Rewrite 5x²+35x using distributive property

Answer:

2.5cm

Step-by-step explanation:

you half the diameter to get the radius

Using the formula for the area of a rectangle, the area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x

From the question, we are to calculate the area of the cellphone shown in the diagram

From the given information,

We have a diagram that shows a cellphone which is rectangular in shape.

Thus,

We will use the formula for finding the area of a rectangle to calculate the area of the cellphone.

Area of a rectangle = Length * Width

From the given information,

Length of the cellphone = 6x²y⁶

Width of the cellphone = 3x⁻³y²

Thus,

Area of the cellphone = 6x²y⁶ × 3x⁻³y²

Area of the cellphone = 6 × 3 × x² × x⁻³ × y⁶ × y²

Area of the cellphone = 18 × x⁻¹ × y⁸

Area of the cellphone = 18x⁻¹y⁸ OR 18y⁸/x

Hence,

The area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x

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Answer:

Step-by-step explanation:

Answer:

You can make 12 possible sundaes with these toppings.

Step-by-step explanation:

Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:

1. Fudge & Chocolate Sprinkles

2. Fudge & Rainbow Sprinkles

3. Marshmallow & Chocolate Sprinkles

4. Marshmallow & Rainbow Sprinkles

-------------------------------------------------------------------------------------------------------------

4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.

Answer:1111

Step-by-step explanation:

Answer: x=14

Step-by-step explanation:

cb=10.

ac=14

The value of X will be 14.

This is a simple mathematics problem that can be solved by using ratios.

Given, AC : BC : AB = 7 : 5 : 8

AC = X ; BC = 10 ; AB = X + 2

AC/ BC = X/ 10 = 7/5  (Ratios can also be represented as fractions)

X/10 = 7/5

On Transposing,

5X = 70

X = 70/5

X = 14

Alternatively,

BC/AB = 5/8 = 10/ (X + 2)

5/8 = 10/ (X + 2)

On Transposing,

80 = 5X + 10

5X = 70

X = 14

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Angle KRL is equal to 34°. The main reason behind this is that KRL is vertically opposite to Angle QRP.

KLR and LRM are complementary angles i.e.

KLR + LRM = 90

Similarly, HRQ and QRP are complementary angles i.e.

HRQ + QRP = 90

HRQ = 56 = LRM (vertically opposite angle)

KLR = KRM - LRM = 90 - 56 = 34

KLR = QRP = 34.

The two geometrical rules applied are,

(a) Vertically Opposite angles are always equal.

(b) Complementary angles are those angles which adds upto make 90 degree angle

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I hope this helps you.

you can check your ans. by sub. in the value of x and y into both the equation which must give you the same answer.

Answer:

------------------------------

Use the formula for permutations:

The number of objects is n = 7 books.

Calculate the factorial:

Ricky will have to wait for 26.78 years to have 200,000 in her account with this investment.

In order to determine the time it takes for Ricky's initial investment to grow to the desired amount, we can use the compound interest formula: A = P(1 + r/n)^(nt)

Where:

A is the final amount in the account (in this case, 200,000)

P is the initial investment (in this case, 20,000)

r is the annual interest rate (in this case, 0.09 for 9%)

n is the number of times interest is compounded per year (in this case, 1 for yearly compounding)

t is the number of years

We are trying to solve for t, so we can rearrange the formula to:

t = ln(A/P) / (n * ln(1 + r/n))

Plugging in the values:

t = ln(200,000/20,000) / (1 * ln(1 + 0.09/1))

t = ln(10) / ln(1.09)

t ≈ 2.303 / 0.086

t ≈ 26.78

Ricky will have to wait approximately 26.78 years to have 200,000 in her account with this investment.

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The statement "About 16% of the students scored 74 or below" is true for the given normal distribution of test scores with an average of 78 and a standard deviation of 4.

Standard deviation is a measure of the amount of variation or dispersion of a set of values from their mean (average) value. It is calculated as the square root of the variance of a set of data. A smaller standard deviation indicates that the values are tightly clustered around the mean, while a larger standard deviation indicates that the values are more spread out.

In the given question,

About 16% of the students scored 74 or below is true. This is because of the empirical rule for normal distributions, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. So, if the average score is 78 and the standard deviation is 4, a score of 74 falls one standard deviation below the mean, which represents about 16% of the total data.

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Answer:

About 97.5%  of the students scored 86 or below.

