)+ \(\bold{{2x}}\) +\(\bold{{(x)^{2}}}\) + \(\bold{{(4)}}\)+ \(\bold{{(4x)}}\) = \(\bold{{110}}\)

\(:\pink\implies\) \(\bold{{3x^{2}}}\) + \(\large\bold{{6x}}\) + \(\bold{{5}}\) - \(\large\bold{{110}}\) = \(\bold{{0}}\)

\(:\pink\implies\) \(\bold{{3x^{2}}}\) + \(\bold{{6x}}\) - \(\bold{{105}}\) = \(\bold{{0}}\)

By taking 3 Out as Common, we are left with the Quadratic Equation :—

\(:\pink\implies\) \(\large\bold{{1x^{2}}}\)+ \(\large\bold{{2x}}\) - \(\large\bold{{35}}\) = \(\large\bold{{0}}\)

x = -b ± √(b)^2— 4 × a × c / 2a

x = -2 ± √(2)^2— 4 × 1 × -35 / 2×1

x = -2 ± √144/2

[ As we know that "144" is square of 12 ]

x = -2 ± 12/2

Hence, x = +5

x +1 = 5+1 = +6

x+2 = 5+2 = +7

Hence, x = -7

x+1 = -7+1 = -6

x+2 = -7+2 = -5

Answer:

Step-by-step explanation:

Let the three consecutive numbers be denoted as :

Identity

It is given that the sum of the squares of these numbers add up to 110.

Taking x = 5

Taking x = -7

Solution

The scientific notation of the given number is 1.24×10⁻⁶.

The given number is 0.00000124.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 0.00000124=1.24×10⁻⁶.

Therefore, the Scientific notation of the given number is 1.24×10⁻⁶.

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Answer:

x = 10/3

Step-by-step explanation:

3x = 2y + 14

y = -6x + 18

3x = 2(-6x+18) + 14

3x = -12x + 36 + 14

15x = 50

x = 50/15

x = 10/3

Answer:

10/3

Step-by-step explanation:

3x= 2y+14-------(1)

y= -6x+18------(2)

from equation (2) put y= -6x+18 into equation (1)

3x= 2(-6x+18)+14

3x= -12x+36+14

3x+12x= 50

15x= 50

dividing bothsides by 16

x = 50/15

x= 10/3

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs