Lesson 18.1 choosing a bank

The difference between Walter and Denise's gas usage is 0.83 - 0.75 = 0.08 gallons. Therefore, Walter uses 0.08 gallons more gas than Denise.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that describes a quantity or amount. Numbers can be represented in various forms, including words, symbols, and numerals. Numbers are also used to measure distance, time, and weight, as well as to express amounts of money. Numbers play a vital role in many areas of life, from science and engineering to economics and finance.

To calculate how much more gas Walter uses than Denise, we need to find the difference between the amount of gas each person uses.

Denise uses 3/4 of a gallon of gas, so 3/4 of a gallon is equal to 0.75 gallons. Walter uses 5/6 of a gallon of gas, so 5/6 of a gallon is equal to 0.83 gallons.

The difference between Walter and Denise's gas usage is 0.83 - 0.75 = 0.08 gallons. Therefore, Walter uses 0.08 gallons more gas than Denise.

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To find how long it will take for Francine's money to grow to $7,500, we can set up the equation:

7500 = 5000(1.005)^(12t)

where t is the number of years. We want to solve for t.

First, divide both sides by 5000:

1.5 = (1.005)^(12t)

Next, take the natural logarithm of both sides:

ln(1.5) = ln(1.005)^(12t)

Using the rule of logarithms that ln(a^b) = b ln(a), we can simplify the right side:

ln(1.5) = 12t ln(1.005)

Finally, divide both sides by 12 ln(1.005):

t = ln(1.5)/(12 ln(1.005))

Using a calculator, we get:

t ≈ 14.6 years

Therefore, it will take about 14.6 years for Francine's money to grow to $7,500.

Thus, the probability that either blue or green or purple will appear on the next spin is 63%.

The proportion between the number of likely occurrences and the total number of potential occurrences.

Given result for the spinner:

probability = favourable outcome / total outcome

probability (blue) = 4/35

probability (Purple) = 3/35

probability (Green) = 15/35

So, probability (either blue or green or purple) = 4/35 + 3/35 + 15/35

= 22/35

= 0.6285

= 62.85

= 63%

Thus, the probability that either blue or green or purple will appear on the next spin is 63% (nearest whole number).

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As It takes Sara 1/2 day to make a birdhouse, the number of birdhouse which will be built after 2/5 day is 4/5 of a birdhouse.

Since it takes Sara 1/2 day to make a birdhouse, we can say that she can make 2 birdhouses in one day.

So, after 1/2 day, Sara will complete 1 birdhouse.

Now, let's see how much of the birdhouse Sara can build after 2/5 day:

2/5 day is equivalent to (2/5) x (1/2) = 1/5 day.

Since Sara can build 1 birdhouse in 1/2 day, she can build 1/2 of a birdhouse in 1/4 day (half of 1/2 day).

Therefore, in 1/5 day, she can build:

= (1/5) / (1/4)

= (1/5) x (4/1)

= 4/5 of a birdhouse.

Full question "It takes Sara 1/2 day to make a birdhouse. How much of the birdhouse will be built after 2/5 day"

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The cubic function family includes the function G(x).

A collection of functions known as the cubic function family may be written as [tex]f(x) = ax3 + bx2 + cx + d,[/tex]  where a, b, c, and d are constants. Cubic functions can have one, two, or three real roots because of their odd degree (3). Real-world phenomena like population growth and decline are frequently modelled using these functions. The coefficient of x3 in the following function [tex]G(x) = -x3 is -1,[/tex]  which is a constant. This function belongs to the family of cubic functions since it may be written in the typical form of a cubic function. As a result, G(x) has a single real root and is a cubic function.

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Answer:a=4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alan made an error in assuming that the distance between -8 and 3 on the x-axis is the same as the distance between -8 and the y-axis, and between 3 and the y-axis. This is not necessarily true, as the distance between two points on a coordinate plane is given by the Pythagorean theorem:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the actual distance between points A and B:

distance = sqrt((3 - (-8))^2 + (-4 - (-4))^2)

distance = sqrt(11^2 + 0^2)

distance = sqrt(121)

distance = 11

So the actual distance between points A and B is 11 units.

Therefore, Alan's error was assuming that the distance between A and B is simply the difference in the x-coordinates, which is not the case.

Answer:

Answer: 4,772.8 cm2

Step-by-step explanation:

The company will need 3,583.2 square inches of paper to make 15 labels.

What is cylinder?

Traditionally, a cylinder was a three-dimensional solid, one of the most fundamental curvilinear geometric shapes. It is a prism with a circle as its base in elementary geometry.

The formula for circumference is:

Circumference = π × diameter

Circumference = 3.14 × 8in

Circumference = 25.12in

So the label will need to be 25.12 inches long.

The height of the label will be the same as the height of the can, which is 9 inches.

To find the total area of the paper needed for 15 labels, we need to multiply the length of each label by its height and then multiply that by the number of labels:

Total area = length × height × number of labels

Total area = 25.12in × 9in × 15

Total area = 3,583.2 square inches

Thus, the answer is 3,583.2 square inches.

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Answer:

If a class has 2/3 girls.

Lets ask ourselves, what does this mean?

It means that 2/3 of the class are girls and therefore 1/3 of the class are boys. I.e. for every 2 girls in the class there is 1 boy in the class.

Therefore the ratio of girls to boys is

2 : 1

Based on the information, we can infer that the gumball machine had 530 blue gumballs, 106 red gumballs, 848 green gumballs, 424 pink gumballs, 212 yellow gumballs.

To find the amount of gum of each color that was in the machine we must perform rules of three as shown below:

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Answer: y = [tex]\frac{3}{2}[/tex]x - 12

Step-by-step explanation:

     First, we will find the slope of the equation. The x-intercept means that when x = 8, y = 0 giving us the point (8, 0). The y-intercept means that when y = -12, x = 0, giving us the point (0 -12).

     Now, we will find change in y over change in x (the slope).

               [tex]\displaystyle \frac{-12-0}{0-8}=\frac{-12}{-8} =\frac{3}{2}[/tex]

     Lastly, we can write our equation using the slope and y-intercept.

               y = [tex]\frac{3}{2}[/tex]x - 12

Answer:

y = 3/2x - 12

Step-by-step explanation:

X-intercept located at (8,0)

Y-intercept located at (0, -12)

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

2 points (8,0) (0, -12)

We see the y decrease by 12 and the x decrease by 8, so the slope is

m = -12 / -8 = 3/2

Y-intercept is = -12

So, the equation is y = 3/2x - 12

A rough estimate of the actual probability is [tex]0.43[/tex], or [tex]43[/tex]%.

When compared to a collection of possible occurrences that do not occur, probability may be thought of as a numerical indicator of how likely it is that an event will occur. All potential outcomes must be known as a set.

Information about the possibility that a certain thing will happen is provided by probability. For instance, meteorologists utilise weather patterns to forecast the likelihood of rain. Probability theory is utilised in epidemiology to comprehend the connection between exposures as well as the risk of health outcomes.

In three of the seven experiments, the volcano erupted once or twice throughout the course of the next half century (trial 1, 3, and 7).

Trial 1: 1 eruption

Trial 2: 0 eruptions

Trial 3: 1 eruption

Trial 4: 0 eruptions

Trial 5: 0 eruptions

Trial 6: 0 eruptions

Trial 7: 2 eruptions

Therefore, the experimental probability that the volcano will erupt in [tex]1[/tex] or [tex]2[/tex] of the next [tex]5[/tex] decades is:

experimental probability [tex]=[/tex] number of successful trials / total number of trials

experimental probability [tex]= 3 / 7[/tex]

experimental probability [tex]= 0.4286[/tex]

So the experimental probability is approximately [tex]0.43[/tex] or [tex]43[/tex]%.

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Answer:

g=9

Step-by-step explanation:

Step-by-step explanation:

70=7(g+1)

70=7g+7

63=7g

9=g

Answer:

Answer: C. 40°

Step-by-step explanation:

The shape in the picture is an isosceles triangle. This is determined because two sides share the same length. This will mean that two angles will also share the same measurement, helping us to find our answer.

Step 2: Write an equation

Now that we have identified the type of triangle, we can write an equation to solve. Two angles will be equal to 70, so subtract 70 twice from 180. It will be taken away from 180, since in a triangle the three angles are equal to 180 degrees. Now we can write the equation!

X= 180-70-70

Step 3: Solve for ∠x

The final step will be to solve using the equation we have created before.

X= 180-70-70

X= 110-70

X= 40

There is the final answer. Hope this helps! Comment below for more questions.

Therefore, the label represented by the rectangle in the figure is 62.4π square inches that is option D.

The lateral surface area of a three-dimensional object is the area of all its faces except for the top and bottom faces (i.e., the base(s) and the top(s)). In other words, it is the surface area of the object's lateral or side faces. The lateral surface area is typically used to describe the surface area of certain geometric solids such as cylinders, cones, and prisms. In the case of a cylinder, for example, the lateral surface area is the area of the curved side of the cylinder, excluding the top and bottom circular faces. For a cone, the lateral surface area is the area of the curved side of the cone, excluding the circular base.

Here,

From the given figure, we can see that the rectangle represents the lateral surface area of the cylinder, which can be calculated using the formula:

Lateral surface area = height x circumference

The circumference of the circle can be calculated as 2πr, where r is the radius. In this case, the radius is given as 4 inches. Therefore, the circumference is 2π(4) = 8π inches.

Substituting the given values, we get:

Lateral surface area = 7.8 x 8π

= 62.4π square inches

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The fοur integers are all equal tο 9, and the range is 12.

The cοllectiοn, analysis, interpretatiοn, presentatiοn, and οrganisatiοn οf data are all tοpics that fall under the umbrella οf statistics, a subfield οf mathematics.

Let's call the fοur integers a, b, c, and d.

Since the median is 9, we knοw that either b οr c must be 9. Let's assume b = 9.

Since the mοde is 9, we knοw that either a, c, οr d must be 9. Let's assume a = 9.

Nοw we have twο cases:

Case 1: c = 9

In this case, we have a, b, c, and d all equal tο 9, which gives us a mean οf 9.

Case 2: d = 21

In this case, we have a = 9, b = 9, c = 12, and d = 21, which gives us a mean οf 12.

Hοwever, we were tοld that the mean is 9, sο we can cοnclude that the first case is the cοrrect οne.

Hence, the fοur integers are all equal tο 9, and the range is 12.

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Complete Question:

Four integers have a mean of 9, a median of 9, a mode of 9 and a range of 12.

Find the four integers

Answer:

a) The surface area of a cuboid is given by the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the cuboid, respectively.

In this case, we are given that:

h = xem

w = 2h = 2xem

l = 3h = 3xem

Substituting these values into the formula for the surface area of a cuboid, we get:

SA = 2(3xem)(2xem) + 2(3xem)(xem) + 2(2xem)(xem)

= 12xem^2

Therefore, the formula for the surface area of this cuboid is SA = 12xem^2.

b) Using the formula SA = 12xem^2, we can calculate the surface area of each cuboid and then add them to find the total surface area.

For cuboid A, x = 3, so the surface area is:

SA(A) = 12(3em)^2

= 108em^2

For cuboid B, x = 5, so the surface area is:

SA(B) = 12(5em)^2

= 300em^2

Therefore, the total surface area of the two cuboids is:

SA(A+B) = SA(A) + SA(B)

= 108em^2 + 300em^2

= 408em^2

So the total surface area of the two cuboids is 408em^2.

The sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ... is 209.

To find the sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ..., we need to use the formula for the sum of an arithmetic sequence:

Sₙ = n/2 (a₁ + aₙ)

where Sₙ is the sum of the first n terms of the sequence, a₁ is the first term of the sequence, aₙ is the nth term of the sequence, and n is the number of terms we want to sum.

In this case, a₁ = 2 (the first term of the sequence), aₙ = 2 + (n - 1) = n + 1 (the nth term of the sequence), and n = 19 (we want to sum the first 19 terms of the sequence).

Therefore, we can plug these values into the formula and get:

S₁₉ = 19/2 ˣ (2 + 19 + 1)

= 19/2 ˣ 22

= 209

So the sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ... is 209.

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Answer:

normally I think credit card

Answer:$41.24

Step-by-step explanation:

when you do mathmatics with $468 and $28.75 you get $41.24! have a good day! <3

Plot and character development can help you predict a novel’s theme by hinting at ideas about what the conflict is and how the main characters are likely to deal with it.