Step-by-step explanation:

The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%

A percentage is a proportion of a number expressed as fraction of a 100

The dimensions in mixed fractions can be expressed as follows;

Height of the box = 1 2/3 feet = 5/3 feet

Width of the box = 4 feet

Length of the box = 5 1/2 feet = 11/2 feet

Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches

The percent of the box that will remain unwrapped is therefore;

Percentage = 60/(227/3) × 100 ≈ 79.3%

The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%

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The statements are classified as Exponential decay and Linear growth.

a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.

c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.

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We need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.

We can use the formula for the sample size required to estimate a population proportion with a specified margin of error and confidence level:

n = (Z^2 * p * (1-p)) / E^2

where:

Z = the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of 1.96)

p = the estimated population proportion from the earlier study

E = the desired margin of error

Substituting the given values, we get:

n = (1.96^2 * 0.33 * (1-0.33)) / 0.03^2

n = 753.69

Rounding up to the next integer, we need a sample size of 754. Therefore, we need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.

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When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle.

When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.

When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.

(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the intersection of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.

(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.

(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.

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The line graph of Greg's data wood look like "It would move upward."

A graph is a visual representation of data that shows the relationship between two or more variables. There are several types of graphs that can be used to display data

If Greg is measuring the height of the plant each day and the plant is continuing to grow for two weeks, then the line graph of his data would move upward. The graph would show an increasing trend as the plant grows taller each day. Therefore, the correct answer is "It would move upward."

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We are adjusting the original rectangular solid and here is what we have:

(a) The lateral area is the sum of the areas of the four sides, which are all rectangles. The two sides with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two sides with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the lateral area is:

2(24) + 2(30) = 48 + 60 = 108 square units

(b) The total area is the sum of the areas of all six faces. The two faces with dimensions 10 x 8 have an area of 10 x 8 = 80 square units each, the two faces with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two faces with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the total area is:

2(80) + 2(24) + 2(30) = 160 + 48 + 60 = 268 square units

(c) The volume is the product of the length, width, and height of the rectangular solid. Therefore, the volume is:

10 x 8 x 3 = 240 cubic units

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The plane degrees off course is 6.79 degrees off at a speed of 541. 92 km / hr relative to the ground.

To find the airplane's course deviation and its ground speed, we need to first determine the velocity vectors of the airplane and the wind.

W x = W x cos(225) = 90 x cos(225) = -63.64 km/hr

Wy = W x sin(225) = 90 x sin(225) = -63.64 km/hr

Magnitude: |R| = sqrt(Rx^2 + Ry^2) = √(536.36^2 + (-63.64)^2) = 541.92 km/hr

Direction: θ = arctan(Ry / Rx) ≈ arctan (-63.64 / 536.36) = -6.79 degrees

So, the airplane is 6.79 degrees off course, and its ground speed is 541.92 km/hr.

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a. The number of red roses left t hours after the store opens [tex]R(t) = 400/2^{t/2}[/tex]    

b. The number of boxes of chocolate left t hours C(t) = 200 - 0.15t

c. One possible solution is t ≈ 7.546 hours after the store opens.

d. there are 194 boxes of chocolates left.

e. you need to arrive at the store no later than 7.504 hours after it opens.

a. The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.:

[tex]R(t) = 400/2^{t/2}[/tex]

b. Let C(t) be the quantity of boxes of chocolate left t hours after the store opens. At first, there are 200 boxes, of which 15% are purchased every hour. We can therefore write:

C(t) = 200 - 0.15t

c. We must solve the equation R(t) = C(t) in order to determine the time at which the number of boxes of chocolates and the number of roses are equal. We obtain: by substituting the formulas we discovered in parts a and b:

[tex]400/2^{t/2} = 200 - 0.15t[/tex]

Simplifying this equation, we get:

[tex]2^{t/2 + 1} + 0.15t - 400 = 0[/tex]

We can solve this equation numerically, using a calculator or a computer program. One possible solution is t ≈ 7.546 hours after the store opens.

d. At 12:30 in the early evening, which is 3.5 hours after the store opens, we can utilize the recipe we tracked down to some extent b to work out the quantity of boxes of chocolates left:

C(3.5) = 200 - 0.15(3.5) = 194.25

We ought to adjust this solution to appear to be legit with regards to the issue. Since we cannot have a fraction of a box, we can round to the nearest integer and state that there are 194 chocolate boxes remaining.

e. To buy 36 red roses, we need to solve the equation R(t) = 36. Substituting the formula we found in part a, we get:

[tex]400/2^{t/2}= 36[/tex]

Simplifying this equation, we get:

2^(t/2) ≈ 11.111

Taking the logarithm of both sides, we get:

t/2 ≈ log2(11.111)

t ≈ 2 log2(11.111)

Using a calculator, we get:

t ≈ 7.504 hours after the store opens.

