5x2 + 2x − 3) − (2x2 − 3x + 7) expressed as a trinomial

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In option (c) A boxplot of the data has a large outlier, we would not be safe constructing the interval based on an SRS of size 24 from the population.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Constructing a one-sample t interval for a population mean is generally safe when the population is not Normal, as long as the sample size is large enough (usually at least 30) or the sample is taken from a population that is not too skewed or has outliers.

Therefore, options (a), (b), and (e) suggest that the sample may come from a population that is roughly Normal or can be transformed to be Normal, and so constructing the interval based on an SRS of size 24 would be safe.

Option (d) suggests that the sample standard deviation is large, but this does not necessarily mean that constructing the interval would not be safe.

It may reduce the precision of the interval, but as long as the sample size is sufficient, the interval can still be constructed.

Option (c) suggests that the sample has a large outlier, which may significantly affect the distribution of the sample and the calculation of the interval.

Therefore, in this circumstance, constructing the interval based on an SRS of size 24 would not be safe.

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A linear graph passes through (0, 0) and (4, 1)  represent a proportional relationship.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Now, For the line passes through (0, 2.5) and (1, 4).

Equation of line is.

⇒ y - 2.5 = (4 - 2.5) / (1 - 0) (x - 0)

⇒ y - 2.5 = 1.5x

⇒ y = 1.5x + 2.5

Hence, It cannot represent a proportional relationship.

For the line passes through (0, 0) and (4, 1).

Equation of line is.

⇒ y - 0 = (1 - 0) / (4 - 0) (x - 0)

⇒ y = 0.25x

Hence, It represent a proportional relationship.

For the line passes through (0, - 1) and (1, - 1).

Equation of line is.

⇒ y - (- 1) = (- 1 - (- 1)) / (1 - 0) (x - 0)

⇒ y + 1 = 0

Hence, It cannot represent a proportional relationship.

For the line passes through (0, 3) and (1, - 2).

Equation of line is.

⇒ y - 3 = (- 2 - 3) / (1 - 0) (x - 0)

⇒ y - 3 = - 5x

⇒ y = - 5x + 3

Hence, It cannot represent a proportional relationship.

Thus, A linear graph passes through (0, 0) and (4, 1)  represent a proportional relationship.

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The area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add or subtract the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.

The length of the rectangle is 0.9 cm.

The width of the rectangle is 0.4 cm.

The diameter of the circle us 0.4 cm, thus the radius = 0.4/2 = 0.2 cm.

The area of the rectangle is:

A = (l)(b)

Substituting the values:

A = (0.9)(0.4)

A = 0.36 sq. cm.

The area of the circle is:

A = πr²

A = (3.14)(0.2)²

A = 0.1256 sq. cm.

The area of the shaded portion is:

Area of shaded portion = area of rectangle - area of circle

Area of shaded portion = 0.36 - 0.1256 = 0.2344 sq. cm

Hence, the area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

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Answer:

So, if we sell 150 flowers total, we can purchase 100 daisies and 50 roses for exactly $300.

Step-by-step explanation:

Let R be the number of roses and D be the number of daisies.

Now we can set the following equations to represent the cost and the total number of flowers,

Cost equation=3.50R + 1.25D

                       = 300

Number of flowers equation= R + D

                                              = 150

We need to find the number of roses and daisies that we can purchase, as according to question the total number of flowers is 150. To find R, we can put value of  the number of flowers in the equation for R in terms of D, and also put this expression for R in the cost equation,

R = 150 - D

3.50R + 1.25D

= 300

3.50(150 - D) + 1.25D

= 300

525 - 3.50D + 1.25D

= 300

-2.25D = -225

D = 100

Therefore, we can buy 100 daisies and the remaining 50 flowers must be roses.

The cost of 100 daisies is 100 × 1.25

= $125

The cost of 50 roses is 50 × 3.50

= $175.

Therefore, the total cost is $125 + $175

= $300.

So, if we sell 150 flowers total, we can purchase 100 daisies and 50 roses for exactly $300.

