Answer: 15 √ 2
Step-by-step explanation:
Equilateral triangles have three equal side lengths, three equal angles of 60 degrees, and three equal altitudes.
You would think that the height of an equilateral triangle would also be equal to it's sides, but it's not. The formula for height is: side/2 x √3
10√6 / 2 * √ 3 = 15 √ 2
The decimal form: 21.2
last semester, a certain professor gave 22 as out of 197 grades. if one of the professor's students from last semester were selected randomly, what is the probability that student received an a? (assume that each student receives one grade.)
According to the question last semester, a certain professor gave 22 as out of 197 grades The probability that a student received an A is approximately 0.1117 or 11.17%.
To calculate the probability that a student received an A, we need to know the total number of grades given and the number of A grades.
Given:
Total number of grades = 197
Number of A grades = 22
The probability of receiving an A can be calculated as:
Probability of receiving an A = Number of A grades / Total number of grades
Probability of receiving an A = 22 / 197
Probability of receiving an A ≈ 0.1117
Therefore, the probability that a student received an A is approximately 0.1117 or 11.17%.
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solve by substitution y=3x+5 and y=x+1
Answer:
x= -2 y= -1
Step-by-step explanation:
To solve by Substitution you would make this equation equal to each other x+1=3x+5 from there you would solve for x subtract x on both sides. and subtracting 5 from both sides 2x= -4 then divide by 2 to get x by itself x=-2 since we now found what the value of x is you can now plug in x into one of the origunal equations and get your answer for y which is y=-1
6 is added to the
product of 7 and a number.
The equation model of the given statement in question is 6 + 7× x.
What are equation models and arithmetic?The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.
In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.
Given that;
6 is added to product of a number and 7
Now,
Let, the number multiplied by 7 be x,
=7*x
6 is added to the product;
= 6 + 7 × x
Therefore, the equation of model will be given as 6 + 7 × x;
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you and a friend tutor for a total of 12 hours. use the tape diagram to find how many hours you tutor.
how many odd integers are between -20 and 10?
9514 1404 393
Answer:
15
Step-by-step explanation:
The given range of numbers is -20 to 10, so is 10-(-20)+1 = 31 numbers. Since the end points of the range are both even, there is one more even number than there are odd numbers in the range. The number of odd numbers is ...
(31 -1)/2 = 15
There are 15 odd numbers between -20 and 10.
Find the equation for the
following parabola.
Focus (3, 4)
Directrix y = 2
A. (x-3)2 = 2(y-2.5)
B. (x-3)2 = 4(y-3)
C. (x-3)2 = (y-4)
D. (y-3)2 = 4(x-3)
Option A is correct.The equation for the parabola is A.(x - 3)^2 = 2(y - 2.5)
The equation for a parabola with a focus (h, k) and a directrix y = a can be expressed as:
(x - h)^2 = 4a(y - k)
The focus is (3, 4) and the directrix is y = 2, we can substitute these values into the equation:
(x - 3)^2 = 4(2)(y - 4)
Simplifying:
(x - 3)^2 = 8(y - 4)
The correct equation for the parabola is:
(x - 3)^2 = 8(y - 4)
Therefore, the answer is option A. (x - 3)^2 = 2(y - 2.5)
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There are 2 squares, 2 triangles, 2 hexagons, and 2 circles in a teacher's bag of shapes. If a student randomly selects 1 shape from the bag, what is the probability that student selects a circle?
How do I get the answer I’m confused
Which describes how the parent function, f(x) = |x|, is transformed to show the function f(x) = 0. 1|x – 3|? It is wider and shifted 3 units to the left. It is wider and shifted 3 units to the right. It is narrower and shifted 3 units to the left. It is narrower and shifted 3 units to the right.
The correct statement about the function is '' It is wider and shifted 3 units to the right''.
Given thatFunction; \(\rm f(x) = |x|\)
We have to determineWhich describes how the parent function, f(x) = |x|, is transformed to show the function f(x) = 0. 1|x – 3|?
According to the questionThe function is;
\(\rm f(x) = |x|\)
First, the function is translated right into 3 units.
