Given:
[tex]f(x)[/tex] is continuous, [tex]f(3)=1,f(1)=6,f(6)=-2,f(-2)=3[/tex].
To find:
The value of [tex]\lim_{x\to 6^+}f(x)[/tex] and [tex]\lim_{x\to -2^-}f(x)[/tex].
Solution:
If a function f(x) is continuous at [tex]x=c[/tex], then
[tex]\lim_{x\to c^-}f(x)=f(c)=\lim_{x\to c^+}f(x)[/tex]
It is given that the function [tex]f(x)[/tex] is continuous. It means it is continuous for each value and the left-hand and right-hand limits are equal to the value of the function.
The function is continuous for 6. So,
[tex]\lim_{x\to 6^-}f(x)=f(6)=\lim_{x\to 6^+}f(x)[/tex]
[tex]\lim_{x\to 6^+}f(x)=f(6)[/tex]
[tex]\lim_{x\to 6^+}f(x)=-2[/tex]
The function is continuous for -2. So,
[tex]\lim_{x\to -2^-}f(x)=f(-2)=\lim_{x\to -2^+}f(x)[/tex]
[tex]\lim_{x\to -2^-}f(x)=f(-2)[/tex]
[tex]\lim_{x\to -2^-}f(x)=3[/tex]
Therefore, [tex]\lim_{x\to 6^+}f(x)=-2[/tex] and [tex]\lim_{x\to -2^-}f(x)=3[/tex].
A particular truck in a transportation fleet was
driven 109,970 miles last year. In comparison,
it was driven 40% less this year. How much
was the truck driven this year?
bro this is middle school work not college
How do I solve a whole number and a fraction?
Answer:
To solve a problem involving a whole number and a fraction, you can first convert the whole number to a fraction by writing it as a fraction with a denominator of 1. For example, if the whole number is 4, you can write it as the fraction 4/1.
Then, you can add or subtract the fractions as you would normally, making sure to find a common denominator if necessary. For example, suppose you want to add the whole number 4 and the fraction 3/5. You can first write 4 as the fraction 4/1, giving you:
4/1 + 3/5
To add these fractions, you need to find a common denominator. A common denominator for 1 and 5 is 5, so you can rewrite the fractions with denominators of 5:
4/1 = 20/5
3/5 = 3/5
Now you can add the fractions:
20/5 + 3/5 = 23/5
So the solution to the problem is 23/5.
If you need to multiply or divide the whole number and fraction, you can treat the whole number as a fraction with a denominator of 1 and then perform the multiplication or division as you would normally with fractions.
Step-by-step explanation:
The double number line shows that Bira has ridden 28m on a carousel, which is 80% of a full rotation on the carousel
The distances that represent the percentages are given as follows:
Distance of 28 m -> 80% of a rotation.Distance of 7 m -> 20% of a rotation.Distance of 35 m -> 100% of a rotation.What is a proportion?A proportion is a fraction of a total amount, used along with the unit measures and basic arithmetic operations to obtain the desired measures in the context of a problem.
28m is 80% of the distance, hence 100% of the distance is obtained applying the proportion as follows:
0.8x = 28
x = 28/0.8
x = 35.
Then the distance that represents 20% of a rotation is calculated as follows:
0.2 x 35 = 7 meters.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any cases not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.3, the probability that the demand will be 200 cases is 0.4, and the probability that daily demand will be 300 cases is 0.3.
Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case.
Probabilty 0.3 .04 .03 Demand/#of cases 100 200 300 EMV
100 $1000 $900 $800 $900
200 $800 $2000 $1900 $1610
300 $600 $1800 $3000 $1800
Required:
You have reason to believe the probabilities many not be reliable due to changing conditions. If these probabilities are ignored, what decision would be made using: (a) the optimistic criterion? b) the pessimistic criterion?
Therefore, In Optimistic Criterion decision of cases : 300 and in Pessimistic Criterion decision of cases : 200
What does probability mean as a process?Probabilities can be written as percentages with a 0%–100% range or proportions with a 0–1 range. An event's probability is measured from 0 to 1, with 0 being the most unlikely scenario and 1 being the most likely. When an event's probability is 0.45 (45%), there are 45 percent (100) odds that it will happen.