Therefore, Sam wrote a total of 38,789 digits. Therefore, the probability that Sam chooses a 0 is approximately 0.026. So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability is calculated by dividing the number of outcomes that satisfy a certain condition (such as rolling a six) by the total number of possible outcomes. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

(a) Sam writes down all the positive integers from 1 to 9999, inclusive. To find the total number of digits Sam wrote, we can count the number of digits in each number and add them up.

Numbers from 1 to 9 have one digit each, so there are 9 numbers with one digit, for a total of 9 digits.

Numbers from 10 to 99 have two digits each, so there are 90 numbers with two digits, for a total of 180 digits.

Numbers from 100 to 999 have three digits each, so there are 900 numbers with three digits, for a total of 2700 digits.

Numbers from 1000 to 9999 have four digits each, so there are 9000 numbers with four digits, for a total of 36000 digits.

Adding up these totals gives:

9 + 180 + 2700 + 36000 = 38789

Therefore, Sam wrote a total of 38,789 digits.

(b) Since Sam chose the digits 1 to 9999, there are 4 digits (0, 1, 2, and 3) that can appear in the thousands place, and 10 digits (0 to 9) that can appear in each of the other three places.

Therefore, the probability of choosing a 0 at random is the number of times 0 appears in the numbers divided by the total number of digits written down.

0 appears as the last digit in 1000 numbers (from 10 to 9990), and as the first digit in 9 numbers (1000, 10000, 2000, 20000, 3000, 30000, 4000, 40000, and 5000). So the total number of times 0 appears is 1000 + 9 = 1009.

The total number of digits Sam wrote is 38,789, so the probability of choosing a 0 at random is:

1009/38789 ≈ 0.026

Therefore, the probability that Sam chooses a 0 is approximately 0.026.

(c) We can find the sum of all the digits Sam wrote by adding up the sum of the digits in each number from 1 to 9999.

The sum of the digits in the numbers from 1 to 9 is 1+2+3+4+5+6+7+8+9=45.

The sum of the digits in the numbers from 10 to 99 can be found by observing that each of the digits from 0 to 9 appears in the tens place the same number of times (that is, 10 times each). Since there are 90 two-digit numbers, each digit appears a total of 10 x 90 = 900 times in the tens place. So the sum of the digits in the tens place is:

900(0+1+2+3+4+5+6+7+8+9) = 45,000

Similarly, each of the digits from 0 to 9 appears in the hundreds place the same number of times (that is, 100 times each). So the sum of the digits in the hundreds place is:

100(0+1+2+3+4+5+6+7+8+9) = 4500

Finally, each of the digits from 0 to 9 appears in each of the four places (thousands, hundreds, tens, and ones) the same number of times (that is, 1000 times each). So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

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The total monthly payment of Ricky with an APR of 3.84 % is given by the equation M = $ 1,208.0523

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.

The monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]

where

M = Total monthly payment

P = The total amount of your loan

I = Your interest rate, as a monthly percentage

N = number of months for paying off your mortgage

Given data ,

Let the monthly payment be represented as M

Now , the number of years n = 20 years

The annual interest rate i = 3.84 %

The total loan amount P = $ 258,000

Now , the monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]

On simplifying , we get

[tex]M = 258,000 [ ( \frac{ 0.0384}{12} ) ( 1 + \frac{ 0.0384}{12} )^{12*30} ] / [ ( 1 + \frac{ 0.0384}{12} )^{12*30} - 1 ][/tex]

[tex]M = 258,000 [ (0.0032 ) ( 1.0032 )^{360} ] / [ ( 1.0032 )^{360} - 1 ][/tex]

On further simplification , we get

M = 258,000 [ 0.0101078417 ] / [ 2.158700543922579 ]

M = 258,000 ( 0.00468237327729 )

M = $ 1,208.0523

Hence , the monthly payment of Ricky is $ 1,208.0523

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The stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

A stem and leaf plot also called a stem and leaf diagram is a way of organizing data into a form that makes it easy to observe the frequency of different types of values. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf.

Given that, 600, 600, 600, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 612, 620, 620, 625, 629, 631, 635, 638, 640, 640, 645, 646, 650, 651, 660, 660, 665, 671, 671, 674, 680, 693, 700, 705, 706, 707, 707, 715, 715, 719,  720,  725, 727, 732, 738, 739 and 745.

a) Split between hundreds place and the tens place.