So, we have:
\(\rm f'(x) =|x-3|\)
The function is enlarged horizontally by a factor of 0.1.
\(\rm f''(x) =0.1|x-3|\)
The above highlights mean that:
\(\rm f'(x) =|x-3| \) will be wider than \(\rm f(x) = |x|\).
Hence, It is wider and shifted 3 units to the right.
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what is a simplified version of -7(2x-3)
Answer:
-14x+21
Step-by-step explanation:
6. approximately 84% of persons age 70 to 84 live in their own household and are income-qualified for home purchases. if four persons are randomly selected from this population, the probability that exactly two of the four live in their own household and are income-qualified is:
The probability that exactly two of the four persons selected live in their own household and are income-qualified is approximately 0.1075 or 10.75%.
Probability of success (p): The probability that a person selected from the population lives in their own household and is income-qualified. From the given information, p = 0.84.
Probability of failure (q): The probability that a person selected from the population does not live in their own household and is not income-qualified. Since q is the complement of p, we have q = 1 - p = 1 - 0.84 = 0.16.
Number of trials (n): We are selecting four persons from the population, so n = 4.
Number of successes (k): We want exactly two persons to live in their own household and be income-qualified, so k = 2.
Now we can calculate the probability using the binomial probability formula:
P(X = k) = C(n, k) * p^k * q^(n-k)
where C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k! * (n-k)!).
Plugging in the values, we get:
P(X = 2) = C(4, 2) * (0.84)²* (0.16)⁽⁴⁻²⁾
Calculating the binomial coefficient:
C(4, 2) = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = 6.
Substituting the values:
P(X = 2) = 6 * (0.84)² * (0.16)⁽⁴⁻²⁾
Calculating the result:
P(X = 2) = 6 * 0.84² * 0.16²
= 6 * 0.7056 * 0.0256
= 0.1075 (approximately)
Therefore, the probability that exactly two of the four persons selected live in their own household and are income-qualified is approximately 0.1075 or 10.75%.
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Evaluate sin2 (pi/4) + cos2 (pi/4).
Answer:
\(sin^2(\pi/4)+cos^2(\pi/4)=1\)
Step-by-step explanation:
Notice that you don't need to evaluate the actual sin and cos functions, since you are in the presence of a well known Pythagorean identity that states that this type of addition of squares for the same angle should equal 1:
\(sin^2(x)+cos^2(x)=1\)
So, as long as the angle "x" is the same in both trig functions, this addition should render "1" (one).
Because in this case the angle involved is the same (in both cases pi/4), the identity is valid.
the hypotenuse of a right triangle has a length of 14 units and side that is 9 units long. which equation can be used to find the length of the reaming side?
According to Pythagorean theorem:
c² = a² + b², where a and b legs and c- hypotenuseTo find the missing length of the leg we'll convert the equation:
14² = 9² + x²Simplify:
196 = 81 + x²x² = 196 - 81x² = 115x = √115\(\large\bf{\underline{\underline{\mathfrak{Question}:}}}\)
The hypotenuse of a right triangle has a length of 14 units and side that is 9 units long. which equation can be used to find the length of the remaining side?
\(\large\bf{\underline{\underline{\mathfrak{Solution}:}}}\)
To solve the problems of a right angle triangle we commonly used Pythagoras theorem. It is the most widely used theorem which helps in finding the missing length of a right angle triangle.
According to Pythagoras theorem, the sum of square of base and the square of perpendicular give us square of hypotenuse.
\(:{\Longrightarrow{\large{\rm{H^2=P^2+B^2}}}}\)
In a right angle triangle there are two legs and a hypotenuse.
