By combinations, we get that there are 20,020 possible 6-topping pizzas.
Given that a pizza parlor offers a choice of 16 different toppings, we need to find the number of 6-topping pizzas that are possible. No double-orders of toppings are allowed. What is the number of 6-topping pizzas that are possible?
The formula for combinations is as follows:
ncr = (n!)/(r! * (n - r)!) where n = 16 (total number of toppings available)
r = 6 (number of toppings required for a pizza)
ncr = (16!)/(6! * (16 - 6)!)
⇒ ncr = (16!)/(6! * 10!)
⇒ ncr = (16 * 15 * 14 * 13 * 12 * 11)/(6 * 5 * 4 * 3 * 2 * 1)
⇒ ncr = (16 * 3 * 5 * 7 * 13 * 11)/(3 * 2 * 2)
⇒ ncr = 20,021
In this situation, the order of the toppings does not matter. Therefore, we cannot have a repeat of the same toppings, as mentioned. Hence the answer to the question is no. Thus, there are 20,020 possible 6-topping pizzas.
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Solve for x and y 100 points
The solution to the system of equations is x = 16/5 and y = 11/5.
What are the four equation systems?Graphing, substitution, elimination, and matrices are the four methods for solving systems of equations.
Using the substitution method, we can find x and y.
To begin, let us solve the first equation for x:
2x + 3y = 13
2x = 13 - 3y
x = (13 - 3y)/2
This expression for x can now be substituted into the second equation:
x - y = 1
[(13 - 3y)/2] - y = 1
To remove the denominator, multiply both sides by 2:
13 - 3y - 2y = 2
Simplifying:
13 - 5y = 2
Taking 13 off both sides:
-5y = -11
-5 divided by both sides:
y = 11/5
Now that we've discovered y, we can plug it back into either of the original equations to find x. Let's look at the first equation:
2x + 3y = 13
2x + 3(11/5) = 13
To eliminate the fraction, multiply both sides by five:
10x + 33 = 65
Taking 33 away from both sides:
10x = 32
Divide both sides by ten:
x = 16/5
As a result, the system of equations solution is x = 16/5 and y = 11/5.
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Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching
jim
rate, in
of the cupric chloride.
min
After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so
he used the data to calculate the following least squares regression equation for predicting the etching rate from
the room temperature:
= 2 + 5
1
-2
What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5
min
The residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min is equals to the -2 μm/min.
The residual for each observation in statistics is the difference between predicted values of y (dependent variable) and observed values of y. That is Residual= observed y value − predicted y.
Here, cupric chloride is used to etch circuit boards. The linear regression equation is, y = 2 + (1/5)x
where, x = temperature in °C
y = etching rate in μm/min
Observed value of etching rate of cupric chloride = 5 μm/min for 25°C
To determine the estimated or predicted value of etching rate of cupric chloride, we substite x = 25, in the above linear equation, y = 2 + (1/5)x
=> y = 2 + (1/5)× 25
=> y = 7
So, Predicted Value = 7 μm/min
Observed Value = 5 μm/min.
Residual = Observed Value - Predicted
= 5 - 7 = -2
Hence, required value is -2 μm/min.
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Complete question:
Calculating and interpreting residuals You might need: Calculator Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching rate, in μm/min of the cupric chloride. After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature: y = 2 + 5/x, What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min. ? Show Calculator
What shape is this cross-section?
The crοss-sectiοn in the image shοwn appears tο be a trapezοid.
What is trapezοid?A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.
The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.
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any statistical test that is used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools would be inappropriate. explain why in a few sentences.
It is not appropriate to use a statistical test to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools because this would only compare the mean ratios of the two groups.
There are several statistical tests that can be used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools.
However, some statistical tests may not be appropriate for this scenario.
The main reason for this is that the normal distribution of data may not be assumed in this situation. This is because student-to-teacher ratios may not be normally distributed, with some schools having much higher ratios than others, resulting in skewed data.