Here,
a) Optimistic Criterion
Demand/#of No. of cases
cases
100 $1,000 $900 $800
200 $800 $2,000 $1,900
300 $600 $1,800 $3,000
Maximum of
Column $1,000 $2,000 $3,000
Maximum
Decision: 300 cases
b) Pessimistic Criterion
Demand/#of No. of cases
cases
100 $1,000 $900 $800
200 $800 $2,000 $1,900
300 $600 $1,800 $3,000
Minimum Of
Column $600 $900 $800
Maximin
Decision: 200 cases
Therefore in Optimistic Criterion decision of cases : 300 and in Pessimistic Criterion decision of cases : 200
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HALPPP, for pre calc
The interval containing the rational zero of f(x) = 3x³ - 5x² + 5x + 7 is given as follows:
-1 < x < 0.
How to obtain the zeros of the function?To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.
The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 3.Constant term of 7.The factors are given as follows:
Factors of 3: {1,3}.Factors of 7: {1,7}.Hence the possible zeros are given as follows:
±1/3, ±1, ±7/3, ±7.
The numeric values for the function are these points are of:
f(-7) = 3(-7)³ - 5(-7)² + 5(-7) + 7 = -1302. f(-7/3) = 3(-7/3)³ - 5(-7/3)² + 5(-7/3) + 7 = -70. f(-1/3) = 3(-1/3)³ - 5(-1/3)² + 5(-1/3) + 7 = 4.6.This means that there is a zero between -7/3 and -1/3, as the function changes from negative to positive, hence the interval is given as follows:
-1 < x < 0.
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PLEASE HELP ASAP
Three key features of a linear function are described as shown.
• The graph of the function has a y-intercept of (0, 3) .
• The function is increasing over its entire domain.
• The x-intercept of the function is (-4, 0).
Step-by-step explanation:
the slope-intercept form is
y = ax + b
a being the slope, b being the y-intercept (the y-value when x = 0), which we get from (0, 3) : 3.
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
we got 2 points, so, let's use them :
(-4, 0) and (0, 3)
x changes by +4 (from -4 to 0).
y charges by +3 (from 0 to +3).
so, the slope is +3/+4 = 3/4.
therefore, our equation is
y = f(x) = (3/4)x + 3
what is the number x such that G.C.F(x,54)=6 and L.C.M(x,54)=432.
By the Application of Prime factorization method the value of x is 48
what is Prime factorization method?
Writing all numbers as the product of primes is a procedure known as prime factorization. Consider the case of the number 20, for instance. We can divide that into two elements. Well, that's four times five, we can say. Furthermore, 5 is a prime number.
Solution:
HCF = ( X, 54 ) = 6
LCM = ( X, 54 ) = 432
a = x b = 54
using property
a * b = LCM * HCF
54a = 6 * 432
a = (6 * 432) / 54
a = 48
Hence the value of x is 48.
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Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 2.8 feet and height labeled 4.2 feet
SA = 2π(2.8)2 + 2.8π(4.2) square feet
SA = 2π(1.4)2 + 2.8π(4.2) square feet
SA = 2π(2.8)2 + 1.4π(4.2) square feet
SA = 2π(1.4)2 + 1.4π(4.2) square feet
You can quickly calculate the radius of a cylinder using an online calculator.
How to Find Radius of a Cylinder?The term "cylinder" refers to a three-dimensional solid shape made up of two circular bases joined by two parallel lines. We may calculate the radius of the cylinder using the formula for cylinder volume.A cylinder's capacity or the quantity of space it takes up are both determined by the cylinder's volume. V = πr²h, a formula, is used to compute it.Cylinder radii (r) √(V / π × h), where V denotes a cylinder's volume, h denotes its height, and (Pi) denotes a mathematical constant having a roughly 3.14 value.Solved Examples on the Radius of a Cylinder Calculator ExampleWhat is the radius of a cylinder with a capacity of 100 cubic units and a height of 5 units?
