The required graph of the function given; h (x) has been attached.
Define a graph?In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.
Here as per the question the graph of the function, h (x) has been attached.
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The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.8 years and a standard deviation of 15.1months. Complete parts (a) through (d).
The answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?
To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,
Z = (X - mean) / standard deviation
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.
(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?
We need to standardize the values of 16 and 18 using the mean and standard deviation provided.
Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.
(c) What is the age at which growth plates fuse for the top 5% of males?
We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).
Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.
Then, we can solve for X using the formula:
Z = (X - mean) / standard deviation
1.645 = (X - 18.8) / (15.1/12)
Simplifying the equation, we get:
X = 18.8 + (1.645)(15.1/12) = 20.24
Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.
(d) What percentage of males have growth plates that fuse before the age of 16?
We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).
Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.
Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.
hence, the answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
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A four-sided shape with the top side labeled as 10.2 cm. The height is labeled 5 cm. A portion of the base from the perpendicular to a vertex is labeled 4 cm. The portion of the base from the perpendicular to the right vertex is 6.2 cm.
What is the area of the figure?
25.5 cm2
45.5 cm2
51 cm2
56.1 cm2
The area of the figure is 51 cm², which is option C.
What is area?In mathematics, area refers to the measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²) or square centimeters (cm²), and can be calculated for a variety of geometric shapes, including squares, rectangles, triangles, circles, and more complex shapes such as trapezoids or polygons.
To find the area of the figure, we need to identify the shape of the figure. From the given information, we know that the figure has a top side, a height, and a base. We are also told that the base is divided into two parts by a perpendicular, and one of the parts is labeled as 4 cm, while the other part from the perpendicular to the right vertex is 6.2 cm.
Based on this information, we can draw the figure as a trapezoid, where the top side is the shorter base, the height is the vertical distance between the two bases, and the longer base is the sum of the two parts of the base.
Using the given information, we can calculate the longer base:
longer base = 4 cm + 6.2 cm = 10.2 cm
Now we can use the formula for the area of a trapezoid to find the area of the figure:
A = (1/2)h(b₁ + b₂)
where h is the height, b₁ is the shorter base, and b₂ is the longer base.
Plugging in the given values, we get:
A = (1/2)(5 cm)(10.2 cm + 10.2 cm) = 51 cm²
Therefore, the area of the figure is 51 cm² , which is option C.
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Complete Question:
A four-sided figure has one side labeled 10.2 cm, a height of 5 cm, and a portion of the base from the perpendicular to a vertex labeled 4 cm. The portion of the base from the perpendicular to the right vertex is labeled 6.2 cm. What is the area of the figure?
Amy and Zack each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long. Zack makes his fence 8 feet long. Whose garden has the better area? How much greater?
Answer:
The answer is Zack garden
answer these questions in detail
Answer:
5. x = 60
6. F' (1, 4)
Step-by-step explanation:
5. The angles shown are same side exterior angles, so they are supplementary (add to 180)
(x + 85) + 35 = 180
x + 120 = 180
x = 180 - 120 = 60
x = 60
6. The line x = 1 is a vertical line, passing through the x=axis at (1, 0). All x coordinates on this line equal 1.
The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)
k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answer: 104%
Step-by-step explanation: 26% times 4 years
Julia drew s sketches of flowers. She split them evenly among her 3 pen pals. Write an expression that shows how many sketches each pen pal received.
Answer:
s/3
Step-by-step explanation:
since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.
the difference of 25 and a number?
Answer: 30 and 5
Step-by-step explanation:
Tentor, Inc., purchases disposable coffee cups on which to print logos for sporting events, proms, birthdays, and other special occasions. The owner received a large shipment of 861 cups this afternoon, and to ensure the quality of the shipment, he selected a random sample of 410 cups and identified 353 as defective.
What is the estimated proportion of defectives in the population? (Round the final answer to 3 decimal places.)
Answer
What is the standard error of the sample proportion? (Round your answer to 3 decimal places.)
Answer
What are the upper and lower bounds for a 98% confidence level? (Round the final answers to 3 decimal places.)
Upper bound is Answer
Lower bound is Answer
It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to√(0.861(1.0.861)/410) = 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?
The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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Explain Why 387 is not a term of the sequence
Answer:
In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.
If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:
an = a1 + (n-1)d
where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.
If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:
a1 = 3
a2 = 8
a3 = 13
a4 = 18
and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:
a129 = a1 + (129-1)d
a129 = 3 + 128(5)
a129 = 643
Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.
Find the critical value t
The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.
What is Critical value?
In statistics, critical value is value that is used to determine whether to reject null hypothesis in hypothesis test. It is based on chosen level of significance, which is the maximum probability of making a Type I error (rejecting true null hypothesis). The critical value is determined by sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.
