5. The corresponding sides of the similar shapes have same
- In the figure given below, what is the value of x? (RED)
2 cm
3 cm
3 cm
2 cm
4 cm
x cm
(GR
4 cm

The discount amount is $213.6

The sale price for the exercise machines is $676.4

The first step is to calculate the discount amount

890 × 24/100

= 890 × 0.24

= 213.6

The next step is to calculate the sale price

890(1-0.24)

890(0.76)

676.4

Hence the discount amount is $213.6 and the sale price of the exercise machine is $676.4

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The amount paid to vehicle A is less than to vehicle B so, Vehicle A is suitable to purchase based on a monthly payment.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

For vehicle A,

The Principal amount of the car, P = $25000,

The rate of interest, r = 5% = 5/100 = 0.05,

The tenure, n = 60 months = 60/12 = 5 years,

Calculate the amount by the formula given below,

A = P (1 + r)ⁿ

Here A is the amount,

Substitute the values,

A = 25000 (1 + 0.05)⁵,

A = $31907.03

Similarly,  for vehicle b

A = 29000 (1 +0.04)⁶

A = $36694.25

As the amount of vehicle A is less than the of vehicle B Therefore, vehicle A is suitable to buy.

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Answer:

x = 8. y = 21

Step-by-step explanation:

x + 8x + 18 = 90

combine like terms

9x + 18 = 90

-18 both sides

9x = 72

divide by 9 both sides

x = 8

______

3y + 27 = 90

-27 both sides

3y = 63

divide by 3 both sides

y = 21

Based on the average profit per game, the total money which this club should expect to earn by the end of the 10-game season is $80.21.

In order to determine a linear equation of the trend line (line of best fit) that models the data points contained in the table, we would have to use a scatter plot.

In this scenario, the number of games would be plotted on the x-axis of the scatter plot while the profit (in dollars) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the trend line on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the data points in the table, a linear equation of the trend line is given by:

y = 8.23x - 2.09

By the end of the 10-game season, the average profit per game is given by:

y = 8.23x - 2.09

y = 8.23(10) - 2.09

y = 82.3 - 2.09

y = $80.21.

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True. You can look at the direction of the line and automatically know if the slope is a positive or negative number.

The linear equation with positive value of slope goes upwards from left to right and linear equation with negative value of slope goes downwards from left to right.

Thus, it is true that you can look at the direction of the line and automatically know if the slope is a positive or negative number.

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Answer:30%

Step-by-step explanation:

Step-by-step explanation:

so,

100% = $130

1 % = 100%/100 = 130/100 = $1.30

the price changed by 169 - 130 = $39.

how many % are that ?

as many % and times 1% fits into $39 :

39 / 1.3 = 30%

the price increase was 30%.

The axis of symmetry of function y = -|x + 10| is at y = 0

Axis of symmetry is an imaginary straight line which divide the function into two equal parts.

Axis of symmetry creates a mirror image of other part.

If we fold the two parts then the parts will superimposed.

Given function,

y = -|x + 10|

is in form y = a |x - h| + k

here , (h, k) is vertex

Comparing the form to the given equation

(h, k) = (-10 , 0)

which means graph is opens upward

and a = -1

Hence, the equation of axis of symmetric is at y = 0

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The quadratic functions in this problem are listed as follows:

The definition of a quadratic function is presented as follows:

y = ax² + bx + c.

In which the leading coefficient a has to assume a value different of zero.

Another format to represent a quadratic function is making the input variable y and the output variable x, which is an exchange of the conventional notation, hence:

x = ay² + by + c.

The non-quadratic functions in this problem are:

All the other functions are quadratic functions, as they have two as the highest exponent, with a leading coefficient different of zero.

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The critical values for the chi-square distribution, with a sample size of 4 and a confidence level of 98 percent, are of:

0.2971 and 13.2767.

The critical value for the chi-square distribution is obtained inserting these following information into a calculator:

In the context of this problem, with a sample size of 4 and a confidence level of 98 percent, the parameters are given as follows:

Inserting these information into the calculator, the critical values are given as follows:

0.2971 and 13.2767.