60|  0   0   0

61|  1    1    1    1    1    1    1    1    1    1    1    2

62|  0   0   5   9

63|   1    5   8  

64|  0    0   5   6

65|  0    1

66|  0    0   5

67|   1     1    4

68|  0

69|  3

70|  0  5   6   7   7

71 |   5  5  9

72|   0  5  7

73|   2  8  9

74|   5

b) Split between the tens place and the ones place.

6|   00  00   00  10   10  10   10   10   10  10  10  10  10  10   12   20   20   25 29   31   35   38   40   40   45   46   50   51   60   60   65   71   71   74   80   93

7|    00   05   06   07   07   15   15   19  20  25  27  32  38  39  45

Therefore, stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

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Answer:

Step-by-step explanation:

To express 799 cm² as a fraction of 0.13 m², we need to convert the units of one of the areas so that they are both in the same units.

1 cm = 0.01 m (since there are 100 cm in 1 meter)

So, we can convert 799 cm² to m² by dividing by (100 cm/m)²:

799 cm² = (799/10000) m²

Now, we can express 799 cm² as a fraction of 0.13 m²:

(799/10000) m² ÷ 0.13 m² = (799/10000) ÷ 0.13

Simplifying this fraction, we get:

(799/10000) ÷ 0.13 = 0.0799 ÷ 0.13

= 0.6138461538

Therefore, 799 cm² is equal to approximately 0.6138 of 0.13 m², or we can say:

799 cm² = (0.6138/1) × 0.13 m²

So, we can express 799 cm² as a fraction of 0.13 m² as:

799 cm² = 0.6138 × 0.13 m² (approximately)

or

799 cm² = 6138/10000 × 0.13 m²

or

799 cm² = 6138/100000 × m².

The 800 readers have a newspaper if the local newspaper has letters to the editor for 40 people if this is the number represents 5%.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

The local newspaper has letters to the editor for 40 people if this is the number represents 5% of all the newspaper readers.

Let x be the total number of newspaper readers.

The value of x can be found as follows:

5 % of x = 40

(5/100)x = 40

x = 40/0.05

x = 800

Thus, the 800 readers have a newspaper if the local newspaper has letters to the editor for 40 people if this is the number represents 5%.

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Complete question:

The local newspaper has letters to the editor for 40 people if this is the number represents 5% of all the newspaper readers how many readers does the newspaper have

If a = 9 and c = 9, the length of b is 3√18.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a right angled triangle with the given length of base and altitude.

Length of base = 9

Length of altitude = 9

We have to find b, which is the hypotenuse.

Using Pythagoras theorem,

Hypotenuse² = Base² + Altitude²

b² = a² + c²

b² = 9² + 9²

b² = 81 + 81

b² = 162

b = √162 = √(18×9) = 3√18

Hence the length of hypotenuse is 3√18.

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Your question is incomplete. Probably the correct question is as follows.

Given a right angled triangle.

a is marked the base, c is marked the altitude and b is marked the hypotenuse.

Find b: If a = 9 and c = 9

The height of the tower is 17.32 meters

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, Ical is 10 meters away from a tower [since angle is not given let the angle of the top of the tower be 60°], we need to find the height of the tower, [see the figure attached]

The whole scene is making a right triangle, so using the concept of trigonometric ratios,

We get,

Tan 60° = height of the tower / distance of Ical from the tower

Tan 60° = height of the tower / 10

Height of the tower = 10 × Tan 60°

Height of the tower = 10 × √3

Height of the tower = 10√3

Height of the tower = 10 × 1.73

Height of the tower = 17.32

Hence, the height of the tower is 17.32 meters

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Answer:

48

Step-by-step explanation:

2*4*6

The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

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The equation that can be used to find x, the number of jerseys is 82.49 = 15.70x + 3.99

The other three equations are incorrect because the equation should be represented by total cost equals cost of each shirt multiplied by number of jerseys plus shipping cost.

Ms Chen purchased 15 jerseys.