In this scenario, a nonparametric statistical test may be more appropriate because it makes fewer assumptions about the distribution of data. The Wilcoxon rank-sum test, for example, may be used to compare the student-to-teacher ratios of the top 10 and bottom 10 schools because it does not assume normality. The Mann-Whitney U test is another nonparametric test that can be used to compare the two groups' ratios.
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Question 53 Look at the performance review below, if you know that person 6 has a perfect score, you can calculate each person's score using the graph. If you know that person 3 hasn't achieved any of their goals this year, Person 5 has an excellent personality and very good job knowledge, and Person 4 is more interested in hanging out at the water cooler than in getting work done, then who must the performance review belong to? Total number of points per employee Peson P2 Pesen3Psen 4 PeronS Person Rating Scale Category Ratings General Quality of Work 4 Very Good Good Job Knowledge Fair Communication Skills Personality Management Ability Contribution to Group Poor 4. Achievement of Goals Person5 2. Person 4 3. Person 3
Without specific details it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. So, based on the information we can define some data as below.
Define the term graph?A graph in x-y axis plot is a visual representation of functions or data points. The dependent or vertical variable represented by y-axis, while the independent or horizontal variable represented by the x-axis.
Without the specific details of the performance review or the names of the employees, I cannot provide an exact answer. However, based on the information given, we can infer the following:
Person 6 : has a perfect score.
Person 3 : not achieved any of their goals.
Person 5 : excellent personality and very good job knowledge.
Person 4: more interested in hanging out at the water cooler.
Given this information, it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. We also do not have enough information to make an informed judgment about the performance of each employee. It is possible that the review could belong to any of the employees, depending on their individual scores and performance.
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In 915. 23, the digit 3 is in the
place.
Answer:
hundreth
Step-by-step explanation:
the 2 is in the tenth and the 3 is in the hundreth
A soccer team won 11 games last year. This year they won 13 games. What was the percent increase in the number of games won?
A) 84.6%
B) 2%
C)15.4%
D)18.2%
The required percent increase in the number of games won is approximately 18.2%.So, Option D) is correct.
What is percentage?In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).
According to question:The percent increase in the number of games won can be calculated as follows:
[tex]$\text{Percent increase} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100%$$[/tex]
In this case, the old value is the number of games won last year, which is 11, and the new value is the number of games won this year, which is 13. Substituting these values into the formula, we get:
[tex]$\text{Percent increase} = \frac{13 - 11}{11} \times 100% = \frac{2}{11} \times 100% \approx 18.18%$$[/tex]
Therefore, the percent increase in the number of games won is approximately 18.18%.
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Mark the approximate location of the point determined by the given real number on the unit circle. a) 3.2 b) 9.5 c) 50 d) 263 a) Choose the unit circle with a point determined by 3.2. OA. OB. OC. 0 D. b) Choose the unit circle with a point determined by 9.5. OA. OB. OC. OD Click to select your answer. b) Choose the unit circle with a point determined by 9.5. OA. B. OC. D. Ay c) Choose the unit circle with a point determined by 50. c) Choose the unit circle with a point determined by 50. OA. OB. OC. OD. Ау AY 09 d) Choose the unit circle with a point determined by 263. OA. B. D. Ау х
The points determined by the real numbers 3.2, 9.5, 50, and 263 are all located on the unit circle at their respective distances from the origin.
The unit circle is a circle of radius 1 centered at the origin of a coordinate system, usually the Cartesian coordinate system. In this system, a point (x,y) is determined by its real number x, where x is the horizontal distance from the origin and y is the vertical distance from the origin. For example, the point determined by the real number 3.2 is located at (3.2, 0), since 3.2 is the horizontal distance from the origin. Similarly, the point determined by the real number 9.5 is located at (9.5, 0).
The point determined by the real number 50 is located at (50, 0). Finally, the point determined by the real number 263 is located at (263, 0). The unit circle is often used in trigonometry to describe the position of points on the circle with an angle in standard position (in radians). For example, if the point determined by the real number 3.2 has an angle in standard position of 3.2 radians, then the point located at (3.2, 0) on the unit circle is the same point. Similarly, if the point determined by the real number 9.5 has an angle in standard position of 9.5 radians, then the point located at (9.5, 0) on the unit circle is the same point. The same is true for the points determined by the real numbers 50 and 263, respectively.
