Answers
Covariance between two variables x and y is -9/56 (= -0.160). Option C
How do we solve for the Covariance between the variables?Covariance between two variables is a measure of how much the variables change together. It's calculated with the formula:
Cov(X, Y) = E[XY] - E[X]E[Y]
Where:
E[XY] is the expected value of the product of X and Y.
E[X] is the expected value of X.
E[Y] is the expected value of Y.
First, we need to calculate E[X], E[Y], and E[XY].
E[X] = ∑ x × g(x) for all x
= 0×(5/14) + 1×(15/28) + 2×(3/28)
= 15/28 + 6/28 = 21/28 = 0.75
E[Y] = ∑ y × h(y) for all y
= 0×(15/28) + 1×(3/7) + 2×(1/28)
=0.5
E[XY] = ∑∑ xyf(x, y) for all (x, y)
= 00(3/28) + 01(3/14) + 02(1/28) + 10(9/28) + 11(3/14) + 12(0) + 20(3/28) + 21(0) + 22(0)
= 0.2143
Now we can substitute these values into the formula for Cov(X, Y):
Cov(X, Y) = E[XY] - E[X]E[Y]
= 0.2143 - (0.75)×(0.5)
= -0.1607
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Related Questions
When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?
Answers
when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.
The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.
In mathematical terms, when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.
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A skateboarder gets paid 10,000 fo4 winning a competition he puts it in a savings account that increases at 7% per year.How much money will he have after 8 years show graph
Answers
The amount of money he will have after eight years of savings would be = 15,600.
How to calculate the total amount of money the skateboarder?To calculate the total amount of money the skateboarder will have after the number of giveyears, the formula that should be used would be given below as follows:
Simple interest = Principal×time ×rate /100
Where:
principal = 10,000
Time = 8 years
Rate = 7%
Simple interest = 10,000×8×7/100
= 560000/100
= 5600
The total amount of money the skateboarder will have will be = 10,000+5600 = 15,600
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help me solve math please
Answers
The measures of central tendency of the dataset, and the measurements in the dataset indicates;
(a) Mode
(b) Mean
(c) Mean, Median
(d) Roughly symmetrical
What is a measure of central tendency?Measures of central tendency are descriptive statistical values that represent the typical value or centerpoint of a data set.
(a) The mean of a data set always has only one value. The mode of the dataset are 11 and 14. Therefore, the measure of central tendency that takes more than one value is the mode. The correct option is therefore;
Mode
(b) The mode will remain the same. The middle value or median will remain the same. The mean, which i the average value will increase. The correct option for measure of central tendency that will be affected by the change is therefore the mean.
Mean
(c) The smallest measurement which is 1, if removed, the mean will change and the median will change from 11 to (10 + 11)/2 = 10.5. The correct options for the measures of central tendency that will change are therefore;
Mean
Median
(d) The distribution of the original dataset can be presented as shown in the histogram, which is symmetrical about the class with one of the modes, indicating that the original data is roughly symmetrical about the class with the mode 11. The correct option is therefore;
Roughly symmetrical
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Angle ADB and CD are straight lines. angle ADC = 5 x angle CDB Work out the size of angle ADC.
Answers
Answer:
Step-by-step explanation:
What the meaning of statement this?
Answers
This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.
The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:
∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))
The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.
The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.
The statement can be interpreted as follows:
"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."
In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.
It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.
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Construct a box-and-whisker
16, 12, 13, 14, 16, 18, 15, 17, 20, 12, 14, 15, 15
graph using the following data.
Answers
Given statement solution is :- Box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).
To construct a box-and-whisker plot using the given data, you first need to find the minimum, maximum, median, and quartiles. Here are the steps to create the box-and-whisker plot for the given data set:
Sort the data in ascending order:
12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 18, 20
Find the median (middle value) of the data set. Since the data set has an odd number of values, the median will be the middle value:
Median = 15
Find the lower quartile (Q1), which is the median of the lower half of the data set.
Counting from the start, the lower half of the data set is:
12, 12, 13, 14, 14
Q1 = 13
Find the upper quartile (Q3), which is the median of the upper half of the data set.
Counting from the end, the upper half of the data set is:
17, 18, 20
Q3 = 18
Find the minimum and maximum values in the data set:
Minimum = 12
Maximum = 20
Now that we have the necessary values, we can construct the box-and-whisker plot:
lua
Copy code
| |
12 | -------------|
13 | |
14 | ----
15 | -------
16 | -------------|
17 | |
18 | ----
20 | |
|_________________|
In this box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).
