X And y values shown x
X. Y
2. 6
5. 15
8. 24

The calculated solution to the inequality is a < 6

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

2a - 10 < 2

Divide through the equation by 2

So, we have

a - 5 < 1

Add 5 to both sides

a < 6

Hence, the solution to the inequality is a < 6 and the graph is attached

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Answer:

85 mph

Step-by-step explanation:

It is because 680 / 8 = 85

Answer: 85 miles an hour

Step-by-step explanation:

divide distance by time

680 / 8 = 85 miles per hour

:)

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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Answer:

Step-by-step explanation:

See the attached file .

Answer:

\(\frac{28}{3}\)

Step-by-step explanation:

If you mean an improper fraction, then \(9\frac{1}{3}=\frac{(9*3)+1}{3}=\frac{27+1}{3}=\frac{28}{3}\)

Answer:

5 * 2 + 3(4 + 2) - 4(5 * 2)

= 10 + 3(6) - 4(10)

= 10 + 18 - 40

= 28 - 40

= -12

Answer:

Step-by-step explanation:

Answer:

Step three

Step-by-step explanation:

(2+8)+8

2+(8+8)    

2+0

2

In the third step Isabel subtracted 8 into 8 not added, in order to evaluate the expression correctly she needed to add 8 into 8 and then add the two.

\((2+8)+8\)

\(2+(8+8)\)

\(8+8=16\)

\(2+16=18\)

\(=18\)

Hope this helps.

Answer:

x = 73

Step-by-step explanation:

Since it's asking for the angle it's going to be inverse (sin-1,cos-1,tan-1)

It only gives you the opposite side and the hypotenuse

You can find the opposite side by going opposite from the missing angle like basically the side that is not being touched by x (The 4) This is the opposite angle

The hypotenuse is always going to be the long angle that is on the opposite side of the right angle (The 6) This is the hypotenuse

The adjacent side is the side not opposite to the x

Remember the acronym SOH CAH TOA

sin-opposite/hypotenuse

cos-adjacent/hypotenuse

tan-opposite/adjacent

The opposite and hypotenuse are the only sides that gave a number so it is sin and is inverse

\(sin^{-1} (\frac{4}{6} ) = .729\)

hope this helps

9514 1404 393

Answer:

  (i) x° = 70°, y° = 20°

  (ii) ∠BAC ≈ 50.2°

  (iii) 120

  (iv) 300

Step-by-step explanation:

(i) Angle x° is congruent with the one marked 70°, as they are "alternate interior angles" with respect to the parallel north-south lines and transversal AB.

  x = 70

The angle marked y° is the supplement to the one marked 160°.

  y = 20

__

(ii) The triangle interior angle at B is x° +y° = 70° +20° = 90°, so triangle ABC is a right triangle. With respect to angle BAC, side BA is adjacent, and side BC is opposite. Then ...

  tan(∠BAC) = BC/BA = 120/100 = 1.2

  ∠BAC = arctan(1.2) ≈ 50.2°

__

(iii) The bearing of C from A is the sum of the bearing of B from A and angle BAC.

  bearing of C = 70° +50.2° = 120.2°

The three-digit bearing of C from A is 120.

__

(iv) The bearing of A from C is 180 added to the bearing of C from A:

  120 +180 = 300

The three-digit bearing of A from C is 300.

Answer:

Minimum=60

First Quartile(Q1)=79

Median=86

Third Quartile (Q3)=89

Interquartile range (IQR)=10

Answer:

1. p value = 0.0203

2. We conclude that the market share for cars are different from what was suggested by the nation wde sales in 2017

Step-by-step explanation:

first we solve for the chisquare of this data.

from the attachment i have uploaded, a table of the ch square that i calculate gave:

Chisquare = 14.99

n = 7

degree of freedom = 7-1 = 6

we formulate hypothesis

H0; no diference in market share

H1: there is difference in market share

alpha = 0.05

we find the p value using the excel formula

CHIDIST(14.99, 6)

p value = 0.0203

the p value lies between 0.01 and 0.025

so we reject null and conclude that market share for for cars are different from what is suggested by nationwide sales in 2017

Answer:

\(\frac{8}{x}\)

Step-by-step explanation:

what is the sum 3/x+9+5/x-9

\(\frac{3}{x} + 9 + \frac{5}{x} - 9 =\)     (add \(\frac{3}{x}\) and \(\frac{5}{x}\))

\(\frac{8}{x} + 9 - 9 =\)            (solve 9 - 9 = 0)

\(\frac{8}{x}\)                           ( your answer)

Answer:

$16

Step-by-step explanation:

The worker's utility function can be represented as a combination of consumption and leisure. Let x be the number of hours worked per day, and c be the amount of consumption. Then, the worker's utility can be represented as:

U(c, 24-x) = f(c) + g(24-x)

where f(c) represents the utility from consumption, and g(24-x) represents the utility from leisure. The worker faces a budget constraint that states the amount of income they earn from work must equal their spending on consumption:

wx = pc

This constraint can be used to solve for the optimal combination of leisure and consumption that maximizes the worker's utility. By combining the utility function and the budget constraint, the worker's problem can be formulated as a maximization problem:

Maximize U(c, 24-x) subject to wx = pc

This problem can be solved using techniques such as Lagrangian optimization or constraint optimization to find the optimal values of c and x that maximize the worker's utility. The solution will depend on the specific forms of the functions f and g, as well as the values of w and p.