Cost of x jerseys including shipping = $82.49

Cost of shipping = $3.99

Cost of each jersey = $15.70

82.49 = 15.70x + 3.99

82.49 - 3.99 = 15.70x

78.50 = 15.70x

x = 78.50 / 5

x = 5

In conclusion, the number of jerseys bought is 5.

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The probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

What is probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

a.

i. P(male) = number of males in the sample / total number in the sample = 154 / 306 ≈ 0.503

ii. P(hybrid) = number of hybrid cars purchased / total number in the sample = 99 / 306 ≈ 0.324

iii. P(hybrid|male) = number of males who purchased a hybrid / total number of males in the sample = 32 / 154 ≈ 0.208

iv. P(hybrid|female) = number of females who purchased a hybrid / total number of females in the sample = 67 / 152 ≈ 0.441

v. P(female|hybrid) = number of females who purchased a hybrid / total number of people who purchased a hybrid = 67 / 99 ≈ 0.677

b.

i. P(male) represents the probability of randomly selecting a male from the sample of 306 people who purchased a Honda Civic.

ii. P(hybrid) represents the probability of randomly selecting a car from the sample that has a hybrid engine.

iii. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male.

iv. P(hybrid|female) represents the probability of selecting a hybrid car given that the person selected is female.

v. P(female|hybrid) represents the probability of selecting a female given that the car selected has a hybrid engine.

c. No, P(hybrid|male) and P(male|hybrid) are not equal. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male, while P(male|hybrid) represents the probability of selecting a male given that the car selected has a hybrid engine. These probabilities are different because the sample is not necessarily representative of the entire population.

Hence, the probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

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Answer: To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the amount of money after the given time period

P = the principal (starting amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, the principal is $6500, the annual interest rate is 2.8% (or 0.028 as a decimal), and the interest is compounded monthly (so n = 12). We want to find the amount after 2 years, so t = 2.

Plugging these values into the formula, we get:

A = 6500(1 + 0.028/12)^(12*2)

A ≈ $7,107.08

Therefore, the amount of money after 2 years is approximately $7,107.08.

Step-by-step explanation:

The missing term in the sequence 5, 11, 17, ?, 31, 41 is B. 23.

We have been given the series 5, 11, 17, ?, 31, 41. We need to find the missing number out of the given sequence.

Let us write the prime numbers upto 50.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47.

By looking into the above prime numbers we can make out our sequence. The series is formed by the alternate prime numbers. Thus we can complete the given sequence as,

5, 11, 17, 23, 31, 41.

Thus we got the missing number as 23 in the sequence 5, 11, 17, 23, 31, 41.

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Find the missing term in the sequence 5, 11, 17, ?, 31, 41.

Answer:

x = 3

y = 6

Step-by-step explanation:

2x - y = 0

3x - 2y = -3

-----------

2x-y = 0 ---> 2x = y ---> y = 2x ----> 3x - 2(2x) = -3 ---> 3x - 4x = -3 ---->

-----> -x = -3 ---> x = -3/-1 = 3 -----> x = 3

y = 2x ----> y = 2 (3) ----> y = 6

Answer:

x es igual a 8.

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

60=4d-8

We move all terms to the left:

60-(4d-8)=0

We get rid of parentheses

-4d+8+60=0

We add all the numbers together, and all the variables

-4d+68=0

We move all terms containing d to the left, all other terms to the right

-4d=-68

d=-68/-4

d=17

Answer:

w = 105° because 180 - (45 + 60) = 75 and 180 - 75 = 105.

Step-by-step explanation:

To find w, we first need to find z.

We can find z by setting up an equation. As we know, all angles in a triangle will add up to 180, we can say that z + 45 + 60 = 180.

We can also rewrite this as 180 - 45 - 60 = z, or 180 - (45 + 60) = z.

Solving this, we get z = 75.

We can also see that w and z are supplementary angles, meaning they will add up to 180.

Therefore, we can come to the conclusion that w + 75 = 180, or 180 - 75 = w.

Solving this we get:

w = 105

Therefore, w = 105°.