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Answer:

−16x − 20y + 17

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer: a) $78 per day

b) $21,352.50

Step-by-step explanation:

a) 60x10=600

600x0.13= $78 per day

b) 15x10=150

150x0.13=$19.50 per day

19.50x365= $7,117.50 per year (with a 15watts lightbulb)

$78x365=$28,470 per year (with a 60watts lightbulb)

$28,470-7,117.50= $21,352.50

The cups of flour required for 2 cups of cashew is 2.6667

The proportion given in the problem is 3 cups of cashews for 4 cups of flour.

From the given proportion we calculate for the quantity of flours required for 2 cups of cashew

3 cups of cashew = 4 cups of flours

2 cups of cashew = ?

cross multiplying

3 * ? = 4 * 2

? = 4 * 2 / 3

? = 8 / 3

? = 2.6667

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Answer: The probability that more than 12 of the entry forms will include an order is 0.624.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The Magazine Mass Marketing Company has received 16 entries in its latest sweepstakes.

The probability that more than 12 of the entry forms will include an order can be found as:

P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P( X = 3) - P(X = 4)

P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)

P(X > 4) = 1 - 0.0009 - 0.0097 - 0.043 - 0.117 - 0.205

P(X > 4) =  0.624

Thus, the probability that more than 12 of the entry forms will include order is 0.624.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

7

Answer:

y = 122

x = 58

Step-by-step explanation:

Parallel line angle rule, corresponding angle are equal

so y = 122

A flat line has 180degree angle

to get x, flat line - y = 180 - 122 = 58

The number of students per teacher is 23.

The number of students per tutor is 8.

The number of tutors needed for 72 students is 9.

In order to determine the number of students per teacher, divide the total number of teachers by the total number of students.

Students per teacher = total number of students / total number of teachers

115 /5 = 23 students per teacher

In order to determine the number of students per tutor, divide the total number of tutors by the total number of students.

Students per tutor = total number of students / total number of tutors  

54 / 6 = 9 students per tutor

The number of tutors needed for 72 students = total number of students / students per tutor

72 / 9 = 8 tutors

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The measures, using the normal distribution and the central limit theorem, are given as follows:

a) Probability of at least 4.03 ounces: 0.9192 = 91.92%.

b) Probability of 74% that it is between 4.04 ounces and 4.16 ounces.

c) Probability of 78% that it is greater than 4.06 ounces.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters regarding the amount of juice squeezed from these oranges are given as follows:

[tex]\mu = 4.10, \sigma = 0.2, n = 16, s = \frac{0.2}{\sqrt{16}} = 0.05/tex]

The probability that the sample mean amount of juice will be at least 4.03 ounces is one subtracted by the p-value of Z when X = 4.03, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (4.03 - 4.10)/0.05

Z = -1.4.

Z = -1.4 has a p-value of 0.0808.

1 - 0.0808 = 0.9192.

Considering the symmetry of the normal distribution, the middle 74% of the measures is bounded by:

Hence the lower bound is:

[tex]Z = \frac{X - \mu}{s}[/tex]

-1.125 = (X - 4.10)/0.05

X - 4.10 = -1.125 x 0.05

X = 4.04.

The upper bound is:

[tex]Z = \frac{X - \mu}{s}[/tex]

1.125 = (X - 4.10)/0.05

X - 4.10 = 1.125 x 0.05

X = 4.16.

The probability is ​78% that the sample mean amount of juice will be greater than the 22th percentile, which is X when Z = -0.77, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

-0.77 = (X - 4.10)/0.05

X - 4.10 = -0.77 x 0.05

X = 4.06 ounces.

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Explanation:

To find x we need to find the unknown side that connects the two triangles using the Pythagorean theorem:

a² + b² = c² (c is always hypotenuse)

So:

a² + 6² = 9²

a² = 9² - 6²

a² = 81 - 36

a² = 45

a = sqrt45

Now we do the same thing for the other triangle:

x² + 5² = sqrt45²

x² + 25 = 45

x² = 20

x = 2√5 or 4.5...

Aanya will now buy each at the cost below

A cherry muffin costs 350 shillings

A blueberry muffin costs 210 shillings

An apple costs 140 shillings

damson ones costs 70 shillings

The information given in the question is interpreted as below

A cherry muffin = 350 shillings

A blueberry muffin = 3 * damson ones

An apple + a blueberry muffin = 1 cherry muffin

A cherry muffin + 2 damson ones = 2 apple + 1 blueberry

from: 1 blueberry muffin, B = 3 * damson ones, D

D = B / 3

Also, An apple, A + B = 1 cherry muffin, C

A = C - B

C + 2D = 2A + B

substituting the values

350 + 2 * (B/3) = 2 * (350 - B) + B

350 + 2B/3 = 700 - 2B + B

collecting like terms

2B/3 + B = 700 - 350

5B/3 = 350

5B = 1050

B = 1050/5

B = 210

Solving for cost of apple

A = C - B = 350 - 210 = 140

Solving for the cost of the damson ones

D = B / 3 = 210 / 3 = 70

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The equation that is used to find the length of the legs of the triangle is

0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0

The area of the triangle is 24 square feet.

