The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.
To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.
First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.
Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.
Using this method, we need to distribute 14 stars among 5 bars, which can be done in
(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.
Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.
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which of these shapes is a right isosceles triangle?
A right isosceles triangle is a triangle with a right angle (90 degrees) and two sides that are equal in length. This means that the triangle is also a special case of an isosceles triangle where the two equal sides are adjacent to the right angle.
To identify a right isosceles triangle among a group of shapes, you should look for the shape that has a right angle and two sides of equal length. One way to check for the right angle is to look for a corner that forms a square angle (i.e., 90 degrees), and one way to check for the equal sides is to compare the length of each side.
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The following question may be like this:
What is a right isosceles triangle?
HELP AAHHHHHHH FFASDF
Answer:
Step-by-step explanation:
Give the starting value a, the growth factor b, and the growth rate r if q = abt = a(1 r)t. write r as a percent. q = 79 (1.002) superscript t a. a. a = 79 b = 1.002 r = 0.2% b. a = 79.158 b = 1.002 r = 0.002% c. a = 79 b = 0.002 r = 1.002% d. a = 79.158 b = 0.002 r = 0.2%
r as a percent is a) a = 79, b = 1.002, and r = 0.2%.
The formula given, q = abt = a(1+r)t, represents exponential growth, where a is the starting value, b is the growth factor, r is the growth rate, t is the time period, and q is the final value after t periods.
Given q = 79(1.002)^t, we can see that:
a = 79 (the starting value)
b = 1.002 (the growth factor)
r = 0.2% or 0.002 (the growth rate, expressed as a decimal)
So, the correct answer is a) a = 79, b = 1.002, and r = 0.2%.
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State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
SAS
Step-by-step explanation:
There are two pairs of congruent sides, and the pair of angles between the congruent sides is also congruent.
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y
-intercept to the nearest integer.
For the given table -
The equation for line of best fit is Y = -1.000 · X + 11.25.
The correlation coefficient is -0.443533.
x and y have negative and strong correlation.
What is correlation coefficient?
A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.
The table of data is given.
The formula for equation of the line of best fit is -
Y = b·X + a
On adding the values in a graphing calculator the equation is -
Y = -1.000 · X + 11.25
Here, the slope is -1 and y-intercept is 11.25.
The formula for correlation coefficient is -
r = [n(∑xy) - (∑x)(∑y)] / [n∑x² - (∑x²)][n∑y² - (∑y²)]
n = Number of values or elements
∑x = Sum of 1st values list
∑y = Sum of 2nd values list
∑xy = Sum of the product of 1st and 2nd values
∑x² = Sum of squares of 1st values
∑y² = Sum of squares of 2nd values
For the given table the values are -
n = 8, ∑x = 68, ∑y = 22, ∑xy = 145, ∑x² = 620, ∑y² = 274
Plug in all the values in the equation -
r = [8(145) - (68)(22)] / [8(620) - (620)][8(274) - (274)]
r = -0.443533
When the values of two variables grow while one variable's values fall. The correlation coefficient would be negative in that situation.
The weak and adverse association is indicated by the coefficient's negative value. And if "r" keeps moving in the direction of -1, the relationship is moving in the negative direction.
Therefore, the equation is Y = -1.000 · X + 11.25 and r value is -0.443533.
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The concession stand at a football game had 3,903 soft pretzels and 2,804 hard pretzels before the game began. When they count the food after the game, there is a total of 1,683 pretzels left. How many pretzels were sold?
Answer:
5024
Step-by-step explanation:
3903+2804= 6707
6707-1683=5024
which of the following is a difference between panel and pooled cross-sectional data? group of answer choices a panel data set consists of data on different cross-sectional units over a given period of time while a pooled data set consists of data on the same cross-sectional units over a given period of time. a panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time a panel data consists of data on a single variable measured at a given point in time while a pooled data set consists of data on the same cross-sectional units over a given period of time. a panel data set consists of data on a single variable measured at a given point in time while a pooled data set consists of data on more than one variable at a given point in time.
From the following, a panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time is the difference between panel and pooled cross-sectional data.
Panel data refers to samples of the same cross-sectional units observed at multiple points in time.
For example we will follow the same set of households X, Y and Z, for each time period we collect data i.e. in 1990 and we will also interview the same households in 1995.
Pooled data occur when we have a “time series of cross sections,” but the observations in each cross section do not necessarily refer to the same unit.