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Solve me the question
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The mean, mean deviation mode, median standard deviation, and coefficients of variation, CV, are as follows;
1. The mean deviation about the mean, median mode are;
2.653, 3.709, and 3.709, respectively
The coefficients of variation are;
0.364, 0.337, 0.337, respectively
The variance is about 9.462
The standard deviation is about 3.076
2. Section A has a higher relative dispersion than section B
3. City 2
4. a. Mean ≈ 43.85
b. Mode 40 - 54 inches
c. Median ≈ 45.16
The variance ≈ 125.8056
Standard deviation ≈ 11.216
Coefficient of variation ≈ 0.268
What is a coefficient of variation?The coefficient of variation of a data quantifies or is a measure of the variability of the values in the set of data.
The mean for the data can be calculated as follows;
Mean = (3×10 + 6×15 + 11×25 + 2×6 + 4×4 + 10×3 + 5×2 + 7×8 + 8×9 + 9×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 7.29
The median is the 86/2 value = 43rd value
10 + 15 + 25 = 50
Therefore, the median is in the class with a frequency of 25, which is 11
The mode of the data, which is the value with the highest frequency in the data set is 11
The mean deviation from the mean is therefore;
(|3 - 7.29|×10 + |6 - 7.29|×15 + |11 - 7.29| ×25 + |2 - 7.29| ×6 + |4 - 7.29| ×4 + |10 - 7.29| ×3 + |5 - 7.29| ×2 + |7 - 7.29|×8 + |8 - 7.29| ×9 + |9 - 7.29| ×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 2.653
The coefficient for the mean deviation about the mean is therefore; 2.653/7.29 ≈ 0.364
The mean deviation about the median is therefore;
(|3 - 11|×10 + |6 - 11|×15 + |11 - 11| ×25 + |2 - 11| ×6 + |4 - 11| ×4 + |10 - 11| ×3 + |5 - 11| ×2 + |7 - 11|×8 + |8 - 11| ×9 + |9 - 11| ×4)/(10+15+25+6+4+3+2+8+9+4)
The mean deviation about the median = 319/86 ≈ 3.709
The coefficient ≈ 3.709/11 ≈ 0.337
The median = The mean deviation about the mode ≈ 3.709
The coefficient is about 0.337
The variance = (10×(3 - 7.29)² + 15×(6 - 7.29)² + 25×(11 - 7.29)² + 6×(2 - 7.29)² + 4×(4 - 7.29)² + 3×(10 - 7.29)² + 2×(5 - 7.29)² + 8×(7 - 7.29)² + 9×(8 - 7.29)² + 4×(9 - 7.29)²)/(10+15+25+6+4+3+2+8+9+4) ≈ 9.462
The standard deviation, s ≈ √(9.462) ≈ 3.076
2. The coefficient of variation, CV, can be used to compare the variability of the datasets comprising of different scales as follows;
CV = Standard deviation/( The mean of the data)
Therefore; CV for section A = 23/79 ≈ 0.2911
CV for section B = 11/64 ≈ 0.172
The higher CV value for section A indicates that the scores of section A have a higher relative dispersion than the scores for the section B
3. The consistency values can be obtained by finding the standard deviation for the values in the data for each city, using a web based tool as follows;
City 1; Mean = 23
Variance = 50/4
Standard deviation, City 1 = (√(50))/2 = 5·√2/2
City 2; Mean = 21.8
Sample variance = 2.2
Standard deviation, City 2 = √(2.2) ≈ 1.483
City 3; Mean = 29.2
Sample variance = 18.7
Standard deviation, City 3 = √(18.7) ≈ 4.324
The standard deviation of city 2, which is the smallest compared tom the other cities, indicates that the City 2, has the most consistent temperature
4. The mean of the data obtained from the data using the midpoint of the data, is; Mean = ∑fx/∑f
Therefore; The mean obtained using an online tool is; 43.85
The mode is the data that occurs most frequently, which is the data with the value; 40 - 54 inches
The median is the value at the middle of the data set, which is the value with a frequency of 53, and in the interval 40 - 54 inches
The median is; 39.5 + (54.5 - 39.5) × (50 - 30)/53 ≈ 45.16
The standard deviation found for the grouped data, using an online tool is as follows;
Variance, σ² ≈125.8056
The standard deviation, σ ≈ √(125.8056) ≈ 11.216
The coefficient of variation is; 11.216/41.83 ≈ 0.268
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Solve for x find the side
Answers
The length of x is 3.42cm
How to determine the value
To determine the value, we have to know the different trigonometric identities.