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Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Comment on his claim. The claim is right. The claim is wrong. Need Help?
Answer: Incorrect
Step-by-step explanation:
Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.
A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.
The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.
The ordering and transportation cost €C for components used in manufacturing process is approximated by the function below, where C is measured in thousands of dollars and is the order size in hundreds_ C(x) = s(x x+3 (a) Verify that C(3) C(6) _ c(3) (b) According to Rolle's Theorem, the rate of change of the cost must be for some order size in the interval (3 answer to the nearest whole number:) components Find that order size (Round vour Need Help? Ialkto Tutor
The value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
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Segment addition and midpoints.
EH=EF+FH, we can replace the found values with EF and FH to get EH=12+7=19.
How to solve the problem?A line segment is a path between two measurable points. Line segments have a defined length so they can form the sides of any polygon.
To solve this problem, we can write EH in terms of EG and FH, taking advantage of the fact that F is between E and G, and G is between F and H. First, notice that EG+GF=EF. Substituting the given values, we get EF=9+3=12.
Then GF+FH=GH, so FH=GH-GF. Substituting in the given values, GH=10 and GF=3, so FH=10-3=7.
Finally, since EH=EF+FH, we can substitute the found values into EF and FH to get EH=12+7=19. Therefore EH = 19
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Answer to where the lines Intersect PLEASE Y=3x-6, Y=2x
Answer:
(6,12)
Step-by-step explanation:
3x - 6 = 2x
x - 6 = 0
x=6
y=2*6
y=12
Please look at the photo and let me know the three answers ASAP!! Thank you!!
a) Increase in the amount spent on entertainment is $1.82
b) Money spent who doesn't work any hours is $11.36
c) Money spent who works 8 hours is $25.92
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
Given line equation is; y = 1.82x + 11.36 Compare with y = mx + c
(a) The slope (m) of the line is 1.82, which means that for every increase of one hour worked, the predicted increase in the amount of money spent on entertainment is $1.82.
(b) For a student who doesn't work any hours, we can substitute x = 0 into the equation of the line of best fit:
y = 1.82x + 11.36
y = 1.82(0) + 11.36
y = 11.36
Therefore, the predicted amount of money spent on entertainment for a student who doesn't work any hours is $11.36.
(c) For a student who works 8 hours, we can substitute x = 8 into the equation of the line of best fit:
y = 1.82x + 11.36
y = 1.82(8) + 11.36
y = 25.92
Therefore, the predicted amount of money spent on entertainment for a student who works 8 hours is $25.92
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the probability that deshawn palys basketball after school is 20% the probability that he talks to friends after school is 45% he says the p b or t is 65% explain dans error
Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
How do we find the error?Given:
Probability of Deshawn playing basketball after school = 20%Probability of Deshawn talking to friends after school = 45%Probability of Deshawn doing either basketball or talking to friends after school = 65%Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%
Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%
The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
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If a can of paint can cover 600 square inches, how many cans of paint are needed to cover 1,880 square inches
Answer:
1,880 sq in ÷ 600 sq in/can ≈ 3.13 cans
If you want you can round that to 4 cans.
which of the following was traditionally an assumption underlying the independent samples t-test question 10 options: a) scores must be drawn from a normally distributed population b) variances should be unequal in both groups c) data should be at the nominal level d)all of the above
The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.
What is a t-test?A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.
The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.
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What is the nth term rule of the linear sequence below?
-5, -2, 1, 4, 7,....
T₁=
Write 735 as the product of its prime factor.
Answer:
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
Step-by-step explanation:
[tex]735 = 7 \times 105[/tex]
[tex]735 = 7 \times 3 \times 35[/tex]
[tex]735 = 7 \times 3 \times 5 \times 7[/tex]
[tex]735 = 3 \times 5 \times {7}^{2} [/tex]
20x50x30x50 = ?