For example we will take household income data on households X, Y and Z, in 1990. And then we will take the same income data on households G, F and A in 1995. Although we are interested in the same data, we are taking different samples (using different households) in different time periods.
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b) A plank of wood 3.5 m long is cut into 5 pieces of equal length. How long, in m, is each piece?
70 cm or 0.7 m
Step-by-step explanation:3.5 x 100 = 350
350 / 5 = 70
question 12
help me asap
Answer:
ED = 4 cm
Step-by-step explanation:
given 2 secants from an external point to the circle, then the product of one secant's external part and the entire secant is equal to the product of the other secant's external part and that entire secant, that is
CD × CE = CB × CA
8(8 + x) = 6(6 + 10) = 6 × 16 = 96 ( divide both sides by 8 )
8 + x = 12 ( subtract 8 from both sides )
x = ED = 4 cm
This composite figure is made up of three simpler shapes. What is the area of
the figure?
5 cm
10 cm
3 cm
4 cm
6 cm
Answer:
The figure is made up of a rectangle and two triangles. The dimensions of the rectangle are 10 cm by 5 cm, so the area of the rectangle is 10 * 5 = 50 cm^2.
Each of the two triangles has a base of 4 cm and a height of 3 cm, so the area of each triangle is (1/2) * 4 * 3 = 6 cm^2. The total area of the two triangles is 2 * 6 = 12 cm^2.
The total area of the figure is the sum of the areas of the rectangle and the triangles: 50 + 12 = 62 cm^2.
Step-by-step explanation:
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 430 gram setting. it is believed that the machine is underfilling the bags. a 21 bag sample had a mean of 421 grams with a standard deviation of 15 . assume the population is normally distributed. a level of significance of 0.1 will be used. find the p-value of the test statistic. you may write the p-value as a range using interval notation, or as a decimal value rounded to four decimal places.
A manufacturer working at the 430 gram setting, and a 21 bag sample had a mean of 421 grams with a standard deviation of 15. The p-value of test statistic is 0.0074.
To test whether the bag filling machine works correctly at the 430 gram setting, we can conduct a one-sample t-test. The null hypothesis is that the true mean weight of the bags filled by the machine is equal to 430 grams, and the alternative hypothesis is that the true mean weight is less than 430 grams.
The test statistic is calculated as:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values given in the problem, we get:
t = (421 - 430) / (15 / sqrt(21)) = -2.77
The degrees of freedom for the t-distribution are n - 1 = 20.
Using a t-table or calculator, we can find the p-value associated with a t-score of -2.77 and 20 degrees of freedom. The p-value turns out to be 0.0074 (rounded to four decimal places).
Since the p-value is less than the level of significance of 0.1, we can reject the null hypothesis and conclude that the bag filling machine is underfilling the bags at the 430 gram setting.
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Find the radius of the circle circumscribed around an equilateral trapezoid, if the bases of the trapezoid are 9 and 15, and the height is 5.
Question content area top
Part 1
A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique, 887 births consisted of 451 baby girls and 436 baby boys. In analyzing these results, assume that boys and girls are equally likely.
a. Find the probability of getting exactly 451 girls in 887 births.
b. Find the probability of getting 451 or more girls in 887 births. If boys and girls are equally likely, is 451 girls in 887 births unusually high?
c. Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)?
d. Based on the results, does it appear that the gender-selection technique is effective?
a. The probability of getting exactly 451 girls in 887 births is 0.0578.
b. The probability of getting 451 or more girls in 887 births is 0.0478. To determine if 451 girls in 887 births is unusually high, we compare this probability to a significance level (alpha) of choice and then either reject or accept the null hypothesis.
c. The probability from part (b) is more relevant for trying to determine whether the technique is effective because it considers a range of outcomes that are consistent with the hypothesis that boys and girls are equally likely.
d. Based on the results, we can reject the hypothesis that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.
What is probability?Probability is the likelihood of an event occurring or not occurring.
Mathematically;
Probability = expected outcomes/possible outcomea. To find the probability of getting exactly 451 girls in 887 births, we can use the binomial distribution with n = 887 and p = 0.5 (since boys and girls are equally likely).