Given that,
\({:\Longrightarrow{\small{\rm{Hypotenuse\:of\:a\:right\:triangle=14\:units.}}}}\)
\(:{\Longrightarrow{\small{\rm{A\:side\:of\:a\:right\:triangle=9\:units.}}}}\)
By putting these values in the Pythagoras theorem we get;
\(:{\Longrightarrow{\small{\rm{14^2=9^2+B^2}}}}\)
Let B = x
\(:{\Longrightarrow{\small{\rm{196=81+x^2}}}}\)
\(:{\Longrightarrow{\small{\rm{196-81=x^2}}}}\)
\(:{\Longrightarrow{\small{\rm{115=x^2}}}}\)
\(:{\Longrightarrow{\small{\rm{\sqrt{115}=x}}}}\)
(Please answer, 100 points)
Find the circumference of each of the following circles. Use 3.14 for π.
(The last one is 25 mi across.)
These were my answers, are they correct:
6a. 53.38
6b. 100.48
6c. 122.46
6d. 78.5
use the formula 2πr
106.76 300.962×3.14×(1/2)×39 = 122.4678.5the c bit I did the whole process cuz the diameter is given and for the d bit i thought what you were trying to say is 25 diameter.
hope it helps and don't forget to put the units wherever necessary.!!!!
when the film is placed into the xcp holder with the smooth side of the film towards the throat, after processing it will appear dark. t/f
The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will lighter, not darker.
The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.
Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.
After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.
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What is the gradient of the line y 7x 3?
The given expression is of the form y=mx+c. Comparing, we get the slope as 7.
The direction and steepness of a line are represented numerically by the slope or gradient of the line. It provides the ratio of how much y rises when x rises by a particular amount. The general form is therefore y=mx+c, where c represents the y-intercept and m represents the slope. This form gives the slope-intercept form.
Given the expression is y=7x+3. Comparing this expression with the general form we get, slope or gradient as 7 and y-intercept as 3. Therefore, the required answer is 7.
The complete question -
What is the gradient of the line y=7x+3?
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Helpppp I have no idea what to do
Answer:
Step-by-step explanation:
All I am saying its not 1 or 3
Find the next term in each sequence. 2,4,8,16, . . . . . .
Answer:2,4,8,16,32,64,128,256,512,1024,2048,4096
Step-by-step explanation:
You just mutiply the number with 2
sec θ + tan θ / tan θ - sec θ + tan θ / sec θ =cos θ cot θ
sec θ + tan θ / tan θ - sec θ + tan θ / sec θ =cos θ cot θ is equivalent to (1+2sin θ)/cos² θ = 1/sin θ.
Let's simplify the given expression:
sec θ + tan θ / tan θ - sec θ + tan θ / sec θ= [(sec θ * sec θ + tan θ * tan θ)/sec θ * tan θ] + [(sec θ * tan θ + sec θ * tan θ)/sec θ * tan θ]
= (1/cos² θ) + (2sin θ/cos² θ)
= (1+2sin θ)/cos² θcos θ cot θ= cos θ/cos θ * sin θ= 1/sin θ
Thus,sec θ + tan θ / tan θ - sec θ + tan θ / sec θ =cos θ cot θ is equivalent to (1+2sin θ)/cos² θ = 1/sin θ.
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In a high school with 1,500 students, which would be the best way to select a random sample of students in order to collect data about teenagers' preferences in music?
A. Ask every other member of the chorus.
B. Ask every student in an AP Calculus class.
C. Ask every 20th student during lunch in the school cafeteria.
D. Ask every 100th student who attends the school's pep assembly.
PLEASE HELPPPPP
The best way to select a random sample of students is "Ask every 20th student during lunch in the school cafeteria".
What is random sampling?The model approach to picking a random sample of students to gather data on teens' music tastes is to ensure that each student has an equal chance of getting chosen. This is known as random sampling, and it assists in reducing biases and ensuring that the sample is representative of the total population.
Option C, Asking every 20th kid during lunch in the school cafeteria, would be the best decision among the possibilities presented.
By picking every 20th student, a decent amount of randomization is achieved, and each student has an equal chance of being included in the sample.
When compared to the other choices, this technique generates a more representative sample.
Hence, the correct answer is C.
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b. in general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; p-value method; critical value method?
The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.
What is the confidence interval?
A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.
In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.
On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.
To summarize:
- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.
- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.
- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.
Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.