These identities are listed thus;
sinetangentcotangentsecantcosecantcosineFrom the information shown in the diagram, we have that;
Opposite side = x
The hypotenuse side = 10
The angle = 20 degrees
Now, using the sine identity, we get;
sin 20 = x/10
cross multiply the values, we get;
x = 10(0.3420
Multiply the values, we have;
x = 3.42cm
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Write the equation in standard form for the circle passing through (5/2, - 6) centered at the origin.
Answers
The equation in standard form for the circle passing through (5/2, -6) and centered at the origin is [tex]4x^2 + 4y^2 = 169.[/tex]
To write the equation in standard form for the circle passing through (5/2, -6) and centered at the origin, we'll use the general equation of a circle:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) represents the center of the circle and r represents the radius.
Given that the circle is centered at the origin (0, 0), we can substitute these values into the equation:
[tex](x - 0)^2 + (y - 0)^2 = r^2\\x^2 + y^2 = r^2[/tex]
Now, we need to determine the radius of the circle. Since the circle passes through the point (5/2, -6), we can find the distance between the origin (0, 0) and this point, which represents the radius.
Using the distance formula:
d = √([tex](x2 - x1)^2 + (y2 - y1)^2)[/tex]
Substituting the values of the point (5/2, -6) and the origin (0, 0):
r = √([tex](5/2 - 0)^2 + (-6 - 0)^2)[/tex]
r = √(([tex]5/2)^2 + (-6)^2)[/tex]
r = √(25/4 + 36)
r = √(25/4 + 144/4)
r = √(169/4)
r = 13/2
Now, we can substitute the value of the radius (r = 13/2) into the equation:
[tex]x^2 + y^2 = (13/2)^2\\x^2 + y^2 = 169/4[/tex]
Multiplying both sides of the equation by 4 to eliminate the fraction:
[tex]4(x^2 + y^2) = 4(169/4)\\4x^2 + 4y^2 = 169[/tex]
Therefore, the equation in standard form for the circle passing through (5/2, -6) and centered at the origin is:
[tex]4x^2 + 4y^2 = 169.[/tex]
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Usually Anna works 36 hours per week. However, last week she worked only 28 hours. Find each percent of change to the nearest whole percent. Label as an increase or decrease.
Answers
Answer:
The percent of change in Anna's working hours is 22%, indicating an increase.
Step-by-step explanation:
Step 1: Calculate the difference:
Difference = 36 hours - 28 hours
Difference = 8 hours
Step 2: Calculate the percent change:
Percent Change = (Difference / Original Value) * 100
Percent Change = (8 hours / 36 hours) * 100
Percent Change ≈ 22.22%
Therefore, the percent change in Anna's working hours is approximately 22.22%, representing an increase.
A school plans to build a wheelchair ramp from the sidewalk to the front entrance of the school. the slope must be 5/32. the entrance to the school is 81cm above the ground. what is the horizontal distance needed for the ramp?
Answers
The horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.
To find the horizontal distance needed for the ramp, we can use the formula:
Horizontal distance = Vertical distance / Slope
Given that the slope must be 5/32 and the entrance to the school is 81 cm above the ground, we can substitute these values into the formula:
Horizontal distance = 81 cm / (5/32)
To divide by a fraction, we can multiply by its reciprocal:
Horizontal distance = 81 cm * (32/5)
Simplifying:
Horizontal distance = (81 cm * 32) / 5
Horizontal distance = 2592 cm / 5
Horizontal distance = 518.4 cm
Therefore, the horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.
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How do you calculate the area of a road? Please help. (Picture shown to calculate the road)
Answers
Calculating the area of a road involves considering the road's shape and cross-sectional profile. There are two common methods for calculating the area:
How to find the area of a roadCross-Sectional Area Method: This method involves measuring the width of the road at regular intervals along its length and taking elevation measurements. By dividing the road into sections and multiplying the width by the corresponding elevation difference, you can calculate the area of each section and sum them up to obtain the total road area.
Digital Terrain Model (DTM) Method: This method uses advanced surveying techniques to obtain a digital terrain model of the road surface. By applying surface area algorithms to the DTM, you can calculate the surface area of the road, considering the elevation data and interpolating the area between points.
