A Bakery sold 382 cakes in one week. this was twice as the day so the previous week. write an equation that can be used to find the number of cakes and that were sold the previous week 
Answer:
164 Cakes
Step-by-step explanation:
382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.
Can you please help me with this.
The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.
The total number of ways to develop the complex would be 665, 280 ways.
How to find the probability ?To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.
Using combinations, we have:
Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)
Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)
Now, we find the probability:
Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members
Probability = (C(28, 6) x C(12, 4)) / C(40, 10)
Probability = 0.3633
How to find the number of ways ?To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:
The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:
P(11, 5) = 11! / (11 - 5)!
Total ways to develop the complex = 12 x P(11, 5)
= 12 x 55440 = 665,280 ways
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What is the the slope-intercept form of (-5,-2)
Answer:
Step-by-step explanation:
we can't say because we don't have a couple of coordinates
Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 44 loaves of bread at the same prices, for a total of $10. How much does a liter of milk cost, and how much does a loaf of bread cost?
The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
What is cost?Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.
The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
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A factory received a shipment of 24 lightbulbs, and the vendor who sold the items knows there are 4 lightbulbs in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the lightbulbs in the sample are defective, he will refuse the shipment. For each of the following, give your responses as reduced fractions. If a sample of 4 lightbulbs is selected, find the probability that all in the sample are defective. If a sample of 4 lightbulbs is selected, find the probability that none in the sample are defective.
The probability that none of the 4 lightbulbs in the sample are defective is 805/1763 as a reduced fraction.
What is probability?
Let's first calculate the total number of ways to choose 4 lightbulbs from 24:
24 choose 4 = (24!)/(4! * 20!) = 10,626
Probability that all 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose all 4 from the 24 is:
4 choose 4 = 1
So, the probability that all 4 lightbulbs in the sample are defective is:
1/10,626 = 1/5313
Therefore, the probability that all 4 lightbulbs in the sample are defective is 1/5313 as a reduced fraction.
Probability that none of the 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose 4 non-defective bulbs from the remaining 20 is:
20 choose 4 = (20!)/(4! * 16!) = 4,845
So, the probability that none of the 4 lightbulbs in the sample are defective is:
4,845/10,626 = 805/1763
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For #1 - 6, use the information given to write the equation of the line in slope intercept form.
1. Line where slope is -32 and y-intercept is 7
1. Line where slope is 5 and x -intercept is 2
1. Line going through the points (-1, -5) and (4, -2)
1. Line going through the points (0, 1) and (2, -2)
1. Line where m = 4 and and b = -76
1. Line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0
An equation of a line where slope is -32 and y-intercept is 7 is y = -32x + 7.
An equation of a line where slope is 5 and x-intercept is 2 is y = 5x - 10.
An equation of a line that is going through the points (-1, -5) and (4, -2) is y = 3x/5 - 22/5
An equation of a line that is going through the points (0, 1) and (2, -2) is y = -x/2 + 1
An equation of a line where m = 4 and and b = -76 is y = 4x - 76.
An equation of a line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0 is y = 3x + 0.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 5)/(4 + 1)
Slope (m) = 3/5
At data point (-1, -5) and a slope of 3/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 5 = 3/5(x + 1)
y = 3x/5 + 3/5 - 5
y = 3x/5 - 22/5
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Expand the expressions and simplify 5(x + 4) + 3(x + 2) =
8x + 4
6x + 18
8x+ 26
7x - 18
Answer:
8x+26
Step-by-step explanation:
distribute the 5 into the numbers in the parentheses. you get (5x+20) then do the same with 3(x+2) which wll be (3x+6) now add like terms, which are 5x+3x=8x and 20+6=26. boom 8x+26.
8x + 26
multiply the outside number by the inside numbers and add them. remember, if the variable is singular example x, then it equals 1 :) I hope this helps you understand, I'm currently doing algebraic expressions.
Which is more, 19 ounces or 1 pound?
Consequently, 1 pound weighs more than 19 ounces.
What additional weight units are there?
The weight can also be expressed in terms of grams, kilograms, pounds, and tons.
What is a pound?Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.
What does ounce mean?The weight unit known as an ounce is 1/16th of a pound.
What fraction of a ton is one pound?A ton weighs 2000 pounds.
16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.
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Find the surface area and volume of the composite solid.
According to the information, the surface area of the solid is 758m² and the volume is 594m³
How to find the surface area of the solid?To find the surface area of the solid we have to perform the following procedure:
12m * 11m = 132m²
132m² * 2 = 264m²
16m * 9m = 144m²
144m² - 18m² = 126m²
126m² * 2 = 252m²
16m * 11m = 176m²
176m² - 66m² = 110m²
3m * 11m = 33m²
33m² * 2 = 66m²
6m * 11m = 66m²
264m² + 66m² + 66m² + 110m² +252m² = 758m²
To find the volume we have to perform the following procedure:
8m * 11m * 9m = 792m³
792m³ - 198m³ = 594m³
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Melissa collected the data in the table.