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Lesson Application Problem 521
Rane Charles and Samran na 5 race on Saturday. They were the top 4 Binishers. Here are
Cras 25.9 minutes
Randy 32.2 minutes
Charte 32.28 minutes
Sam: 25.85 minutes
who won first place? Who won second place? Third? Fourth?
Answer:
1st to 4th: Sam, Cras, Randy, Charte
Step-by-step explanation:
The places are determined by putting the times in increasing order.
time, place, name
25.85, 1st place, Sam
25.90, 2nd place, Cras
32.20, 3rd place, Randy
32.28, 4th place, Charte
_____
Additional comment
Sometimes it is easier to compare values when they all have the same number of decimal places.
The domain in a set of ordered pairs is always the y-coordinate.
True or False
Answer: False
Step-by-step explanation: It is false because the y-coordinate is the range.
Earth has a diameter of 7,926 miles. What is its diameter in kilometers? (1 mile = 1.6 kilometers)
A. 49,553 km
B. 120,586 km
C. 1,392,650 km
D. 12,682 km
The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.
To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.
Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:
Diameter in kilometers = Diameter in miles × Conversion factor
Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile
Diameter in kilometers = 12,681.6 kilometers
Rounding this value to the nearest whole number, we get 12,682 kilometers.
Therefore, the correct answer is option D: 12,682 km.
Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.
Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.
Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.
In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.
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In the diagram, the radius is 7 and tangent AB has length of 24. Determine the length of OA rounded to the nearest whole number
Given the radius r and the tangent line AB, the length of the line OA is 24 units
How to determine the length OA?The radius r and the tangent line AB meet at a right angle.
By Pythagoras theorem, we have:
AB² = OA² + r²
So, we have:
24² = OA² + 7²
Rewrite as:
OA² = 24² - 7²
Evaluate
OA² = 527
Take the square root of both sides
OA = 23
Hence, the length of OA is 24 units
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The monthly profit of an artist co-op store if she were equally on the 13 orders if the profit one month is 3849 which is the best estimate of each owner share
Answer:
The best estimate of each owner share is 296
Step-by-step explanation:
Now, we know that that the profit was shared equally and we have 13 recipients of the share
The best estimate for each owner’s share is to divide the amount shared in the month by the number of the recipients
That would be 3,849/13 = 296.08
This is best estimated as 296
A pack of 6 batteries of the same type cost £2.79 By calculating the price per battery,
determine if this a better value. you must show your working out
\(\large{\rm{\underline{\underline{Answer:}}}}\)
Given, 6 batteries for £2.79
(They are of same type, so each of them are of same cost. )
~Simply divide the total price of 6 batteries by 6 to get the price of each battery,
\( = \dfrac{£2.79 }{6} \)
\( = £ \dfrac{279}{100 \times 6} \)
\( = £ \dfrac{46.5}{100} \)
\( = £0.465\)
Thus, cost of each battery is £ 0.465 (ans)
¿Para qué sirven las viñetas o numerales en un juego de patio? rapido las necesito ya porfavor
Las viñetas o numerales en un juego de patio se utilizan para marcar el progreso de un juego o actividad.
Por ejemplo, en un juego de rayuela, cada viñeta representa un paso hacia el objetivo final y los jugadores avanzan saltando sobre las viñetas en un orden determinado.
En otros juegos, las viñetas o numerales se utilizan para llevar un registro de la puntuación de los jugadores o para determinar el orden en que deben realizarse las acciones.
En resumen, las viñetas o numerales son un elemento importante en muchos juegos de patio y pueden ser utilizadas de diversas maneras para marcar el progreso, la puntuación o el orden de las acciones en un juego.
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True or False
Stock Prices are easy to predict?
oml, this is false. truely false!!
hope this helps ya! :)
Find the output, y, when the input, x, is -5.
The output, y, when the input, x, is -5 is -2
How to determine the value of the output y?The input is given as:
-5
This means that
x = -5
This is so because x represents the input
From the graph, we have the following highlight
The line of the graph passes through the point x = -5
On the graph;
When x = -5, the value of y is -2
This means that the output, y, when the input, x, is -5 is -2
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