The probability of getting k girls is given by the formula:
P(k girls) = (n choose k) * p^k * (1-p)^(n-k)
Plugging in the values, we get:
P(451 girls) = (887 choose 451) * 0.5^451 * 0.5^436
P(451 girls) = 0.0578 (rounded to four decimal places)
b. To find the probability of getting 451 or more girls in 887 births, we can add up the probabilities of getting 451, 452, 453, ..., up to 887 girls. The cumulative binomial distribution is used to determine the probability of getting k or fewer girls:
P(k or fewer girls) = sum((n choose i) * p^i * (1-p)^(n-i), i = 0 to k)
Since we want the probability of getting 451 or more girls, we can subtract the probability of getting 450 or fewer girls from 1:
P(451 or more girls) = 1 - P(450 or fewer girls)
= 1 - sum((887 choose i) * 0.5^i * 0.5^(887-i), i = 0 to 450)
= 0.0478
d. To determine if the gender-selection technique is effective, we need to compare the probability of getting 451 or more girls (from part (b)) to a significance level (alpha) of our choice.
Using an alpha set to 0.05, the probability of getting 451 or more girls in 887 births is 0.0478, it is less than 0.05. Therefore, we reject the hypothesis that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.
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Consider the information given in Example 3. Describe and correct the error in predicting the number (n) of students in the school who watch zero movies each week.
Answer:its hard to say
HELPP ITS THE FINAL PART OF THE TEST!!
Answer:
Graph C.
The question asks for the graph that consists of:
Non-negative values
Values that are, at most, 80
This means that any graphs where a value goes below 0 or above 80 do not work. C is the only graph that does not go below 0 or above 80.
what is the probability that the sample mean annual insurance cost is greater than $620? show your work.
The probability of the sample mean annual insurance cost being greater than $620 is very low, that is 0.00317% which indicating that it is unlikely to happen by chance.
Probability is a branch of mathematics that deals with the likelihood of an event happening. It is used in various fields, such as insurance, finance, and science.
To calculate the probability, we need to use the central limit theorem, which states that the distribution of sample means of a population approaches a normal distribution as the sample size increases. We also need to know the mean and standard deviation of the population.
Assuming that the population is normally distributed, we can use the following formula to calculate the probability:
z = (x - μ) / (σ / √(n))
where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we don't know the population mean and standard deviation, but we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 100 insurance costs with a mean of $600 and a standard deviation of $50.
Now, we can calculate the z-score:
z = (620 - 600) / (50 / √(100)) = 4
The z-score of 4 indicates that the sample mean of $620 is 4 standard deviations away from the mean of $600. We can use a standard normal distribution table or a calculator to find the probability of getting a z-score of 4 or higher. The probability is very small, approximately 0.0000317 or 0.00317%.
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A leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. At that
rate, how many gallons of water will the faucet leak in
48 hours?
Show your
work.
Answer:
Step-by-step explanation:
We can start by finding the amount of water the leaky faucet loses in one hour:
5 gallons / 20 hours = 0.25 gallons per hour
This means that the leaky faucet loses 0.25 gallons of water every hour.
To find how many gallons of water the faucet will leak in 48 hours, we can multiply the rate of leakage per hour by the number of hours:
0.25 gallons/hour x 48 hours = 12 gallons
Therefore, the leaky faucet will lose 12 gallons of water in 48 hours.
A rectangular prism measures 7 1/2 cm by 12 cm by 15 1/2 cm. ****If you are stuck, think about how many cubes with 1/2 cm edge lengths fit into 1 cubic centimeter*** Calculate the number of cubes with edge length 1/2 cm that fit in this prism. Cubes What is the volume of the prism in centimeters cubed? centimeters cubed
Number of cubes with edge length 1/2cm that fit in the prism is 11160 and the volume of the prism is 1395 cubic centimeter
Dimensions of the rectangular prism = [tex]7\frac{1}{2}[/tex] cm × 12 cm × [tex]15\frac{1}{2}[/tex] cm
Convert the mixed fraction to the simple fraction
The dimensions of the rectangular prism = 15/2 cm × 12 cm × 31/2 cm
The volume of the rectangular prism = w × l × h
Where
w is the width
l is the length
h is the height
The volume of the rectangular prim = 15/2 × 12 × 31/2
= 1395 cubic centimeter
The side off the cube = 1/2 cm
Volume of the cube = a^3
= (1/2)^3
= 0.125 cubic centimeter
Number of cubes will fit in rectangular prism = Volume of rectangular prism / Volume of the cube
= 1395 / 0.125
Divide the terms
= 11160 cubes
Therefore, 11160 cubes will fit in the rectangular prism and the volume of the prism is 1395 cubic centimeter
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Which ordered pair is the solution to the equation 2x + 3y = x + 5y
a.) (1, 3)
b.) (4,2)
Answer:
B
Step-by-step explanation:
We start by trying out option A
2(1) + 3(3) = 9
1 + 5(3) = 15
9 and 15 are not equal to one another.