Therefore, you must arrive at the store no later than 7.504 hours after it opens in order to purchase 36 red roses.

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Michelle can make 6 floor boards for her car.

To determine how many floor boards Michelle can make, we need to divide the total length of wood she has (13.2 meters) by the length of each floor board (2.2 meters).

The number of floor which boards Michelle can make is:

= 13.2 meters / 2.2 meters/floor board

= 6 floor boards

Therefore, Michelle can make 6 floor boards for her car using the 13.2 meters of wood she has.

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The answer of the given question based on the graph is ,  The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.

To dilate line f by scale factor of one half with center of dilation at origin, we  multiply coordinates of each point on line f by 1/2.

The equation of line f can be found by using the points A and B:

slope of line f = (0 - 2)/(2 - 0) = -1

y-intercept of line f = 2

Therefore, the equation of line f is y = -x + 2.

To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:

A' = (0, 2)*1/2 =(0, 1)

B' = (2, 0)*1/2 =(1, 0)

So A' is located at (0, 1) and B' is located at (1, 0) after dilation.

Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.

If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.

To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':

slope of f' = (0 - 1)/(1 - 0) = -1

y-intercept of f' = 0

Therefore, the equation of f' is y = -x.

Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

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Answer:

the 36th term is 187.

Step-by-step explanation:

To find the 36th term of a sequence, we need to know the rule that generates the sequence. Without that rule, we cannot find the 36th term.

However, if we assume that the sequence is an arithmetic sequence (meaning that there is a common difference between consecutive terms), we can use the given terms to find the common difference and then find the 36th term.

The common difference is found by subtracting the second term from the first term, or the third term from the second term.

Using the first and second terms, we get:

17 - 12 = 5

Using the second and third terms, we get:

22 - 17 = 5

Since both calculations give the same result, we can be confident that the common difference is 5.

Therefore, to find the 36th term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Using a1 = 12, d = 5, and n = 36, we get:

a36 = 12 + (36 - 1)5

a36 = 12 + 175

a36 = 187

So, if the sequence is an arithmetic sequence with a common difference of 5, then the 36th term is 187.

The balance in the account after 6 years is $2,466.69.

What is compound interest?

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

We can use the formula for compound interest to find the balance in the savings account after 6 years:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

where:

A is the balance in the account after t years

P is the initial deposit, which is $2,225

r is the annual interest rate, which is 1.625%

n is the number of times the interest is compounded per year, which is 4 (since it's compounded quarterly)

t is the number of years, which is 6

Plugging in these values, we get:

[tex]A = 2,225(1 + 0.01625/4)^{(4*6)}\\A = 2,225(1.0040625)^{24}[/tex]

A = 2,225(1.108227)

A = 2,466.69

Hence, the balance in the account after 6 years is $2,466.69.

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The probabilities are as follows:

(a) P(A')= 0.7

(b) P(A∪B) =  0.3

(c) P(A'∩B) =  0

(d) P(A∩B') =  0.1

(e) P[(A∪B)'] =  0.7

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7

(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3

(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0

(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1

(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7

Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.

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Answer:

it's complex but i will justify wait me

Answer:

40%

Step-by-step explanation:

2/5=x/100

cross multiply and you get 5x=200

by isolation the variable you will get x=40

therefore, 40% of Canadians read at least 10 books a year

Thus, the height of flagpole from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

Using the trigonometric ratios in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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Step-by-step explanation:

From 1860 to 2018 is  158 years

 Use compounding formula

$ 28.95    =   $ 1   ( 1 +i) ^158       where i is decimal inflation rate %

[tex]\sqrt[158]{28.95}[/tex]  = 1 + i

i = .0215       = 2.15 %

Answer:

f(x) - g(x) = 2x² + 6x - 4

Step-by-step explanation:

f(x) - g(x)

= 3x² + x - 3 - (x² - 5x + 1) ← distribute parenthesis by - 1

= 3x² + x - 3 - x² + 5x - 1 ← collect like terms

= 2x² + 6x - 4