Solution:
The radius of a cylinder (r) is equal to (V / h).
= √(100 / π × 5)
= 2.523 units
As a result, a cylinder's radius is 2.523 units.
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Answer:
Step-by-step explanation:
its a
Please give me detailed information
The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.
What are the characteristics of a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Calculation:Given that ΔHPS≅ΔCNF.
We can see that angle H in triangle HPS is obtuse whereas angle N in triangle CNF is obtuse so comparing this we get,
6x - 29 = 115
6x = 144
x = 24
Comparing angle C and angle P we get
4z - 32 = 36
4z = 68
z = 17
Now the remaining angle in trinagle CNF is angle F which is 3y - 1 as we know that sum of angles in a triangle is 180 and the angle C and N are 36 and 115 we can say that F is 29
Now to find y we equalise it to 29
3y - 1 = 29
3y = 30
y = 10.
The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.
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Can don help me on this please?
Step-by-step explanation:
always remember that 100% is the whole.
so, 15% means 15/100 of the whole.
1/5 = 0.2 = 20/100 of the whole.
so, Target is taking 15/100 off the price.
Walmart is taking 20/100 off the price.
20/100 is bigger than 15/100, so Walmart deducts more off the price, and has therefore the lower and therefore better sale price.
Target sale price :
100/100 - 15/100 = 85/100 × 80 = $68
in short
80 × (1 - 0.15) = 80 × 0.85 = $68
Walmart sale price :
100/100 - 20/100 = 80/100 × 80 = $64
in short
80 × (1 - 0.20) = 80 × 0.80 = $64
Which rational expression is equivalent to this expression?
4/x-3. A) X-3/x+2•x+2/4. B) X-3/x+2/ 4/x+2. C) x+2/x-3• 4/x+2. D) x+2/x-3/ 4/x+2
The rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.
What is rational function?A rational function is one that can be written as a polynomial divided by a polynomial. The domain of a rational function is the set of all numbers except the zeros of the denominator.Given is the expression as follows -
f(x) = 4/(x - 3)
[A] -
{x - 3/x + 2} • {x + 2/4} = {x - 3/4}
[B] -
{x - 3}/{x + 2} / {4/x + 2} = {x - 3}/{x + 2} × {x + 2/4} = {x - 3/4}
[C] -
{x + 2/x - 3} • {4/x + 2} = {4/x - 3}
[D] -
{x + 2/x - 3} / {4/x + 2} = {(x + 2)²/ 4x - 3}
Therefore, the rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.
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Cans of paint weigh 6 pounds each. Let x represent the number of cans of paint and y represent the total weight of the cans. Write the equation to this situation as slope intercept form (y=mx+b). Then create a table of possible values
The equation for the relationship between the number of cans of paint, x, and the total weight of the cans, y, in slope-intercept form is y = 6x + 0. This equation can be derived from the formula for the slope-intercept form of a line, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the weight of each can of paint is 6 pounds and there is no y-intercept (the line passes through the origin), the slope of the line is 6 and the y-intercept is 0.
A table of possible values for the number of cans of paint, x, and the total weight of the cans, y, based on this equation is shown below:
x (number of cans of paint) y (total weight of cans)
1 6
2 12
3 18
4 24
5 30
As the table shows, for each additional can of paint, the total weight of the cans increases by 6 pounds. This is because each can of paint weighs 6 pounds, and the weight of the cans is equal to the number of cans multiplied by the weight of each can.
Answer: y = 6x
Step-by-step explanation:
For each can of paint (x) 6 pounds is added. This is represented as;
y = 6x
For the table of possible values, we will plug a value in for x, and then evaluate the function for y. See attached.
y = 6(1) = 6
y = 6(2) = 12
y = 6(3) = 18
(Factoring Algebraic Expressions MC)
Factor −7x2 + 35x.
−7x(x + 5)
7x(−x + 5)
7(−x2 + 35x)
x(7x + 35)
Answer:
7x ( - x + 5 )
Step-by-step explanation:
- 7x² = 7x × - x
35x = 7x × 5
- 7x² + 35x = 7x ( - x + 5 )
Two logarithmic functions are graphed f(x) = log (x) and g(x) = log3(x). Describe the effect on the shape of their graphs.