This means it has to be the other option, B.
The table shows how many hours Sara spent at several activities one Saturday.
Activity Hours
Soccer practice 222
Birthday party 333
Science project 111
What is the ratio of hours spent at soccer practice to hours spent at a birthday party?
The ratio of hours spent at soccer practice to hours spent at a birthday party are 2 for every 3.
What is a ratio?
A ratio is produced by comparing or condensing two related pieces of data. Looking at the reciprocity of the relationship allows us to calculate the number of times one quantity is equal to another. To put it simply, a ratio is a number that can be used to represent one thing as a proportion of another.
We are given that for soccer practice, Sara spends 2 hours and for birthday party, she spends 3 hours.
So, the ratio of hours spent at soccer practice to hours spent at a birthday party is 2 for every 3.
Hence, the ratio is 2 for every 3.
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Question: The table shows how many hours Sara spent at several activities one Saturday.
Activity "Hours
Soccer practice 2
Birthday party 3
Science project 1
What is the ratio of hours spent at soccer practice to hours spent at a birthday party?
Choose 1 answer:
1 for every 2
2 for every 1
2 for every 3
3 for every 2
6. Ming uses 3/ 4 cup of peanuts and 1/ 4 cup of raisins to make a snack. Which statement correctly compares the fractions?
*
10 points
A. 3/4 = 1/4
B. 1/4 > 3/4
C 3/4 < 1/4
3/4 > 1/4
Answer:
3/4 > 1/4
Step-by-step explanation:
3/4 is 75%, and 1/4 is 25 percent. 3/4 is greater than 1/4!
Use proportions to determine 23% of what number is 81.3. Round to the nearest hundredth.
The total mass of a box and some oranges was 25 kg. The total mass of
the same box and some apples was 11 kg. The mass of the oranges was
3 times the mass of the apples.
Find the mass of the oranges.
In a case whereby the total mass of a box and some oranges was 25 kg. The total mass of the same box and some apples was 11 kg. The mass of the oranges was 3 times the mass of the apples, the mass of the oranges is 21kg.
How can the mass of the oranges be determined?The concept that will be used here is simplificatiopn.
We can set up as:
let a represent the box
let b represent the orange
lect c represent the apple
Then a + b = 25
a+ c = 11 ....................................................(2)
b = 3c.......................................(3)
substract equation 2 from 1
b-c = 11 ....................................(4)
substitute eqn 3 into 4
b-c = 14
3c - c =14
2c= 14
c= 7
from eqn 3
b = 3c
b = 3*7 =21
Then mass of orange = 21 kg
from eqn 2
a+ c = 11
a= 11-7= 4
mass of empty box = 4kg
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A cylindrical measuring jug has a total volume of 500 ml and its radius is 3 cm. There are markings on the jug to show every 100 ml. What is the distance, in cm, between each of these markings?
Answer:
The volume of a cylinder can be calculated using the formula:
V = πr^2h
Where r is the radius and h is the height. In this case, the volume is 500 ml, or 0.5 liters. To convert liters to cm, we can use the conversion factor 1 liter = 10 cm^3. Therefore, the height of the jug can be calculated as follows:
0.5 liters = 0.5 x 10 cm^3 = 500 cm^3
V = πr^2h
500 = π x (3 cm)^2 x h
h = 500 / (π x (3 cm)^2)
Approximating π as 3.14, we get:
h = 500 / (3.14 x (3 cm)^2)
h = 500 / (3.14 x 9 cm^2)
h = 500 / 28.26 cm^2
h = 17.67 cm
So the height of the cylindrical measuring jug is approximately 17.67 cm. Therefore, the distance between each marking, which represents 100 ml of volume, is 17.67 cm / 5 = 3.534 cm.
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
To determine the distance between each of the markings, we need to determine the height of the jug for each 100 ml increment.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. We know the volume of the jug is 500 ml, or 0.5 liters, and the radius is 3 cm, so we can solve for the height:
0.5 liters = π * (3 cm)^2 * h
h = 0.5 liters / π * (3 cm)^2
h = 0.5 liters / 9π cm^2
Now that we have the height of the jug per 100 ml, we can divide it by 5 to determine the height between each marking:
Marking height = h / 5
= 0.5 liters / 9π cm^2 / 5
= 0.1 liters / 9π cm^2
So the distance between each of the markings is the height of the jug for each 100 ml increment divided by 5.