The chosen method depends on available data, accuracy requirements, and project needs. It is essential to refer to engineering standards and guidelines specific to your region or project for accurate and appropriate road area calculations.
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Two hens can lay 2 eggs in 2 minlutes if that is the maximum speed how many hens can lay 500 eggs in 500 minutes
Answers
To determine how many hens are needed to lay 500 eggs in 500 minutes, we divide 500 eggs by the number of eggs laid by each hen in 500 minutes. In this case, 500 eggs divided by 250 eggs per hen equals 2 hens.
So, you would need two hens to lay 500 eggs in 500 minutes at their maximum speed.
an amount of 27000 is invested in a fund that pays 11,15% simple interest per year. the total amount in this fund after 129months will equal
Answers
The total amount in the fund after 129 months will be approximately $59,392.90.
To calculate the total amount in the fund after 129 months, we need to use the formula for simple interest:
A = P(1 + rt)
Where:
A = Total amount (including interest)
P = Principal amount (initial investment)
r = Interest rate per period
t = Number of periods
Given:
P = $27,000
r = 11.15% per year (or 0.1115 as a decimal)
t = 129 months
First, we need to convert the interest rate from a yearly rate to a monthly rate since the time period is given in months. We divide the yearly rate by 12 to get the monthly rate:
monthly interest rate = 0.1115 / 12 = 0.0093 (rounded to four decimal places)
Now, we can plug in the values into the formula and calculate the total amount (A):
A = $27,000(1 + 0.0093 * 129)
A = $27,000(1 + 1.1997)
A = $27,000 * 2.1997
A ≈ $59,392.90
Therefore, the total amount in the fund after 129 months will be approximately $59,392.90.
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A house on the market was valued at 432,000. After several years, the value decreased by 9%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answers
Answer:
$393,120
Step-by-step explanation:
To find the decrease in the house's value in dollars, we need to calculate 9% of the initial value:
Decrease in value = (Initial value) * (Percentage decrease) = $432,000 * 9%
Converting the percentage to a decimal:
Decrease in value = $432,000 * 0.09 = $38,880
The house's value decreased by $38,880.
Now, to find the current value of the house, we need to subtract the decrease in value from the initial value:
Current value = Initial value - Decrease in value = $432,000 - $38,880 = $393,120
The current value of the house is $393,120.
Hope this helps!
ejemplos sobre experimentos aleatorios con orden,remplazo y sin repeticion
Answers
De acuerdo con la información, podemos inferir que un ejemplo de experimento aleatorio con orden y reemplazo: Lanzar un dado y registrar el resultado en cada lanzamiento.
¿Qué ejemplo podemos encontrar de un experimento aleatorio con orden, remplazo y sin repetición?Los experimentos aleatorios tienen diferentes formas de aplicación según su tipo, a continuación explicamos algunos:
Orden implican registrar los resultados en secuencia, mientras que los experimentos.Sin orden no tienen en cuenta el orden en que ocurren los resultados.Con reemplazo, los elementos pueden repetirse en cada selección, mientras que en los experimentos.Sin reemplazo, los elementos seleccionados ya no están disponibles para selecciones posteriores.De acuerdo con lo anterior, UN ejemplo de experimento aleatorio con orden y reemplazo: Lanzar un dado y registrar el resultado en cada lanzamiento.
Question in English
Give examples of randomized experiments with order, replacement, and no repetition.
Answer in English
Based on the information, we can infer that an example of a random experiment with order and replacement: Throw a die and record the result on each throw.
What example can we find of a random experiment with order, replacement, and no repetition?Random experiments have different forms of application depending on their type, some of which are explained below:
Order involve recording the results in sequence, while experiments. Orderless do not take into account the order in which the results occur. With replacement, items can be repeated in each selection, while in experiments. Without replacement, the selected items they are no longer available for subsequent selections.
Based on the above, ONE example of a random experiment with order and replacement: Roll a die and record the result on each roll.
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If you know the answer please put the answer and the explanation thank you.
Answers
In the class, Lucy's score is 6.
How to work out Lucy's score?In statistics, the median is the middle value in a sorted, ascending or descending list of numbers. Thus, it represents the midpoint of the data.
The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.
Since Lucy is one of the 29 students in the class and her score was the same as the median score for her class.
Thus, the median score will be 15th score (i.e. the midpoint of 29). Using the frequency in of each score from the figure, let's keep adding the frequency until we reach 15 and we will then check the corresponding score at the 15th position:
2 + 2 + 4 + 7 = 15
Thus, the the corresponding score at the 15th position is 6.