To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.
Using a t-distribution table with 21 degrees of freedom (n-1), we find that critical value for a 99% confidence level is approximately 2.819.
Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).
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Jackson has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $27.40? Round to the nearest cent.
Jackson's total cost after the discount and before tax would be $24.67.
Calculating discounted price :When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.
To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).
Here we have
Jackson has a 10% discount at his local hardware store.
Let 'x' be the cost before tax
After a 10% discount,
The amount that Jackson could pay 90% of the cost
Given that he wants to buy $ 27.40
The cost of items after discount = 90% of 27.40
= [ 90/100 ] × 27.40
= [ 0.9 ] × 27.40
= 24.66
Therefore,
Jackson's total cost after the discount and before tax would be $24.67.
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Working with Actual Interest Earned
Daniela puts $550 in a CD that earns 3.5% APR, compounded quarterly,
for 2 years. She is taxed at a rate of 15% on the interest she earns.
The total amount of interest is $33.75.
What percentage of the original principal is this?
We can use the procedures below to calculate what proportion of the original principal the overall amount of interest represents. This total amount of interest received corresponds to about 5.34% of the initial investment.
What is an interest?Divide the principal even by rate of interest, the time period, and other factors to arrive at simple interest. Simple return Equal principal + interests + hours is the marketing formula.The most typical technique to figure out interest is to use a portion of the principal sum. He would only pay his share of the 100% interest, for example, if somebody borrows $100 from the a partner and pledges to repay the loan with 5% interest. $x (0.05) = $5. When, you must pay interest.when you lend money after borrowing it and adding interest. Interest is often determined as an indicator of the overall of the loan total. The interest rate of the loan is the name given to this percentage.
Determine the total interest that was earned in Step 1.
It states that $33.75 was earned in interest overall.
Step 2: Determine the interest generated before to taxes.
The sum of the interest earned after tax can be determined by dividing the entire sum of the interest by (1 + rate of taxation), where the rate of tax is given as a decimal. Daniela was subject to a tax of 15% on the investment earnings. The tax rate in this instance is 15%, which really is equal to 0.15.
Interest gained before taxes is equal as $33.75 / (1 Plus 0.15), that results in a value of $29.35.
3. Determine the initial principal.
The $550 that Daniela first put into the CD is referred to as the original primary.
Compute the proportion of the initial principle in step four.
By dividing the sum of interest generated after tax by the original principal and multiplying the result by 100 as express it as a percentage, one can determine what proportion of the original principal the entire amount of interest represents.
(Interest paid before taxation / Original principal) / 100 equals the percentage of the original principal.
= ($possess / $550) w x 100
≈ 5.34%
Hence, the total interest earned is equivalent to roughly 5.34% of the initial capital.
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Jasper's aunt gave him a big bin of 500 beads made out of assorted materials to use for the wind chimes he makes. Jasper takes out a handful of beads, looks at the types of beads, then puts them back. Here are the materials of the handful he selected: glass, clay, wood, glass, wood, clay, metal, clay, wood, glass, wood, clay, metal, wood, clay Based on the data, estimate how many glass beads are in the bin. If necessary, round your answer to the nearest whole number.
We can estimate that there are approximately 134 glass beads in the bin.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.
There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:
4/15 ≈ 0.267
We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as:
0.267 x 500 ≈ 134
Therefore, we can estimate that there are approximately 134 glass beads in the bin.
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Will mark brainliest if answer is correct
Using factorization and simplifying the equations, the points of intersections are (-2, 0), ( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 ) and ( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )
What is the points of intersection of both functionsWe are given two equations:
y = 4x² - 3x + 3
y = x³ + 7x² - 3x + d
and we know that they intersect at x = -4, so we can substitute -4 for x in both equations:
y = 4(-4)² - 3(-4) + 3 = 49
y = (-4)³ + 7(-4)² - 3(-4) + d = -64 + 112 + 12 + d = 60 + d
So, at x = -4, we have y = 49 and y = 60 + d. Since the graphs intersect, these two equations must be equal:
49 = 60 + d
Solving for d, we get:
d = -11
Therefore, the two equations become:
y = 4x² - 3x + 3
y = x³ + 7x² - 3x - 11
We can now set them equal to each other:
4x² - 3x + 3 = x³ + 7x² - 3x - 11
Simplifying and rearranging, we get:
x³ + 3x² - 8x - 14 = 0
We can try to factor this expression by testing possible roots. One possible root is x = 2, because if we substitute 2 for x, we get:
2³ + 3(2)² - 8(2) - 14 = 8 + 12 - 16 - 14 = -10
Since this expression evaluates to a non-zero value, x = 2 is not a root. Similarly, we can test x = -1:
(-1)³ + 3(-1)² - 8(-1) - 14 = -1 + 3 + 8 - 14 = -4
This expression also evaluates to a non-zero value, so x = -1 is not a root. Finally, we can test x = -2:
(-2)³ + 3(-2)² - 8(-2) - 14 = -8 + 12 + 16 - 14 = 6
This expression evaluates to zero, so x = -2 is a root. Using long division or synthetic division, we can divide the cubic polynomial by x + 2 to get:
x³ + 3x² - 8x - 14 = (x + 2)(x² + x - 7)
The quadratic factor x² + x - 7 can be factored using the quadratic formula, giving us:
x² + x - 7 = [ -1 ± √(1 + 4*7) ] / 2
= [ -1 ± 3√(7) ] / 2
Therefore, the three intersection points are:
(-2, 0)
( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 )
( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 18 , 27 , . . . Find the 8th term.