When x = 4, what is the residual?
–3
–1
1
3
From the data in the table, we can conclude that when x = 4, then the residual will equal -1.
How to determine the residualTo determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.
So, Residual = Gven value - Predicted value.
When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.
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Answer:
The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.
Step-by-step explanation:
In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.
If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.
differentiate with respect to x the implicit function sin(y)+x^2y^3-cos(x)=2y
Answer:
To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.
First, we will take the derivative of both sides of the equation with respect to x:
d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]
Next, we will differentiate each term on the left side of the equation:
cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx
We can simplify this equation by moving all the terms involving dy/dx to the left side:
cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]
Now we can solve for dy/dx by isolating it on one side of the equation:
dy/dx [2 - sin(y)] = cos(x) - 2xy^2
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Oriana's Pizza Kitchen has an oven that is shaped like a
rectangular prism. Inside, the oven is 5 feet wide and 4
feet deep so it can bake
their super large pizzas. It is also 3 feet high. What is
the oven's volume?
12 ft³
15 ft3
60 ft³
20 ft³
Answer:
Step-by-step explanation:
I believe I missed the lesson on how to solve for x and y from this photo. Any help would be appreciated!
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
Explain about the Pythagorean theorem:The Pythagorean Theorem, a well-known geometric principle that states that the square just on hypotenuse (the side across from the right angle) of a right triangle equals the sum of the squares on its legs, is also known as the
a² + b² = c².
For the larger triangle, applying Pythagorean theorem:
4² + (4√3)² = x²
x² = 16 + 16*3
x² = 16 + 48
x² = 64
x = 8
Then, x - 6 = 8 - 6 = 2
Now applying Pythagorean theorem for smaller triangle:
y² + (x - 6)² = 4²
y² = 4² - 2²
y² = 16 - 4
y² = 12
y² = √12
y = 2√3
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
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5. Jay cuts identical squares from the corners of a
rectangular sheet of paper as shown in the adjoining
figure. Find the area of remaining portion.
The area of the remaining portion of the sheet is -4x² + 12x + 6.
How to find the area of a figure?Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.
Therefore, the area of the remaining portion can be found as follows:
area of the rectangle = 3(4x + 2)
area of the rectangle = 12x + 6
Therefore,
area of each square cut out = x²
area of the 4 square cut out = 4x²
Therefore,
area of the remaining portion = 12x + 6 - 4x²
area of the remaining portion = -4x² + 12x + 6
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someone help me plss
The fraction of the panel, that is left after cutting out the hole is [tex]\frac{11}{12}[/tex]
What are the areas of some common plane figuresThe area of a rectangle equals the product of its 2 sides. The area of a triangle is equal to half of the product of the base and height.. If we choose one of the sides as the base, then for area calculation, for height we have to use the height of the opposite vertex from this base. To find it, we have to drop a perpendicular from the opposite vertex onto the base. The area of a parallelogram is the product of the length of the base and the perpendicular distance between the two parallel sides of the parallelogram. Area of a trapezium = half of the product of the distance between the parallel sides and the sum of the length of the parallel sides. Area of a circle is [tex]\pi r^2[/tex], in which r is the radius of the given circle. Sometimes the plane figure maynot be a standard shape. In that case we have to divide the figure into suitably many parts such that, each part is a standard figure whose area we can calculate. Also sometimes we can represent an area as the difference of the area of two standard figures. In that case to find the area we have to take the difference of the areas of the two standard figures.
In our question. Initial area of the panel is (3)(2) = 6 square ft.
Area of the cutout = (1)([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{2}[/tex] square ft.
Using the formula, fraction left = [tex]\frac{6 - \frac{1}{2}}{6} = 1 - \frac{1}{12} = \frac{11}{12}[/tex]
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Required fraction left is 11/12 square feet.
What is area of rectangle?
A rectangle is a geometric shape that has four sides and four right angles. It is a type of quadrilateral and is characterized by its two pairs of parallel sides. The opposite sides of a rectangle are congruent, which means they have the same length, and the adjacent sides are perpendicular to each other.
The area of a rectangle is the total amount of space inside the rectangle and is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is Area = length x width
For example, if a rectangle has a length of 6 units and a width of 4 units, the area can be calculated as:
Area = 6 units x 4 units = 24 square units
The area of the panel is 3 feet x 2 feet = 6 square feet
The area of the hole is 1 foot x 1/2 foot = 1/2 square feet
Therefore, the area left is 6 square feet - 1/2 square feet = 11/2 square feet
The fraction left is (11/2 square feet) / (6 square feet) = 11/12
Therefore, the required correct option is C.