Responses
ABy decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
BBy decreasing the base number the graph was affected horizontally. A lower base number caused the graph to spread out faster along the x-axis.
By decreasing the base number the graph was affected horizontally. A lower base number caused the graph to spread out faster along the x-axis.
CBy decreasing the base number the graph was affected horizontally. A lower base number caused the graph to become more compressed.
By decreasing the base number the graph was affected horizontally. A lower base number caused the graph to become more compressed.
DBy decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a faster rate.
A. By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
What is a logarithm function?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, its logarithm in base 10 is 3, or log₁₀ 10³= 3.
Given function are
f(x) = log x and g(x) = log₃ x.
The rate of raise of the graph g(x) is more than that of the graph f(x).
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give an example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is your point of discontinuity removable or essential
An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function
f(x) = x^2.This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous.
At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.
The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.
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mai rode on a train at a rate of speed of 70 miles per hour for 3 hours than she rode in a ar at a rate of speed of 50 miles per hour for 2 hours what is the difference between the number of miles ai rode on the train and the number of miles she rode in the car
The difference between the number of miles travelled on train and car is 110 miles
How to determine the difference between the number of milesFrom the question, we have the following parameters that can be used in our computation:
Distance 1 (train): 70 miles per hour for 3 hoursDistance 2 (car): 50 miles per hour for 2 hoursThe difference between the distance covered can be calculated as
Distance difference = The difference of the product of speed and time
Substitute the known values in the above equation, so, we have the following representation
Distance difference = 70 * 3 - 50 * 2
Evaluate the products
This gives
Distance difference = 210 - 100
Evaluate the
Distance difference = 110 miles
Hence, the distance difference is 110 miles
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A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 41 feet, with a population standard deviation of 12.1. The mean braking distance for SUVs equipped with tires made with compound 2 is 46 feet, with a population standard deviation of 9.0. Suppose that a sample of 66 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance.
State the null and alternative hypotheses.
Determine critical value.
Calculate value of test statistic. Round your answer to two decimal places.
State conclusions
The critical value is -2.70
What is a null hypothesis?
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.
Here, we have
The objective of this experiment is to compare two compounds, designed to reduce braking distance, used in tire manufacturing to prove if the braking distance of SUVs equipped with tires made with compound 1 is shorter than the braking distance of SUVs equipped with tires made with compound 2.
So you have 2 independent populations, SUV's equipped with tires made using compound 1 and SUVs equipped with tires made using compound 2.
Two samples of 66 braking tests are made and the braking distance was measured each time, the study variables are determined as:
X₁: Braking distance of an SUV equipped with tires made with compound one.
Its sample mean is X[bar]₁= 41 feet
And the Standard deviation S₁= 12.1 feet
X₂: Braking distance of an SUV equipped with tires made with compound two.
Its sample mean is X[bar]₂= 46 feet
And the Standard deviation S₂= 9.0 feet
We don't have any information on the distribution of the study variables, nor the sample data to test it, but since both sample sizes are large enough n₁ and n₂ ≥ 30 we can apply the central limit theorem and approximate the distribution of both variables sample means to normal.
The researcher's hypothesis, as mentioned before, is that the braking distance using compound one is less than the distance obtained using compound 2, symbolically: μ₁ < μ₂
The statistical hypotheses are:
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
α: 0.05
The statistic to use to compare these two populations is a pooled Z test
Z= {(X[bar]₁-X[bar]₂) - (μ₁ - μ₂)}/√S₁²/n₁+S₂²/n₂ ≈ N(0;1)
Z = {(41-46)-0}/√146.41/66+81/66
Z = -5/1.85
Z = -2.70
The rejection region of this hypothesis test is one-tailed to the right, so you'll reject the null hypothesis to small values of the statistic. The critical value for this test is:
Z(α) = Z(0.05) = -1.645
Decision rule:
If Z(H₀) ≥ -1.645, then you do not reject the null hypothesis.
If Z(H₀) < -1.645, then you reject the null hypothesis.
Since the statistic value is greater than the critical value, the decision is to not reject the null hypothesis.
At a 5% significance level, you can conclude that the average braking distance of SUVs equipped with tires manufactured used compound 1 is greater than the average braking distance of SUVs equipped with tires manufactured used compound 2.
Hence, the critical value is -2.70.
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An airplane had a total of 387 seats. The number of coach class seats is 2 more than 4 times the number of first class seats. How many of each type of seat are there on the plane?
Answer:
coach seats is 310 and first class seats are 77
Step-by-step explanation:
x+4x+2=387
5x+2=387
5x=385
x=77
4x+2
4(77)+2=310
Answer:
There are 77 first-class seats. We can use this information to now define the number of seats in coach. And there are 310 seats in coach.
Step-by-step explanation:
a coin is flipped, and a number cube is rolled. what is the probability of getting heads on the coin and a number less than 3 on the number cube
The probability of getting heads on the a coin and a number less than 3 on cube is given as 1/6.
How to find the probability for an event?In order to find the probability take the ratio of the favorable outcome to the total possible outcome.
The set of total possible outcomes is known as sample space.
The number of elements in the sample space is given as,
Possible outcomes for coin × Possible outcomes for cube
= 2 × 6 = 12
The given two events flipping of coin and rolling of cube are mutually independent.
Which implies it is not the case of conditional probability.
The favorable number of outcomes are as below,
Number of head × Number of numbers less than 3
= 1 × 2 = 2
Now, the probability is given as,
P(getting head on coin and less than 3 on cube) = 2/12 = 1/6
Hence, the probability of getting the required outcome is given as 1/6.
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which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. each sample is a simple random sample.
All the given three conditions are true for conducting a two proportion significance test.
To check the significance of two proportions, following conditions should be met
Data of each group must be collected from the population using a random sampling. That means data values must be independent.Population should be independent of each other.The two populations must be approximately or normally distributed. To check the assumption of the normality, we have the following condition: “The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.” If this condition is met, we say that populations are normally distributed.Hence, all the three conditions must be met to conduct a two-proportion significance test.
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Calculate the area
Of this square
The area of the shape as shown in the diagram is 11.25 cm².
What is area?Area is the region occuppied by a plane shape.
To calculate the area of the shape, we use the formula below.
Formula:
A = LW+l²................ Equation 1Where:
A = Area of the shapeFrom the diagram,
Given:
L = 4.5 cmW = 2 cml = 1.5 cmSubstitute these question into equation 1
A = (4.5×2)+(1.5²)A = 9+2.25A = 11.25 cm²Hence, the area of the shape is 11.25 cm².
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Fwam is a high school basketball player. In a particular game, he made some free throws (worth one point each) and some three point shots. Fwam made a total of 10 shots altogether and scored a total of 18 points. Graphically solve a system of equations in order to determine the number of free throws made, x, and the number of three point shots made, y.
Answer:
x = 6 ans y=4
Step-by-step explanation:
The number of free throws made = x
The number of three points shots made = y
We can make an equation
x+y= total shots made
x+y= 10
So if we want "x",
x=10-y (First equation)
x is one point
y is three point
We can make another equation on how much points gained
(1)x + 3(y) = total points gained
x + 3y =18
If we want "x" ,
x =18-3y (second equation).
Now that we got two equation solve the question with simultaneous equations
x=10-y
x=18-3y
Substitute "x=18-3y" into equation 1
18-3y=10-y
10-y=18-3y
3y-y=18-10
2y=8
y=4 (Three points shots)
x=10-y
x=10-4
x=6 (Free throws made)
Therefore , x=6 and y=4
What is 37,056 rounded to the nearest thousand?
Answer:
Step-by-step explanation:
40k
An experiment was conducted in which planks of wood painted red and green were shown to pigeons to investigate a pigeon's ability to select a certain color. Pigeons could accurately select the color of the plank of wood 20 percent of the time. A simulation was conducted in which a trial consisted of a pigeon being shown eight planks of wood and its number of successes being recorded. This process was repeated many times, and the results are shown in the histogram.