The solution of the equation are y=9 and x=4

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE are given that the system of equation;

5x+6y=26 and 10x-6y=-2

5x+6y=50

-1(-x+6y=26)

X-6y=-26

Then Eliminate the y and combine evrything

6x=24

Divide 6 both sides

X=4

Then, substitute the x

-(4)+6y=50

-4+6y=50

Add 4 both sides

6y=54

y=9 and x=4

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Answer:

13.5

Step-by-step explanation:

If y and x have a proportional relationship, we can write this relationship as:

y = kx

where k is the proportionality constant.

To find the value of k, we can use the information that "y = 9 when x = 2":

9 = k(2)

Solving for k, we get:

k = 9/2

Now we can use this value of k to find the value of y when x = 3:

y = (9/2)(3) = 27/2 = 13.5

Therefore, the value of y when x = 3 is 13.5.

Answer:

Step-by-step explanation:

(2x + 3)(3x - 2) + (3 - 4x)(2x + 3) - 4x² + 9     FOIL the first and second set of parentheses.

6x² - 4x + 9x - 6 + 6x + 9 - 8x² - 12x - 4x² + 9   Combine like terms

-6x² - x + 12     Factor.

(-3x + 4)(2x + 3)

Note that where you have a square with a side of 20dm is inscribed in a circle, the area of the shaded region is At = [tex]\approx[/tex] 257.08dm²

A square is a geometrical shape with four equal sides and four equal angles, each measuring 90 degrees.

In the figure we will determine the area of the shade:

The formula is given as follows:

1/2(Area of the Square) + ∡AB + ∡DC

Note that the above equation subsists because:

i)  the shaded region comprises of two congruent or similar triangles since the diagonals of a Square will bisect each other equally creating 4 congruent triangles.

ii) A square in a circle will always create 4 equal Chords.

Thus, imputing the figures we have:
(20dm)²/2 + [π ((20√2)/2)² - (20dm)²]/4

= 200 + [200π -400]/4
= 200 + (50π -100)
= 100 + 50π

= 257.079632679

[tex]\approx[/tex] 257.08dm²

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Full Question:

A square with a side of 20 dm is inscribed in a circle. Determine the shaded area shown in the figure.

Answer:

Step-by-step explanation:

-15

Answer: the positive value of tan(1/2x) in simplest radical form with a rational denominator is √(2/3).

Step-by-step explanation:

Using the half-angle formula for tangent, we have:

tan(1/2x) = ±√((1-cos(x))/(1+cos(x)))

Substituting cos(x) = 1/5, we get:

tan(1/2x) = ±√((1-1/5)/(1+1/5))

= ±√(4/6)

= ±√(2/3)

Since we are looking for the positive value, we have:

tan(1/2x) = √(2/3)

Therefore, the positive value of tan(1/2x) in simplest radical form with a rational denominator is √(2/3).

Answer:

Step-by-step explanation:

sin(x)=sqrt(24)/5=2*sqrt(6)/5

tan(x/2)=sin(x)/(1+cos(x))

Thus, tan(x/2)=sqrt(6)/3

The number of coins Mark have is 48.

Joey has 25 collectible coins which is 9 more than 1/3 the number Mark has. Therefore, the number of coins Mark have can be calculated as follows:

Let's write the equation for the word problem before solving.

Hence,

let

x = number of coins Mark has

Therefore,

Number of coins Joey have = 9 + 1  /3 x

Hence,

25 = 9 + 1  / 3 x

25 - 9 = 1 / 3 x

16 = 1 / 3 x

cross multiply

x = 16 × 3

x = 48 coins

Therefore,

number of coins Mark have = 48 coins

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Answer:

R=47/pi

Step-by-step explanation:

If the of circumference of the circle is 94 cm, the diameter is 94/pi makin the radius 47/pi.

Another form of energy that is in the electromagnetic spectrum is X - rays

The electromagnetic spectrum is the range of all the electromagnetic waves.

Since electromagnetic spectrum contains more than just the visible light that you see, its range is given by the pneumonic RMIVUXG where

So, the frequencies of the electromagnetic waves increase as we go from top to bottom and its wavelength decreases as we go from top to bottom.

So, another form of energy that is in the electromagnetic spectrum is X - rays

Learn more about electromagnetic spectrum here:

https://brainly.com/question/23423065

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