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if a square has length of its side is 8cm then find length of its diagonal
Answer:
8√2 cm
Step-by-step explanation:
A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Find the probability of getting exactly one tail.
The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
What is probability?Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
In the given question,
There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH)
We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:
P(HHT) = (1/2) * (1/2) * (1/2) = 1/8
P(HTH) = (1/2) * (1/2) * (1/2) = 1/8
P(THH) = (1/2) * (1/2) * (1/2) = 1/8
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8
Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
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A bus traveled on a level road for 2 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 3 hours. Find the average speed on the level road if the entire trip was 225 miles.
By answering the presented question, we may conclude that As a result, the average speed on the flat road is 57 miles per hour.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
Let's apply the formula:
distance = time speed
The bus went for 2 hours on the level road, hence the distance travelled is:
1 distance = x 2
The bus went for 3 hours on the twisting route, hence the distance travelled is:
3 distance2 = (x - 20)
Because the bus's total distance travelled is 225 miles, we may write:
distance1 plus distance2 equals 225
Substituting distance1 and distance2 expressions yields:
x × 2 + (x - 20) × 3 = 225
When we simplify this equation, we get:
2x + 3x - 60 = 225
5x = 285\sx = 57
As a result, the average speed on the flat road is 57 miles per hour.
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a red car travels 20km in one hour .
a blue car travels 130km in the sAME TIME
which car thas greater average speed???
Answer:
The answer is the Blue car
Step-by-step explanation:
let Red car be x
let blue car be y
x=120km---->1hr
y=130km----->1hr
Average speed =distance(km)/time(hr)=km/hr
let A be average speed
A(x)=120/1=120km/hr
A(y)=130/1=130km/hr
therefore,
the blue car has the greatest average speed
4. Greta's neighborhood is having a picnic to celebrate the end of the school year. She has been
asked to prepare potato salad. Greta actually has to work at 2pm when the picnic is scheduled, so
she asks Lynn, the neighbor coordinating food, if she can drop off the potato salad at the park
when she goes into work at 10am. Lynn is not sure this will work. Describe why Lynn is hesitant
and what might happen if Greta's potato salad sits out in the sun until the picnic begins at 2pm.
Then offer at least one suggestion to solve Greta and Lynn's problem.
Lynn is hesitant to allow Greta to drop off the potato salad at 10am .
How to solve Greta and Lynn's problem?Greta could make the potato salad the night before and keep it in the refrigerator to solve the problem she and Lynn were having. She could then transport the potato salad at a safe temperature in a cooler filled with ice packs on the day of the picnic.
She could ask Lynn to store the potato salad in a cooler or refrigerator until the picnic starts when she gets to the park. Along these lines, the potato salad will be protected to eat and won't represent a gamble of food contamination.
The mayonnaise in Greta's potato salad will spoil, leading to the growth of bacteria that could result in foodborne illness, if it is left outside in the sun until the picnic begins at 2 p.m. The potato salad may cause nausea, vomiting, diarrhea, and stomach cramps in those who consume it.
Because food safety guidelines state that perishable foods, like potato salad, should not be kept at room temperature for more than two hours, Lynn is hesitant to let Greta drop off the potato salad at 10 a.m.
If the potato salad is left out in the sun from 10 a.m. to 2 p.m., bacteria can grow on it, and eating it could make you sick.
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C. The table below shows the ages in years of 42 children at a birthday party. AGE(YEARS) NO OF CHIDREN 7 2x 8 3x 9 4x-1 10 X 11 X-2 (i). Find the value of x. (ii). Calculate, correct to the nearest whole number the mean age. (iii). Find the probability of selecting at random a child whose age is less than 9 years. 12 x-3 CURT
(1) The value of X is equal to 4 (2) The mean age is 3. (3) The probability of randomly selecting a child under the age of 9 is approximately 0.83.
How to calculate the average?
The formula for calculating the average of given numbers is equal to the sum of all values divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.
(i). Given that there are a total of 42 children on the birthday, finding the value of x:
2x + 3x (4x-1) + x + (x-2) + (x-3) = 42
11x - 6 = 42
11x = 48
x = 4
Therefore, the value of x is equal to 4.
(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:
Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42
= (14 + 24 + 27 + 40 + 22 +12) / 42
= 139/42
= 3.31
Rounded to the nearest whole number, the average age is 3.
(iii). The probability of randomly selecting a child under 9 is obtained by adding the number of children aged 7, 8 or 9 (because we want children under 9) and dividing by the total number of children:
Number of children under 9 years = 2x + 3x + (4x-1)
Number of children under 9 years = 9x - 1
Number of children under 9 = 9(4)–1
Number of children under 9 years = 35
Probability of choosing a child under 9 = number of children under 9 / total number of children
Probability of choosing a child under 9 = 35/42
The probability of choosing a child under 9 years old is ≈ 0.83
Thus, the probability of randomly selecting a child under the age of 9 is approximately 0.83.