Therefore, the median score is 6 and consequently Lucy's score is 6.
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the sum of two numbers is 59. the didference between the two numbers is 11 which is the smaller of the two numbers
Answers
The larger number is 35.Let's assume the two numbers are represented by the variables "x" and "y," where "x" is the smaller number.
Equation 1: x + y = 59 (The sum of the two numbers is 59)
Equation 2: x - y = 11 (The difference between the two numbers is 11, with the smaller number being y)
According to the given information, the sum of the two numbers is 59, which can be expressed as:
x + y = 59
The difference between the two numbers is 11, with "x" being the smaller number. This can be expressed as:
y - x = 11
We can now solve these two equations simultaneously to find the values of "x" and "y."
Rearranging the first equation to solve for "y" gives us:
y = 59 - x
Substituting this value of "y" into the second equation:
(59 - x) - x = 11
Simplifying the equation:
59 - 2x = 11
Subtracting 59 from both sides:
-2x = 11 - 59
-2x = -48
Dividing both sides by -2:
x = -48 / -2
x = 24
Therefore, the smaller number is 24. To find the larger number, we substitute the value of "x" into the first equation:
24 + y = 59
y = 59 - 24
y = 35.
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My checking account balance was $443 on February 1st and $872 on February 7th. Show the rate of change
Answers
Answer:
$61.29 per day.
Step-by-step explanation:
Checking account balance on February 1st: $443
Checking account balance on February 7th: $872
Difference in balances: $872 - $443 = $429
Number of days between February 1st and February 7th: 7 days
Rate of change = Difference in balances / Number of days
Rate of change = $429 / 7 days
To find the rate of change per day, divide the difference in balances by the number of days:
Rate of change = $429 / 7 days ≈ $61.29 per day
Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.
Is 2x + 4 the same as 4 + 2x? ANSWER??????????//
Answers
Answer:Yes
Step-by-step explanation:
By the communitive property, they are equal to each other.
Pls answer correctly quickly
Answers
Answer:
3
Step-by-step explanation:
tan(A) = y-coordinate / x-coordinate
tan(A) = -3 / -1
tan(A) = 3/1
tan(A) = 3
Therefore, the value of tan(A) is 3.
A cylindrical steel pipe with a liquid is 21 cm long with radius 0, 4 cm and its hollow part is of radius 0, 1 cm. What is the volume of liquid, in litres, in the pipe? A. 9000 litres B. 9400 litres C. 9900 litres D. 10100 litres
Answers
Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.
To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.
Given:
Length of the cylindrical steel pipe (hollow part) = 21 cm
Radius of the solid cylinder = 0.4 cm
Radius of the hollow cylinder = 0.1 cm
First, let's calculate the volume of the solid cylinder (hollow part):
V1 = π × [tex]r1^2[/tex] × h
V1 = π × [tex](0.4 cm)^2[/tex] × 21 cm
Next, let's calculate the volume of the hollow cylinder:
V2 = π × [tex]r2^2[/tex] × h
V2 = π × [tex](0.1 cm)^2[/tex] × 21 cm
Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:
Volume of liquid = V1 - V2
Let's calculate these values:
V1 = π ×[tex](0.4 cm)^2[/tex] × 21 cm ≈ 10.572 cm³
V2 = π × [tex](0.1 cm)^2[/tex] × 21 cm ≈ 0.693 cm³
Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³
To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:
Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L
Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.
Therefore, none of the options A, B, C, or D provided is the correct answer.
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jasmine made a pitcher of lemonade. One pitcher contains 12 glasses of lemonade. asmine serves 4 glasses of lemonade, how many more glasses, &, can she Choose the answer that represents the correct equation and solution.
Answers
Jasmine has 8 glasses of lemonade remaining in the pitcher.
Jasmine made a pitcher of lemonade, which contains 12 glasses of lemonade. She served 4 glasses of lemonade, and we need to determine how many more glasses she has left.
To solve this problem, we can subtract the number of glasses served from the total number of glasses in the pitcher:
12 (total glasses) - 4 (glasses served) = 8 (glasses remaining)
Therefore, Jasmine has 8 glasses of lemonade left in the pitcher after serving 4 glasses.
In terms of the equation, we have:
Total number of glasses - Number of glasses served = Number of glasses remaining
Or:
12 - 4 = 8
So, the correct equation and solution are:
12 - 4 = 8
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Determine the equation of the midline of the following graph.