Please answer someone!!
Answer: 1500000
Step-by-step explanation:
use a calculator
Answer:
1,500,000
Step-by-step explanation:
Breaking it up into an easier problem:
20x50 = 1,000
30x50=1,500
1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.
Thus, the answer is 1,500,000
If tan2 0 = 6 find the exact answer sec2 0
Therefore, the exact value of sec²(θ) is 7.
What is trigonometry?
The branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry.
We can use the trigonometric identity:
tan²(θ) + 1 = sec²(θ)
Substituting tan²(θ) = 6 into the identity gives:
sec²(θ) = tan²(θ) + 1
sec²(θ) = 6 + 1
sec²(θ) = 7
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Therefοre, the exact value οf sec²(θ) is 7.
What is trigοnοmetry?Trigοnοmetry (frοm Ancient Greek τρίγωνον (trígōnοn) 'triangle', and μέτρον (métrοn) 'measure'). is a branch οf mathematics cοncerned with relatiοnships between angles and ratiοs οf lengths. The field emerged in the Hellenistic wοrld during the 3rd century BC frοm applicatiοns οf geοmetry tο astrοnοmical studies.
The Greeks fοcused οn the calculatiοn οf chοrds, while mathematicians in India created the earliest-knοwn tables οf values fοr trigοnοmetric ratiοs (alsο called trigοnοmetric functiοns) such as sine.
Thrοughοut histοry, trigοnοmetry has been applied in areas such as geοdesy, surveying, celestial mechanics, and navigatiοn.
We can use the trigonometric identity:
tan²(θ) + 1 = sec²(θ)
Substituting tan²(θ) = 6 into the identity gives:
sec²(θ) = tan²(θ) + 1
sec²(θ) = 6 + 1
sec²(θ) = 7
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Samantha and Christian own competing taxicab companies. Both cab companies charge a one-time pickup fee for every ride, as well as a charge for each mile traveled. Samantha charges a $3.50 pickup fee and $1.30 per mile. The table below represents what Christian's company charges.
Christian's company charges $0.8 per mile than Samantha's.
What is the rate of change?In Mathematics and Geometry, the rate of change can be calculated by using the following mathematical equation (formula);
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x for Christian's company;
Rate of change, m = (43.50 - 22.50)/(20 - 10)
Rate of change, m = 21/10
Rate of change, m = 2.1
Therefore, the difference between the charges by Christian's company and Samantha's company can be calculated as follows;
Difference in charges = 2.1 - 1.30
Difference in charges = $0.8.
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PLEEASSEEE HELLP
What is m
if cell phone companies screen text messages, then freedom of speech is threatened. thus, freedom of speech is not threatened, because cell phone companies do not screen text messages. which of the following correctly expresses the form of this argument? a. if c then f. b. not f. c. all c are f. d. if c then f. e. if c then f. not
The correct option that expresses the form of the given argument is "d. if c then f."Explanation:In the given argument, it is stated that if cell phone companies screen text messages, then freedom of speech is threatened.
But as cell phone companies do not screen text messages, so freedom of speech is not threatened. This is a conditional argument, and it can be expressed in the form of a hypothetical syllogism.
The hypothetical syllogism is a syllogism that has a conditional statement in its premises. It is also called a chain argument or transitive argument. The form of the hypothetical syllogism is "If A, then B. If B, then C.
Therefore, if A, then C."In the given argument, it can be expressed in the form of the hypothetical syllogism as follows:If cell phone companies screen text messages, then freedom of speech is threatened. If freedom of speech is threatened, then cell phone companies screen text messages. Therefore, if cell phone companies do not screen text messages, then freedom of speech is not threatened.This can also be represented as "if C then F."Therefore, the correct option that expresses the form of the given argument is "d. if c then f."
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Ngozi is twice older than Ada and agens is one third as old as Ada if the sum of their age is 30 what is ngozi age
Answer:
Ngozi is 45 years old
Step-by-step explanation:
N = 2A
AG = 1/3A
A + AG = 30
Subsitute AG with 1/3A.