Based on the results of the simulation, which of the following is closest to the probability that there were at most three successes in a trial?
The probability that there were at most three successes in a trial is approximately 0.9.
It looks like the histogram shows the probability mass function (PMF) for the number of successes in a trial. The PMF for a random variable gives the probability of each possible value of the random variable.
To find the probability that there were at most three successes in a trial, we need to add up the probabilities of 0, 1, 2, and 3 successes. From the histogram, it looks like the probabilities of these values are approximately 0.2, 0.4, 0.2, and 0.1, respectively. Adding these up, we get an approximate probability of 0.2 + 0.4 + 0.2 + 0.1 = 0.9.
Therefore, the probability that there were at most three successes in a trial is approximate $\boxed{0.9}$.
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What is the surface area of the box shown? Will give Brainliest!!
Answer:
304
Step-by-step explanation:
To find the surface area of a rectangular prism with length 4, width 10, and height 8, you can use the formula 2 * (length * width + width * height + height * length).
Plugging in the given values, the surface area is equal to 2 * (4 * 10 + 10 * 8 + 8 * 4) = 2 * (40 + 80 + 32) = 2 * 152 = 304.
Answer: 304
Step-by-step explanation:
could any one please help me with this question
Answer:
10°
Step-by-step explanation:
The sum of the measures of the exterior angles of any polygon, one per vertex, is 360°.
x + 3x + 4x + 5x + 6x + 8x + 9x = 360
36x = 360
x = 10
In a polygon, an exterior angle is supplementary to its adjacent interior angle.
The smallest exterior angle is x, and x = 10.
Answer: 10°
A book shelf is 3 1/2 feet long. Each book on the shelf is 5/8 inches wide. How many books will fit on the shelf?
67 books will fit on the shell.
How many inches are in a feet?One foot has 12 inches (in) (ft). In the US customary and imperial measurement systems, both feet and inches are units of length. The foot has had many different definitions throughout history, but since 1959, it has been defined as exactly 0.3048 meters, and the inch as 2.52 centimeters. The meter is the International System of Units' base unit of length (SI).
12 inches are one foot.In the given question,
36 inches make 3 feet.42 inches equals 3 1/2 feet.Then the number of books
= 42 / (5/8)
= 42 (8/5)
= 336/5
= 67 1/5
Finally, we round 67.2 to the nearest LESSER integer number and obtain
67.
Hence, 67 books will fit on the shell.
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Please show your work
Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week
Answer:
$530--------------------------------
If the amount of sales for current week is x, Jamie's earning is:
150 + 0.15x = 229.50Solve it for x:
150 + 0.15x = 229.500.15x = 229.50 - 1500.15x = 79.50x = 79.50/0.15x = 530Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
um consider it serious or don't :)
The quadratic equations, or the equations that are quadratic in form, for this problem is given as follows:
6(2x + 4)² = 2x + 4 + 2.x^4 - 6x² - 27 = 0.6x^4 = -x² + 5.What is a quadratic equation?The degree of a function is given by the highest exponent that appears in the definition of the function.
A quadratic function is a function that has a degree of 2.
The standard format of a quadratic function is given as follows:
y = ax² + bx + c.
(in which the coefficient a must assume a value different of zero).
The quadratic function in this problem is given as follows:
6(2x + 4)² = 2x + 4 + 2.
As (2x + 4)² = 4x² + 16x + 16, meaning that the highest exponent would be of 2.
However, equations of the fourth degree can also be quadratic in form, as long as the exponents go as follows: 4, 2 and 0.
Hence these following equations are also quadratic in form:
x^4 - 6x² - 27 = 0.6x^4 = -x² + 5.They are classified as quadratic in form because a transformation such as y = x² can make them quadratic.
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One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?
X f
5+ 2
4 3
3 2
2 1
1 1
0 1
Answer:
the mean (i.e. the average)
Step-by-step explanation:
There's no clear outlier or inconsistency therefore the mean should be used.