Solve for x. P S (6x-21)° T Q R
Answer:
x = 11
Step-by-step explanation:
You want to know the measure of x in a square marked with one portion of the bisected corner angle as being (6x -21)°.
AngleWe presume quadrilateral PQRS is a square, so each of the corner angles is 90°, and each of the diagonals bisects the corner angles. That mean ...
(6x -21)° = 90°/2
6x = 66 . . . . . . . . . . divide by °, add 21
x = 11 . . . . . . . . . . . divide by 6
A theater sells adult and children tickets. Adult tickets sell for $10 and child sells for $5. Yesterday they sold off 50 tickets and made $40. How many adult and child tickets did the theater sell?
The theater sold 30 adult tickets and 20 children tickets.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Let, The number of adult tickets be 'x' and the number of children tickets be 'y'.
Therefore, 10x + 5y = 400...(i) and x + y = 50...(ii)×10 ⇒ 10x + 10y = 500...(iii)
Now, Subtracting equation (i) from equation (iii) we have,
5y = 100.
y = 20, and hence x = 30.
So, They have sold 30 adult tickets and 20 children tickets.
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Find the sum of 2√5 and 3√7
Answer:
the sum of 2rude 5 is 4.47-(answer)and the sum of 3 rude 7 is 7.79-(answer).
Hi there, here's your answer:
Given the question [tex]2\sqrt{5} + 3\sqrt{7}[/tex]
Since these two roots have no common factors, we can either leave the expression as it is, or simplify using the values of the roots.
In which case, [tex]\sqrt{5} = 2.236[/tex] and [tex]\sqrt{7} = 2.645[/tex]
On simplifying, we get
[tex]2\sqrt{5}[/tex] = 2 × 2.236 = 4.472
And
[tex]3\sqrt{7}[/tex] = 3 × 2.645 = 7.935
Thus, the sum will be 4.472 + 7.935 = 12.407
Hope it helps! Please mark as Brainliest!
*FIND THE SLOPE OF THE LINE THROUGH EACH PAIR OF POINTS*
d. (-4, 3) and (-6, -8)
e. (-7, -1) and (-7, 2)
f. (9, 4) and (-6, 4)
slope = y2 - y1
______
x2 - x1
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-8}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{(-4)}}} \implies \cfrac{-11}{-6 +4} \implies \cfrac{ -11 }{ -2 } \implies \cfrac{11 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-7}-\underset{x_1}{(-7)}}} \implies \cfrac{2 +1}{-7 +7} \implies \cfrac{ 3 }{ 0 } \implies \stackrel{\textit{vertical line}}{{\Large \begin{array}{llll} unde fined \end{array}}} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{9}}} \implies \cfrac{ 0 }{ -15 } \implies \stackrel{\textit{horizontal line}}{\text{\LARGE 0}}[/tex]
keep in mind that whenever you notice the x-coordinates are the same, it's a vertical line, and whenever the y-coordinates are the same, is a horizontal line.
express 2x^2 + 8x in the form a(x + b)^2 + c
The vertex form equivalent to the given expression; 2x² + 8x as required to be determined in the task content is; 2 (x + 2)² + 8.
What is the vertex form equivalent of the expression?The vertex form equivalent of the given expression can be determined as follows;
2x² + 8x
2 (x² + 4x)
2 ( (x + 2)² + 4)
= 2 (x + 2)² + 8.
Ultimately, the vertex form equivalent of the given expression as required is; 2 (x + 2)² + 8.
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40° rcm Find the value of z. zem This sector of a circle has radius r and perimeter 20 cm. find the value of z
The value of length of z is 5.06 cm.
What is the value of length z?
The value of length of z is calculated by determining the radius of the sector as shown below;
The formula for the perimeter of a sector is given as;
P = 2r + (θ/360) × 2πr
where;
r is the radius of the sector20 cm = 2r + (40/360) x 2πr
20 = 2r + 0.7r
20 = 2.7r
r = 20/2.7
r = 7.4 cm
A perpendicular bisector of 40⁰ will cut line z into two equal parts, the length of half of z is calculated as;
sin (20) = (z/2) / r
r x sin (20) = (z/2)
2r x sin (20) = z
2 x 7.4 cm x sin(20) = z
5.06 cm = z
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