Answer: 205.031(nearest thousandth)
or 205.03125
Step-by-step explanation:
The length of a rectangle is 2 units more than the width. The area of the rectangle is
24 square units. What is the width, in units, of the rectangle?
The width of the rectangle is 4 units.
What is rectangle?
Rectangle is a four sided polygon or specifically a particular type of parallelogram having two opposite sides are equal and one angle is right angle that is 90°. It has four vertices and two diagonals intersect each other.
Given that,
The length of a rectangle is 2 units more than the width.
Let, the width of the rectangle is w units.
Then the length of the rectangle is w+2 units.
Area of any rectangle is length × width
= (w+2)×w square units
Given that,
The area of the rectangle is 24 square units.
Equating both the values we get,
w(w+2)= 24
We have to solve the equation for w.
Multiplying the bracket term with w we get,
w²+ 2w = 24
⇒ w² + 2w- 24=0
⇒ (w+6)(w-4)=0
so either w= -6 or w=4
As width cannot be negative so w= 4.
Hence, the width of the rectangle is 4 units.
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Which equation shows how to find a percentage?
O
part
10
=
percent
100
part
100
=
percent
10
percent
whole
=
part
whole
percent
whole
part
whole
The equation that shows how to find a percentage is:
part/whole = percent/100
This equation can be used to solve for any of the three variables, given the values of the other two.
4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
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1C. What do you do if you're collecting data and you're unable to survey everyone in a group because the group is
too large?
If the group is too large to survey everyone, you may consider using a sampling technique to select a representative subset of the group for the survey.
How to use Sampling Technique?Here are some common sampling techniques you could use:
Simple random sampling: randomly select individuals from the group to be surveyed.Stratified sampling: divide the group into subgroups based on certain criteria, and then randomly select individuals from each subgroup to be surveyed.Cluster sampling: divide the group into clusters, randomly select some of the clusters, and survey everyone in the selected clusters.Systematic sampling: select individuals from the group at regular intervals.When selecting a sampling technique, it's important to consider the size of the group, the available resources, and the research question. It's also important to ensure that the sampling technique is unbiased and representative of the group being studied.
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Briana helps her mother make a quilt The quilt is 6 feet wide and 12 feet long
Briana and her mother will need to measure and cut the fabric for the quilt. They will need to decide on a pattern and color scheme for the quilt. They will need to sew the pieces of fabric together to create the quilt top. They will need to layer the quilt top with batting and backing fabric and then quilt the layers together. Finally, they will need to bind the edges of the quilt.
8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving AC > EF, given BC = EF. Upload the entire proof below.
Given:
BC = EF
Prove:
AC > EF
STATMENT REASON
1. 1.
2. 2. Betweenness
3. AC > BC 3.
4. 4.
The given information and the transitive property of inequalities, we can prove that [tex]AC[/tex] is greater than [tex]EF[/tex] .
What is the transitive property of inequalities?Statement Reason
[tex]BC = EF[/tex] Given
Betweenness Given
[tex]AC > BC[/tex] Given
[tex]AC > EF[/tex] Transitive property [tex](3, 1)[/tex]
Explanation:
[tex]BC = EF[/tex] Given: Given statement that BC is equal to EF.
Betweenness Given: Given statement that states the concept of betweenness, where BC is between AC and EF.
AC > BC Given: Given statement that [tex]AC[/tex] is greater than BC.
[tex]AC > EF[/tex] Transitive property: Using the transitive property, we can conclude that [tex]AC[/tex] is greater than EF (based on statement 3 and 1).
Therefore, using the given information and the transitive property of inequalities, we can prove that AC is greater than [tex]EF[/tex] .