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Answer:

Step-by-step explanation:

∠2 = 2x + 108°

Each of the other two angles in the triangle is

(180° - (2x+108°))/2 = 36° - x

36° - x = 47°

x = -11°

Answer:

Perimeter = 12 1/2 in

Area = 9.375 in

Step-by-step explanation:

Perimeter:

(3 3/4) + (3 3/4) + (2 1/2) + (2 1/2) = 12 1/2

Area:

(3 3/4) * (2 1/2) = 9.375

Answer:

P = 12 1/2 in

A = 9 3/8 in²

Step-by-step explanation:

L = 3 3/4 in

W = 2 1/2 in

Area:

A = L × W

A = (3 3/4 in)(2 1/2 in)

A = 15/4 in × 5/2 in

A = 75/8 in²

A = 9 3/8 in²

Perimeter:

P = 2(L + W)

P = 2(3 3/4 in + 2 1/2 in)

P = 2(15/4 in + 5/2 in)

P = 2(15/4 in + 10/4 in)

P = 2(25/4 in)

P = 25/2 in

P = 12 1/2 in

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

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The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

1 to 4

Step-by-step explanation:

I don't think u want the explanation

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

The relative frequency of the first class is 0.25.

Relative frequency is a term used to describe the proportion of times an event occurs in a set of data, compared to the total number of events. In other words, it's the ratio of the frequency of the event to the total frequency of all events.

To determine the relative frequency of the first class, we need to first find the frequency of the first class. The frequency is the number of times the event occurs in the data set. Let's say the frequency of the first class is "f". Then, the relative frequency can be found by dividing the frequency of the first class by the total number of events (let's say it's "n").

Relative frequency = f / n

We round our answer to three decimal places to make it easier to understand and compare to other data.

If there are 100 total events and the frequency of the first class is 25, then the relative frequency would be:

Relative frequency = 25 / 100 = 0.25

Complete Question:

Determine the relative frequency of the first class. round your answer to three decimal places when 100 total events and the frequency of the first class is 25

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Answer:

Explained below.

Step-by-step explanation:

The data provided is for the number of times each family member verbally assaults another person throughout the first 24 hours.

Use Minitab to compute the descriptive statistics.

Go to Stat → Basic Statistics → Display Basic Statistics

A dialog box will open.

Select the variable.

Select 'Statistics'.  

Another dialog box will open.

Select the statistics required.

Press OK.

Select "Graphs'.

Select Histogram.

Press OK

The output is attached below.

(1)

The mean of the data is, Mean = 10.

(2)

The median of the data is, Median = 8.50.

(3)

The mode of the data is, Mode = 5.

(4)

The inequality statement for the mean, median and mode is:

Mean > Median > Mode

A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the histogram of the distribution.

Also if the Mean > Median > Mode then the distribution is skewed to the right.

For a skewed distribution the best of central tendency is the median.

So, the measure of central tendency that is most appropriate for this dataset is, Median = 8.50.

(5)

The range of the data set is:

Range = Maximum - Minimum

           = 19 - 4

           = 15

Thus, the range is 15.

(6)

The population of interest is the number of times the family members verbally assaults another person throughout the first 24 hours.

(7)

Consider the Minitab output.

The standard deviation of the data set is, SD = 5.60.

Answer:

\(x=16-2y\)

Step-by-step explanation:

\(\mathrm{Subtract\:}\frac{1}{4}y\mathrm{\:from\:both\:sides}\)

\(\frac{1}{8}x+\frac{1}{4}y-\frac{1}{4}y=2-\frac{1}{4}y\)

\(\mathrm{Simplify}\)

\(\frac{1}{8}x=2-\frac{1}{4}y\)

\(\mathrm{Multiply\:both\:sides\:by\:}8\)

\(8\cdot \frac{1}{8}x=8\cdot \:2-8\cdot \frac{1}{4}y\)

\(\mathrm{Simplify}\)

\(x=16-2y\)

Final Answer: \(x=16-2y\)

Answer:

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b) where a=3x and b=5.

(3x+5)(3x−5)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Go to where it says -8 on the y-axis then rise 4 and run 1

Answer:

60

Step-by-step explanation:

180 - 120 = 60

Answer:

D. \(10^{\circ}\)

Step-by-step explanation:

Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).

Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).

By the inscribed angle theorem, \(\alpha=84^{\circ}\).

Thus, \(\beta=20^{\circ}\).

By the inscribed angle theorem, \(x=10^{\circ}\).

The given shape of the distribution is not symmetric.

Given that, a box plot shows donations in dollars to charity.

We need to describe the shape of the distribution.

Donations to Charity ($) =

20 40 60 80 100 120 140 160 180 200 220

so, as we can see,

The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.

Hence, the given shape of the distribution is not symmetric.

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Answer:

12

Step-by-step explanation: