The width of a rectangle is w + 4 and the length of the rectangle is 2w + 3. Which expression represents the area of the rectangle?

Answer: 65

Step-by-step explanation:

Therefore , the solution of the given problem of percentage comes out to be the initial annual heating cost was about £1438,26 before the 15% increase.

A number or statistic that is stated as an amount of 100 is referred to as "a%" in statistics. The forms "pct," "pct," or "pc" are additionally uncommon. The common way to indicate it is with a representation "%," though. The ratio to the total sum is flat, and there are no indicators. Percentages are actually integers because they almost always add up to 100. To suggest that a number indicates a percentage, either the word "fraction" or a representation for percentage (%) must come before the number.

Here,

Assume that the annual heating expense was x prior to the 15% increase.

=> x + 0.15x = 1.15x was the new bill after the 15% price rise.

We can write: Because we are aware that the new price following the increase is £1654:

=> 1.15x = 1654

We must find x in order to determine the initial bill before the increase:

=> x = 1654/1.15

=> x ≈ 1438.26

Therefore, the initial annual heating cost was about £1438,26 before the 15% increase.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

Answer:

8%

Step-by-step explanation:

[tex]= .08[/tex]

This is the answer as a decimal. To change a decimal to a perfect multiply the decimal by 100%

[tex].08 \times 100\% = 8\%[/tex]

Step-by-step explanation:

2(x+10y)+2(7x^2-x+9y)

= 2x+20y+14x^2-2x+18y

= (14x^2+38y) units^2

Answer/Step-by-step explanation:

We know that sin 60° = √3/2, and we can use this information to find cos 60°:

cos 60° = √(1 - sin^2 60°) = √(1 - 3/4) = √(1/4) = 1/2.

To find the measure of angle 3, we can use the formula:

cos(180° - 2x) = -cos(2x)

We want to solve for x when cos 2x = √(√3/2) = √3/2 * 1/√2 = √3/2√2

cos(180° - 2x) = -cos(2x)

cos(2x) = √3/2√2

180° - 2x = 150° or 210°

x = 15° or 35°

Therefore, the measure of angle 3 can be either 15° or 35°.

The probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615. This is because out of the 13 balls, 6 of them have even numbers.

To calculate the probability, we use the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcomes would be the number of even numbers, which is 6. The total number of outcomes would be 13 (the total number of balls in the bag). Therefore, the probability of selecting a ball that has an even number is 6/13.

Another way to look at this is to think of the probability as the ratio of favorable outcomes to total possible outcomes. In this case, the ratio is 6:13, which can be simplified to 3:6 or 1:2. Since one out of every two outcomes is favorable, the probability is 0.5, which is the same as 6/13.

To further understand the concept of probability, consider the example of a fair coin. If a fair coin is flipped, the probability of getting either heads or tails is 50%. This is because the ratio of favorable outcomes (one head and one tail) to total possible outcomes (two heads and two tails) is 1:2.

In conclusion, the probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615.

To know more about  probability refer here:

https://brainly.com/question/11234923

#SPJ11

When we write out the system of equations, we will get:

[tex]x+y=18[/tex]

[tex]x-y=-8[/tex]

We can then use elimination to get just one variable.

[tex]x+y=18[/tex]

[tex]x-y= -8[/tex]

Which gives us: [tex]2x=10[/tex]

We then divide by 2 and get: [tex]x=5[/tex]

We next plug that into one of the two equations and solve for the other variable: [tex](5)+y=18[/tex]

We subtract 5 from both sides and get: [tex]y=13[/tex]

So the two numbers are 13 and 5.

Answer:

14 = 2 x 7

28 = 2² x 7

56 = 2³ x 7

The equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.

An exponential decay function can be written as f(x) = ab^x where b is the base of the exponential function and a is the initial value. If b is between 0 and 1, the function will exhibit exponential decay. Since we need a vertical shrink of 3/4, we can set b = 3/4.

We also need a vertical shift of 10 units, so we add 10 to the function. The resulting function is: f(x) = 10 - (3/4)^x. Therefore, the equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.

To know more about exponential decay function refer here:

https://brainly.com/question/14355665#

#SPJ11

Answer:

Hey Sweetheart!

z=4

4x4x4= 64

Hope this Helps!!!

The statement "we have data that is a continuous variable. it is a measurement of time between events. this is a situation where we should evaluate a histogram for a likely exponential distribution" is true because when dealing with continuous data representing time between events, it is common to evaluate a histogram to determine if it follows an exponential distribution.

If the data represents the time between events and it is a continuous variable, it is common to evaluate the histogram to see if it follows an exponential distribution. The exponential distribution is often used to model the waiting time between independent events that occur at a constant average rate, and it has a continuous range of values that can be plotted as a histogram.

To evaluate whether the data follows an exponential distribution, you can plot a histogram and visually check if it has a single peak and a decreasing tail, which are characteristic of the exponential distribution. You can also use statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test to assess the goodness-of-fit between the data and the exponential distribution.

Learn more about exponential distribution here

brainly.com/question/22692312

#SPJ4

The right triangle has a 90-inch perimeter.

A right triangle is one with a 90 degree inner angle. Its longest side is the hypotenuse, which is also the side of the right triangle that faces the right angle. The two arms of a right angle are made up of height and base.

To get the length of the other right triangle leg, let's apply the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse and a and b are the triangle's legs.

We are aware that c = 41 inches and, let's say, a = 40 inches for one of the legs. Hence, we may find b:

40² + b² = 41²

1600 + b² = 1681

b² = 1681 - 1600

b² = 81

b = √81

b = 9

Hence, the other leg is 9 inches long.

We can now determine the triangle's perimeter:

Perimeter = a + b + c

Perimeter = 40 + 9 + 41

Perimeter = 90 inches

To know more about right triangle visit:-

https://brainly.com/question/632231

#SPJ1

Based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.

The population in statistics refers to the total set of people or things that we are attempting to analyse and make conclusions about. Typically, this group is too big to see or measure directly, so we use statistical methods to infer some of its features from a smaller collection of people or things, known as a sample. A representative portion of the population was selected for the sample in order to learn more about the population as a whole. The purpose of statistical analysis is to draw conclusions about the population using data from the sample.

The number of weeks in a month= 4.

Using the given table the estimated number of sales for the month are:

Salted caramel: 51 x 4 = 204

Gingerbread: 31 x 4 = 124

Mint: 99 x 4 = 396

Hence, based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.

Learn more about equations here:

https://brainly.com/question/29657983

#SPJ1

One possible equation Ross can make is 9 - 7 + 8 = 10

Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.

One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.

Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.

Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.

One possible equation Ross can make is:

9 - 7 + 8 = 10

Learn more about arithmetic operations here

brainly.com/question/30553381

#SPJ4

Answer:

The equation of a vertical line in the graph, which is parallel to y-axis is x = a. The slope of a vertical line is infinity or undefined as it has no y-intercept and the denominator in the slope formula is zero.

Step-by-step explanation:

The three ordered pairs that are most likely the added data points are:

B: (4,10), (4,11), (4,12)

C: (8,9), (8,10), (8,11)

D: (10,10), (10,11), (10,12)

In order to determine the added data points, we first need to note that the data points have a slightly linear pattern with a negative slope. Also, a linear regression on the points will give us:  linear regression on the given data points, we obtain the equation: y = -1.2x + 10.8

In selecting the three added data points, a good criterion will be for the points to be as close as possible to the original line of best fit. The data points in option A are close to slope 1 so adding them will significantly shift the line of best fit. The data points in options B, C, and D are in a vertical line and will not shift the line of best fit. So, they are most likely the best data points to add.

Learn more about the line of best fit here:

https://brainly.com/question/17013321

#SPJ1

Therefore , the solution of the given problem of unitary method comes out to be the parking lot has 60 trucks.

It is possible to accomplish the objective by using this widespread convenience, pre-existing variables, or all significant components from the initial Diocesan adaptable survey that adhered to a specific methodology. If it doesn't, both of the essential components of a term confirmation outcome will undoubtedly be lost, but if it is, there is going to be another opportunity to contact the entity.

Here,

Let's begin by giving the unknowns variables:

x = number of vehicles

Van count = 4 times

Since there are 205 cars overall, the number of lorries is equal to (205 - 11x).

The value of x can be determined using the second bit of knowledge:

=> 4x/3 = (205 - 11x)/2

When we simplify this solution, we obtain:

=> 8x = 3(205 - 11x)

=> 8x = 615 - 33x

=> 41x = 615

=> x = 15

We can now determine the quantity of vans:

Van count = 4x = 4(15) = 60

Consequently, the parking lot has 60 trucks.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1  

The approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%

To find the approximate percent decrease in the number of customers from Saturday to Sunday, we first need to calculate the decrease in the number of customers:

Decrease = Saturday customers - Sunday customers

Decrease = 135 - 90

Decrease = 45

The percent decrease can be found by taking the decrease as a percentage of the original value (Saturday customers):

Percent decrease = (Decrease / Saturday customers) x 100%

Percent decrease = (45 / 135) x 100%

Percent decrease = 33.33%

Rounding to the nearest percent, we get that the approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%.

Learn more about  calculations of percent decrease:https://brainly.com/question/30404835

#SPJ11

Your question is incomplete, but probably the complete question is :

You work as a cashier in a supermarket. On Saturday, you had 135 customers. On Sunday, you had 90 customers. What is the approximate percent decrease in the number of customers from Saturday to Sunday?

33%

45%

50%

90%

225%

None of these statements must be true

=========================================

Explanation:

Let's go through the answer choices one at a time.

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

A)

Consider the set {4,5,6}. It has a mean of (4+5+6)/3 = 15/3 = 5. We add up the values and then divide by the number of values (3 in this case).

Now consider the set {3,5,7}. I've added 1 to the largest element and subtracted 1 from the smallest. This will spread the data set out further. The mean is still 5 because (3+5+7)/3 = 15/3 = 5. The center hasn't changed. But the data is more spread out so the variance is larger for this new set.

Therefore, the sets {4,5,6} and {3,5,7} do NOT have the same variance. We cross choice A off the list.

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

B)

Recall that

[tex]\text{standard deviation} = \sqrt{\text{variance}[/tex]

For example, if the variance is 36 then the standard deviation would be [tex]\sqrt{36} = 6[/tex]

Because of the connection of the standard deviation and variance, both measure how spread out a set is. Furthermore, it means the sets {4,5,6} and {3,5,7} do NOT have the same standard deviation. We can cross choice B off the list.

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

C)

This statement is clearly not true because the sets {4,5,6} and {3,5,7} are not the same, but they produce the same mean. We can cross choice C off the list.

Choice D is the only thing left so it must be the final answer.

The estimated joint probability for the "low income and 21-35 age group" cell is 0.108.

In the table given, individuals are cross-classified by their income level and age group. We have to find the estimated joint probability for the "low income and 21-35 age group" cell. The joint probability of the low income and 21-35 age group is calculated as follows;

From the given table, the number of people in the "low income and 21-35 age group" cell is 120.The total number of people in the sample = 120 + 100 + 75 + 150 + 160 + 100 + 160 + 180 + 160 = 1105.

The estimated joint probability for the "low income and 21-35 age group" cell is:P(Low income, 21-35 age group) = 120/1105P(Low income, 21-35 age group) = 0.108. Therefore, the estimated joint probability for the "low income and 21-35 age group" cell is 0.108.

To know more about probability , refer here

https://brainly.com/question/30034780#

#SPJ11

Answer:

linear

Step-by-step explanation:

gradient 1 = [tex]\frac{-3-12}{6-3}[/tex] = -5

gradient 2 = [tex]\frac{-18+3}{9-6}[/tex] = -5

therefore, the graph is linear as the gradient is constant

Answer:

(-3, 6.4)

Step-by-step explanation

First draw a line across the y axis about 4.2 blocks in

Then go to doing your reflections with ease

If Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The line y = 4.2 is a horizontal line that is 1.8 units above the x-axis (since the y-coordinate of T is 2).

When a point is reflected across a horizontal line, its y-coordinate is negated with respect to the line.

So, the y-coordinate of the reflected point T' will be:

y-coordinate of T' = (-3, 6.4)

Hence, if Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ2

The relationship between the types of quadrilaterals such as rectangles, trapezoids and rhombi can be quantified in terms of sides and angles.

Rectangles and trapezoids

Squares and rhombi

Squares and trapezoids

Rhombi and trapezoids

Find out more on trapezoids at https://brainly.com/question/4458080

#SPJ1

Answer:

120

Step-by-step explanation:

The median of 20 is the most accurate to use, since the data is skewed.

A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous data. It is a bar graph-like structure where the bars represent the frequency or proportion of data in specific intervals or ranges of values. The x-axis represents the range of values, and the y-axis represents the frequency or proportion of data in each range. Histograms are commonly used in statistical analysis to represent the distribution of data, especially when dealing with large datasets.

Here,

The data is not evenly distributed, as there are many donations at the lower end and fewer donations at the higher end. Therefore, the median, which represents the middle value in the data set, is a better measure of center than the mean, which can be influenced by extreme values. The median donation in this data set is $20.

To know more about histogram,

https://brainly.com/question/30354484

#SPJ1

Answer:

The answer is D, I'm not sure but I believe it's supposed to be

0.1(55-7)= 300

Step-by-step explanation:

The statement that best describes the chord of a circle is a chord is any segment in which the end points are found on the arc of the circle. (option a).

A chord of a circle is a line segment that connects two points on the circle. The two endpoints of the chord are called the endpoints of the chord, and they lie on the circumference of the circle.

Therefore, option (a) that states that a chord is any segment in which the endpoints are found on the arc of the circle is the correct answer.

It is important to note that a chord does not have to pass through the center of the circle. If a chord passes through the center of the circle, it is called a diameter. A diameter is the longest chord of a circle, and it divides the circle into two equal parts called semicircles.

The correct answer to the question is option (a), which states that a chord is any segment in which the endpoints are found on the arc of the circle.

To know more about circle here

https://brainly.com/question/483402

#SPJ4

Complete Question:

which of the following best describes the chord of a circle?

a) a chord is any segment in which the endpoints are found on the arc of the circle.

b) a chord is a triangle inside of a circle.

c) a chord is the arc formed from the segment.

d) a chord is a square inside of a circle.

Answer:

The volume is 1474.45 mm^2

Step-by-step explanation:

First, you have to find the radius. To do this, you divide the diameter by 2. This means that the radius is 8.

Then you use the formula V=3.14*r^2*(h/3)

V=3.14*8^2*(22/3)=1474.45 mm^2