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Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Write the complex number in rectangular form. If necessary, round to the nearest tenth.
24( cos 275° + i sin 275°)
Answer:
Step-by-step explanation:
We first have to find cos 275 and sin 275 and then put them into the formula:
cos 275 = .0872
sin 275 = -.9962
Therefore,
24(.0872 - .9962i) distributes to
2.1 - 23.9i
Leah said on her birthday: “Today I am exactly three times as old as I was four years ago.“ And that was true. In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“?
in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
How to determine In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“Let's start by setting up an equation based on the given information.
Let Leah's current age be represented by "x". Then, we know that:
x = 3(x-4)
Expanding the right side of the equation:
x = 3x - 12
Bringing the "x" term to the left side and simplifying:
2x = 12
x = 6
So Leah is currently 6 years old. Now we want to find out how many years it will take for her to be exactly twice as old as she was four years ago. Let's represent this number of years as "y". Then we can set up another equation:
6 + y = 2(6 - 4 + y)
Simplifying:
6 + y = 2(2 + y)
6 + y = 4 + 2y
2 = y
So in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
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What does a residual value of –0.8 mean in reference to the line of best fit?
The given point is 0.8 units above the line of best fit.
The given point is 0.8 units below the line of best fit.
The line of best fit is not appropriate to the data.
The line of best fit has a slope of 0.8.
Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723
Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.
The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:
y = –38x + 922.
Therefore, the answer is y = –38x + 922.
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Therefore , the solution of the given problem of angles comes out to be the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6.
An angle's meaning is what?The point of intersection of the paths joining a skew ends yields the skew's greatest and smallest walls. A crossroads may be where two paths converge. Angle is another outcome of two things interacting. They approach dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various configurations between their endpoints.
Here,
Regarding the illustrated diagram, the appropriate statements are:
=> m∠3 + m∠4 + m∠5 = 180°
This is accurate since every triangle's internal angles add up to 180°.
=> m∠5 + m∠6 = 180°
This is true because a triangle's internal angle and outside angle are always equal to 180 degrees.
=> m∠2 + m∠3 = m∠6
This is accurate because, based on the information provided,
the exterior angle at angle 2 (m2) of the triangle is equal to the corresponding interior angle at angle 6 (m6) of the triangle.
Therefore, the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. are always true in relation to the given figure.
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Use L’hospital if it applies
Lim x—> infinity
(lnx)^3/x^2
The calculated value of the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
Calculating the limits of the derivativesTo apply L'Hopital's rule, we need to take the derivative of the numerator and denominator separately with respect to x.
We can apply this rule repeatedly until we get a determinate form.
lim x → ∞ [(ln x)^3 / x^2]
Taking the derivative of the numerator:
= 3(ln x)^2 (1/x)
Taking the derivative of the denominator:
= 2x
Applying L'Hopital's rule again by taking the derivative of the numerator and denominator:
= lim x → ∞ [6(ln x) / x]
Taking the derivative of the numerator:
= 6/x
Taking the derivative of the denominator:
= 1
Applying L'Hopital's rule one last time:
= lim x → ∞ 6 / x^2
= 0
Therefore, the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
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Which is the best estimate of the difference between 67/8 and 1/82
Answer:
8.36
Step-by-step explanation:
67 - 1
8. 82
= 2747 - 4
328
=2743
328
= 8.36
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.
What is Compound interest?
Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.
Now,
Using the given formula:
N = (-log(1 - i * A / P)) / (log(1 + i))
where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250
N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))
N = (-log(1 - 175)) / (log(1.0025))
N = (-log(0.9883)) / (0.0025)
N = 376.48
Rounding up to the nearest whole number, it will take 377 months to pay off the loan.
Therefore, it will take approximately 31 years and 5 months to pay off the loan.
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Try It
For a project, the teacher asked a group of seven students to each count the number of pedestrians that cross the street where they live on a certain day. The data collected had a range of 33 Sox of the seven data values
are shown below Find the missing data value
29,
15
22,,
11,
31,
15
The missing data value in the project is 25.5.
What is range?Range is a statistical measure that represents the difference between the highest and lowest values in a dataset. It is calculated by subtracting the smallest value in the dataset from the largest value.
According to question:To find the missing data value, we need to use the given range and the known data values.
The range is the difference between the highest and lowest values in the data set. So, if we sort the given data values in increasing order, we have:
11, 15, 15, 22, 29, 31
The range is 33, which means that:
highest value - lowest value = 33
31 - 11 = 33
So, the missing data value must be between 22 and 29 (since those are the values that are next to each other in the sorted list). To find the exact value, we can take the average of 22 and 29:
(22 + 29) / 2 = 25.5
Therefore, the missing data value is 25.5.
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