A + 1/3A = 30
1 1/3 A = 30
A = 22.5
AG = 7.5
Ngozi = 45
Find the value of x:
Nonresponse bias occurs when ________.
A) the population has been divided into strata
B) portions of the population are excluded from the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents
Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.
Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.
Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.
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Find measure of arc EBA
Therefore, the measure of the arc of the circle is 180 degrees.
What is circle?A circle is a geometrical shape that consists of all points that are equidistant from a single fixed point called the center. It is a closed curve, which means that it has no endpoints and is continuous. The distance between any point on the circle and its center is called the radius of the circle, denoted by the letter 'r'. The diameter of the circle is the distance across the circle through the center and is twice the length of the radius, denoted by the letter 'd'. The circumference of a circle is the distance around the circle and is given by the formula C = 2πr or C = πd, where π (pi) is a mathematical constant approximately equal to 3.14159. Circles are important in mathematics and geometry because of their symmetry, and they are used in a variety of real-life applications such as wheels, clocks, and planetary orbits.
by the question.
To find the measure of the arc of a circle given certain central angles, we need to know the angle measure of the entire circle. Since a circle has 360 degrees, we can add up the given central angles and set them equal to 360 degrees to find the measure of the missing arc.
So, the measure of the missing arc is:
360 - (30 + 100 + 50 + x) = 360 - 180 = 180 degrees
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Work out the angle x. Give your answers to the nearest whole number. ABCD is a rectangle. ABC is an isosceles triangle, with AB = AC. A B X X = 11 cm O 13 cm [2] C B A X C 15 cm X = O 19 cm [3] D ABC is a right-angled triangle. D lies on BC, and DC = DB. BC = 16 cm. A X = t 23 cm O [4] C B
WILL GIVE AS BRANLIEST ANSWER IF THE ANSWER IS GIVEN IN UNDER 7 MINS
The value of the missing sides of the triangle given above include the following;
2.)X = 65°
3.) X = 60°
4.) X = 20°
How to calculate the value of the missing side of the triangles?For question 2.)ABC = isosceles triangle
AB = AC = 13 cm
BC = 11cm
There is an angle bisector at <A which divides lime BC into two equal parts at D.
BD = 11/2 = 5.5 cm
Cos∅ = adjacent/hypothenuse
Cos X = 5.5/13
cos X = 0.423076923
X = Cos -1(0.423076923)
X = 65°
For question 3.)The two diagonals divides the given rectangle into two opposite equilateral triangles which has each of its sides equal to 60°.
For question 4.)ABC = right angle triangle
Line D divides BC into two equal parts = DC and DB
BC = 16cm (opposite)
DC = 16/2 = 8cm
AB = 23 cm( adjacent)
AC = hypothenuse = BC²+ AB²
AC² = 16²+23²
= 256 + 529
= 785
AC = √785
= 28
<CAB = sin ∅ = opposite/hypothenuse
sin∅ = 18/28
= 0.642857142
∅= sin -1 (0.642857142)
∅ = 40°
Therefore X = 40/2 = 20°
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Please help!
The object above is symmetrical through Z. If Y = 11 inches, Z = 13 inches, and H = 6 inches, what is the area of the object?
A. 6.5 square inches
B. 78 square inches
C. 31 square inches
D. 156 square inches
the correct area of the symmetrical object is option (B). 78 square inches.
Definition of SymmetryIf two more identical parts can be separated from a form and arranged in an orderly fashion, the shape is said to be symmetrical. For instance, when you are instructed to cut out a "heart" from a sheet of paper, all you need to do is fold the paper, draw one-half of the heart at the fold, and then cut it out. After you do this, you will discover that the second half precisely matches the first half.
In the first part of the object
Area of the object=½×H×Z
=½×13×6
=39 square inches
Given that object above is symmetrical through Z.
So, the area of 2nd part of object will also be 39 square inches
Hence total area is 78 square inches.
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