We know that the area of a triangle is given by the formula

1/2 × base × height.

Now in the attached figure we can see that the length of the base is x feet

The height of the right-angled triangle is (x+2) feet.

So the area of the triangle will be:

area = 1/2 · (x) · (x+2)

or, area = 0.5x(x+2)

But the area of the triangle is 24 square feet. Therefore the Equation to find the legs will be 0.5x(x+2) = 24.

Now if we use the properties of Pythagoras theorem we can write the formula as

hypotenuse² =  sum of squares of legs

10² = x² + (x+2)²

Therefore we get the second equation.

Now simplifying the above equation we get:

10² = x² + (x+2)²

or, 2x² + 4x - 96 = 0

or, x² + 2x - 48 = 0

This is the third option.

Therefore the required equation are:

0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0 .

Disclaimer: The missing image of the triangle is attached below.

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The broker charged $100.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total shares = 1000

Price for each shares= $5.

So, the total price of 1000 shares= $5000

If broker is charging a flat percentage of 2% for a trade.

Then, the broker charged for 1000 trade

= 5000 x 0.02

= $100.

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Step-by-step explanation:

please recheck your question..

There is no question attached.

hope it helps..

Answer:

[tex]\frac{8}{31}[/tex]

Step-by-step explanation:

the reciprocal of a number n is [tex]\frac{1}{n}[/tex]

given

3 [tex]\frac{7}{8}[/tex] ← express as an improper fraction

= [tex]\frac{31}{8}[/tex] , then

reciprocal = [tex]\frac{1}{\frac{31}{8} }[/tex] = [tex]\frac{8}{31}[/tex]

Answer:

[tex]\displaystyle \frac{8}{31}[/tex]

Step-by-step explanation:

First, we will turn 3 ⅞ into an improper fraction.

   [tex]\displaystyle (3*\frac{8}{8} )+(\frac{7}{8} )=\frac{24}{8} +\frac{7}{8} = \frac{31}{8}[/tex]

Next, we will find the reciprocal. This means we flip the numerator and the denominator.

[tex]\displaystyle \frac{31}{8} \rightarrow \frac{8}{31}[/tex]

The probability that C and D would be odd according to the given task content is; 1/4.

It follows from the task content that the probability that C and D would be odd be determined.

Given that the C and D are each chosen from a set 1, 2, 3, 4.

The probability that C is odd would be;

P (C is odd) = 2/4 = 1/2

Also; P ( D is odd) = 1/2

Consequently, the probability that C and D would be odd is;

= 1 / 2 × 1 / 2

= 1 / 4.

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Answer:

Even and Positive

Step-by-step explanation:

Answer:

C ≈ 207.3 ft

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( where r is the radius ) , then

C = 2π × 33 = 66π ≈ 207.3 ft ( to the nearest tenth )

Answer:

103.67 feet

Step-by-step explanation:

using C = pi d

The number sentence 4.8 < √32 is true

A number sentence is an arrangement of numbers and mathematical operation symbols

Given:

For 3 1/3 < √7

3 1/3 = 3.33 and √7 = 2.65

3.33 < 2.65

This is not true

For 4.8 < √32

√32 = 5.66

4.8 < 5.66

This is true

For |-3.2| < |-3.1|

|-3.2| = 3.2                Note: when you see sign | | you neglect the sign

|-3.1| = 3.1

3.2 < 3.1

This is not true

For 5.3×10⁵ < 9.76× 10⁴

5.3×10⁵ = 5.3×100000 = 530000

9.76× 10⁴ = 9.76×10000 = 97600

530000 < 97600

This is not true

Therefore, the number sentence 4.8 < √32 (4.8 < 5.66) is true. So option B is the answer

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Answer:

(15x+3)° = 108 (vertically opposite angles)

15x = 108-3

15x = 105

x = 105/15

x =7