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Ejercicio 1.9. En el ΔPQR, A y B son los puntos medios de PQ y RQ respecvamente.
Si RP = 16, m∠P = 58° y m∠Q = 38°, obtenga
AB y m∠BAQ.
The length of line segment AB is equal to 8 units.
The magnitude of m∠BAQ is equal to 58°.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector can be defined as a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
This ultimately implies that, the length of line segment AB can be calculated by using the following mathematical equation;
RP = 2AB
AB = RP/2
AB = 16/2
AB = 8 units.
Since A and B are the midpoints of PQ and RQ respectively, we have the following angles;
m∠P + m∠Q + m∠R = 180° (sum of all interior angles of ∆PQR)
58° + 38° + m∠R = 180°
m∠R = 180° - (58° + 38°)
m∠R = 84°
Since PR || AB, we have;
m∠R = m∠ABQ = 84° (corresponding angles).
m∠Q + m∠ABQ + m∠BAQ = 180° (sum of all interior angles of ∆ABQ).
m∠BAQ = 180° - (84° + 38°)
m∠BAQ = 180° - 122°
m∠BAQ = 58°.
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Complete Question:
In the ΔPQR, A and B are the midpoints of PQ and RQ respectively. If RP = 16, m∠P = 58°, and m∠Q = 38°, obtain AB and m∠BAQ.
Find a formula for the exponential function passing through the points
(-3, 5/8 ) and (3, 40).
The exponential function is y=5.[tex]2^x[/tex].
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Here the exponential function is [tex]y=ab^x[/tex]
Since (-3,5/8) is on the graph, -[tex]\frac{5}{8}[/tex]=[tex]ab^{-3}[/tex] -----> 1
Since (3, 40) is on the graph, 40=[tex]ab^3[/tex] ------> 2
So, [tex]\frac{ab^3}{ab^{-3}}=\frac{40}{\frac{-5}{8}}[/tex]
=> [tex]b^{3+3}=8\times8[/tex]
=> [tex]b^6=2^6[/tex]
=> b = 2
put b=2 into 2 then,
=> 40= [tex]a\times2^3[/tex]
=> 8a=40
=> a =5
Then the exponential function is y=5.[tex]2^x[/tex].
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How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
2 only can you solve associative, identity and inverse of this
The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.
Solving the associative, identity and inverse of this the setThe set 2Z is defined as follows:
2Z = {2n | n ∈ Z, a * b = a + b}
Associative element:
There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.
Let a, b, and c be arbitrary elements of 2Z:
a = 2n₁
b = 2n₂
c = 2n₃
Then we have:
a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)
(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)
Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.
Identity element:
There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.
Let e be an arbitrary element of 2Z:
e = 2n
Then we have:
ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z
ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z
Therefore, e = 2n is an identity element in 2Z.
Inverse element:
There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.
Let a be an arbitrary element of 2Z:
a = 2n
Then we need to find an element b in 2Z such that ab = ba = e = 2.
We have:
ab = ba = 2n*b = 2
Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.
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6. WRITING IN MATH Describe why the
difference of squares pattern has no middle term
with a variable. Example w-121
The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
How do you find a middle term?When expanding a binomial expression in the form of (a + b)ⁿ, the middle term can be found using the following formula:
Middle term coefficient = nC(k), where k = (n+1)/2 if n is odd, and k = n/2 or (n/2 + 1) if n is even. The middle term coefficient is then multiplied by the product of a raised to the power of (n-k) and b raised to the power of k.
The difference of squares pattern is a special algebraic pattern that arises when we factor a polynomial that is the difference between two perfect squares. For example,
x² - y² = (x+y)(x-y)
When we apply this pattern to the expression w - 121, we can rewrite it as:
w² - 11²
And, we can use the difference of squares pattern to factor it as:
(w + 11)(w - 11)
Notice that there is no middle term with a variable in this factorization. This is because when we multiply (w + 11)(w - 11), the middle term cancels out.
To see why this happens, let's expand the product:
(w + 11)(w - 11) = w² - 11w + 11w - 121
The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
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Approximately of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
The fraction of Earth that is not made up of ocean = 1/4.
Explain about the fraction:The numbers we are familiar with are whole numbers, such as 1, 2, and so on.
Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.
In essence, a fraction explains how a portion of a group interacts with the entire group.
Given that-
fraction of Earth made up of water = 3/4The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water
The fraction of Earth that is not made up of ocean = 1 - 3/4
The fraction of Earth that is not made up of ocean = (4 - 3)/4
The fraction of Earth that is not made up of ocean = 1/4
Thus, the fraction of Earth that is not made up of ocean = 1/4.
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Complete question:
Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?