What is plot?

The sequence of events in a book, movie, or other narrative where each event has an influence on the subsequent one in accordance with the law of cause and effect is known as the plot. The causal events of a narrative can be conceived of as a collection of occurrences linked together by the connector "and so." Plots can be simple—like in a traditional ballad—or complicated and intertwined, with each element occasionally referred to as a subplot or imbroglio.

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Answer : 3 [tex]\frac{17}{21}[/tex]

:)

Therefore , the solution of the given problem of equation comes out to be Kate's complete journey took her about 5.22 hours.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of another algorithm that can analyze data given by y + 7, split 12 to two parts, and produce y + 7, leveling produces b + 7 in this instance.

Here,

First, let's construct the solution utilizing the distance formula:

Walking distance plus cycling distance equals total distance.

Distance equals speed times time.

=> [(x+2)(x-3)] + [(3x+5)(x)] = 74

Simplifying and finding x's value:

=> x² - 4x - 9 + 3x² + 5x = 74

=> 4x² + x - 83 = 0

Making use of the quadratic formula:

=> x = [-1 + √(1 - 4(4)(-83))] / 8

=> x = [-1 ± √(1337)] / 8

=> x ≈ 4.11 or x ≈ -5.11

We can disregard the bad outcome because time cannot be negative.

Consequently,

=> x = 4.11.

Now that we know how long the full journey took, we can:

=> Time taken = x + (x-3)

=> Time spent = 2x - 3

=> Using x instead of 4.11:

=> Duration: 5.22 hours

As a result, Kate's complete journey took her about 5.22 hours.

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Anna needs to pay N$8,500 + N$1,062.50 = N$9,562.50 in two and a half years from now to meet her obligation.

What is Simple interest?

Simple interest is a type of interest that is calculated based only on the principal amount of a loan or investment. It is a fixed percentage of the principal that is charged for the use of money over a specified period of time.

First, let's calculate the interest on the loan for three and a half years.

Interest = Principal * Rate * Time

where the principal is N$20,000, the rate is 5%, and the time is 3.5 years.

Interest = 20,000 * 0.05 * 3.5 = N$3,500

So Anna owes N$20,000 + N$3,500 = N$23,500 in total at maturity.

Next, let's subtract the payments Anna plans to make from the total amount she owes to find out how much she still needs to pay:

N$23,500 - N$8,000 (planned payment) - N$2,000 (planned payment) - N$5,000 (planned payment) = N$8,500

So Anna still needs to pay N$8,500 to meet her obligation.

Finally, we need to calculate how much she should pay in two and a half years from now. We can use the simple interest formula again, this time with a principal of N$8,500, a rate of 5%, and a time of 2.5 years.

Interest = Principal * Rate * Time

Interest = 8,500 * 0.05 * 2.5 = N$1,062.50

So Anna needs to pay N$8,500 + N$1,062.50 = N$9,562.50 in two and a half years from now to meet her obligation.

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Answer: Out of the 150 people surveyed, 36 preferred relish on a hot dog.

To estimate how many people in attendance would prefer relish on a hot dog, we can use the proportion of people in the sample who preferred relish:

36/150 = x/8,450

Solving for x, we get:

x = (36/150) * 8,450 = 2,028

Therefore, an estimated 2,028 people in attendance would prefer relish on a hot dog.

The answer is option C: 2,028.

Step-by-step explanation:

The maximum daily profit the company can earn is $2,350.

In mathematics, a graph of a function is a visual representation of the relationship between the input and output values of the function.

It is a set of points in a coordinate plane that represents the values of the function for different inputs.

The function P(x) = −6x² + 180x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.

Therefore, the maximum daily profit the company can earn is $2,350.

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Answer:

4-2(16x+8)^1/3=-8

-2(16x+8)^1/3=-12

(16x+8)^1/3=6

16x+8=216

16x=208

x=13

Checking if x=13 is an extraneous solution:

4-2[16(13)+8]^1/3=-8
4-2(208+8]^1/3=-8

4-2(216)^1/3=-8

4-2(6)=-8

4-12=-8

-8=-8

Not an extraneous solution.