Answers
The equation of the midline of the graph is y = -2
How to determine the equation of the midline of the graph.From the question, we have the following parameters that can be used in our computation:
The graph
Where we have
Max = 1
Min = -5
Using the above as a guide, we have the following:
Midline, y = (Max + MIn)/2
substitute the known values in the above equation, so, we have the following representation
y = (1 - 5)/2
Evaluate
y = -2
Hence, the equation of the midline of the graph is y = -2
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-2log (6x + 1) = -6.
Answers
Find the volume of each composite figure to the nearest whole number.
Answers
The volume of the composite figure in this problem is given as follows:
76 ft³.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:
Volume = length x width x height.
The figure in this problem is composed by two prisms, with dimensions given as follows:
2 ft, 6 ft and 3 ft.2 ft, 4 ft and 8 - 3 = 5 ft.Hence the volume is given as follows:
2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.
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Please help me with this
Answers
Step-by-step explanation:
I'm pretty sure you just use the law of cosines in this case.
c= sqrt(a^2+b^2﹣2ab (cos γ))
where a is a Side, b is a Side, γ is Gamma or the angle. Sqrt means square root
In your case, a is 20, b is 13, and γ is 93. Just plug it into the formula now :). I got 24.41751 ish.
4. Set up a linear system of equations for the following application problem. Remember to
follow the steps of problem solving. DON'T FORGET TO DECLARE YOUR VARIABLES.
Use the graphical method to solve the system and remember to write a verbal answer for your
solution.
The campus bookstore recently sold a total of 144 calculators. Some of these were the cheap
Basic Grapher model (which sells for $23 each) and the rest were the exquisite SuperGrapher
model (which sells for $90 each). The bookstore received a total of $10347 from that sale of
these two calculators. Use your mastery of algebra to help the bookstore find how many
Basic Graphers and how many SuperGraphers were sold.
Invisni
TOTAL
Answers
The system of equations that represents this is:
x + y = 144
x*23 + y*90 = 10347
Solving it, we conclude that they sold 39 of the Basic ones and 105 of the Super ones.
How to set up the system of equations?To do this, first we need to define the variables we will be using. Let's define:
x = number of basic graphers sold.
y = number of SuperGraphers sold.
They sold a total of 144 items, so x + y = 144
And they earned a total of $10347, then we can write:
x*23 + y*90 = 10347
Then the system of equations that represents this is:
x + y = 144
x*23 + y*90 = 10347
The graph of this system is on the image below, there we can see that the solution is (39, 105).
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Multiplicative Comparison
Kendra and Madison draw dolphins in art class. Kendra draws
4 dolphins. Madison draws 6 times as many dolphins as Kendra.
How many dolphins does Madison draw?
Let d stand for the number of dolphins Madison draws.
Which bar model represents the problem?
Kendra 4
Madison 6
Kendra
Madison 4 4 4
d
4
4
Kendra 4
Madison 4
Kendra
Madison
4 4 4
4
4
6 6 6
d
6
6
6
Answers
Kendra | | | |
Madison | | | | | | | | | | | | | | | | | | | | | | | |
Madison drew 24 dolphins.
To solve this problem, we need to use the information given in the problem and represent it in a bar model. Let's use the following bar model:
Kendra: 4 dolphins
Madison: 6 times as many dolphins as Kendra
Kendra | | | |
Madison | | | | | | | | | | |
From the model, we can see that Kendra drew 4 dolphins and we don't know how many dolphins Madison drew, which is represented by "d". The problem tells us that Madison drew 6 times as many dolphins as Kendra, so we can multiply Kendra's number of dolphins by 6:
Kendra: 4 dolphins
Madison: 6 x 4 = 24 dolphins
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627 x 26
how do you solve this problem using standard algorithm
Answers
627 x 26 equals 16,302 when solved using the standard algorithm.
The steps below can be used to solve the multiplication issue 627 x 26 using the conventional algorithm:
627 and 26 should be written one above the other, with the larger number appearing above and the smaller number beneath.
Start by adding each digit of the top number to the ones digit of the bottom number (six). Write the answers below the line after multiplying 6 by 7 and then by 2.
1254 -- a 6 x 7 partial product
1254 -- a half 6 x 2 product
Repeat the process by moving the bottom number one position to the left after that. Multiply 2 by 7 and then by 2, and then write the results one space to the left of the line below the line.
1254 x 627
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