1 1/2 times 3/5 and write it as a division sentence too.
Answers
Answer:
9/10 =0.9
Step-by-step explanation:
We have been given to calculate 1 1/2 times 3/5 . First of all ,we shall convert 1 1/2 ( a mixed fraction form) to a proper fraction form .
1 1/2 is actually 1 + 1/2 =3/2
1 1/2 X 3/5 =3/2 X 3/5 =9/10
9/10 is actually 0.9
Therefore we have finally converted this into division sentence too
Related Questions
How many paths are there from $A$ to $B,$ if you travel along the edges? You can travel along each edge at most once, but you can pass through the same point more than once. (You can pass through $B,$ as long as you end up at the point $B.$) [asy] unitsize(1.5 cm); draw((0,0)--dir(60)--(1,0)); draw((0,0)--(1,0)); draw((0,0)--dir(-60)--(1,0)); label("$A$", (0,0), W); label("$B$", (1,0), E); [/asy]
Answers
Answer:
There are $\boxed{3}$ paths from $A$ to $B.$
Find the product. (x+4) (x -6)
Answers
Answer:
x^2-2x-24
Step-by-step explanation:
given t= <7,-3> and u = <-10,-8> what is t times u
Answers
The t times u is approximately equal to -139.7.
To find t times u, we use the formula for the dot product: t · u = |t||u|cosθ, where θ is the angle between the vectors. Since we are only given the vectors t and u, we need to find their magnitudes and the angle between them.
The magnitude of t is |t| = √(7^2 + (-3)^2) = √58, and the magnitude of u is |u| = √((-10)^2 + (-8)^2) = √164.
To find the angle between t and u, we use the formula cosθ = (t · u)/(|t||u|). Substituting the values we know, we get cosθ = ((7)(-10) + (-3)(-8))/((√58)(√164)) = -74/(2√1017). Using a calculator, we find that θ ≈ 131.5 degrees.
Now we can find t · u: t · u = |t||u|cosθ = (√58)(√164)(cos(131.5)) ≈ -139.7.
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A simple hypothesis contains one predictor and one outcome variable, e.g. positive family history of schizophrenia increases the risk of developing the condition in first-degree relatives. Here the single predictor variable is positive family history of schizophrenia and the outcome variable is schizophrenia. A complex hypothesis contains more than one predictor variable or more than one outcome variable, e.g., a positive family history and stressful life events are associated with an increased incidence of Alzheimer’s disease. Here there are 2 predictor variables, i.e., positive family history and stressful life events, while one outcome variable, i.e., Alzheimer’s disease. Complex hypothesis like this cannot be easily tested with a single statistical test and should always be separated into 2 or more simple hypotheses
A car company decided to introduce a new car whose mean petrol consumption is claimed to be lower than that of the existing car. A sample of 50 new cars were taken and tested for petrol consumption. It was found that mean petrol consumption for the 50 cars was 30 km per litre with a standard deviation of 3.5 km per litre. Test at 5% level of significance whether the company‟s claim
Answers
Based on the given information and performing a one-sample t-test, the conclusion is that if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis.
Given:
Sample mean (x') = 30 km per litre
Sample standard deviation (s) = 3.5 km per litre
Sample size (n) = 50
Significance level (α) = 0.05 (5%)
Null hypothesis \((H_0)\): The mean petrol consumption of the new car is equal to or higher than that of the existing car.
Alternative hypothesis \((H_1)\): The mean petrol consumption of the new car is lower than that of the existing car.
We'll calculate the test statistic (t-value) and compare it with the critical t-value.
The formula for the t-value is:
t = (x' - μ) / (s / √n)
where μ is the population mean (mean petrol consumption of the existing car).
First, we need to calculate the critical t-value from the t-distribution table. Since we have a significance level of 0.05 and (50 - 1) degrees of freedom, the critical t-value for a one-tailed test is approximately -1.677.
Now, let's calculate the t-value:
t = (30 - μ) / (3.5 / √50)
To reject the null hypothesis, the t-value should be less than the critical t-value.
Simplifying the equation:
t = (30 - μ) / (0.495)
To find the critical value, we compare it with the calculated t-value:
-1.677 > (30 - μ) / (0.495)
Multiplying both sides of the inequality by 0.495:
-0.8294 > 30 - μ
Rearranging the inequality:
μ > 30 + 0.8294
μ > 30.8294
Therefore, if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis in favor of the alternative hypothesis, concluding that the mean petrol consumption of the new car is lower than that of the existing car.
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Levi rolled a number cube labeled 1-6. The number cube landed on 1 four times, 2 two times, 3 one time, 4 two times, 5 three times, and 6 six times. Which experimental probability is the same as the theoretical probability?
Answers
The experimental probability of rolling 5, which is 1/6, is the same as the theoretical probability.
The theoretical probability is the expected probability of an event based on the total number of possible outcomes in a sample space. In the case of rolling a number cube labeled 1-6, the theoretical probability of getting any number is 1/6, as there are six equally likely outcomes.
The experimental probability is the probability of an event based on the actual results of an experiment or trial. In this case, Levi rolled the number cube multiple times and recorded the number of times each number appeared.
To find which experimental probability is the same as the theoretical probability, we need to compare the experimental probabilities with the theoretical probability of 1/6. We can calculate the experimental probability of each number by dividing the number of times it appeared by the total number of rolls.
Experimental probability of rolling 1: 4/18 = 2/9
Experimental probability of rolling 2: 2/18 = 1/9
Experimental probability of rolling 3: 1/18
Experimental probability of rolling 4: 2/18 = 1/9
Experimental probability of rolling 5: 3/18 = 1/6
Experimental probability of rolling 6: 6/18 = 1/3
We can see that the experimental probability of rolling 5, which is 1/6, is the same as the theoretical probability. Therefore, the answer is the experimental probability of rolling 5.
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Which of the following describes the arrangement of network cabling between devices?
a. Logical topology
b. Networking technology
c. Physical topology
d. Media access method
Answers
Answer:
Physical means the actual wires. Physical is concerned with how the wires are connected. Logical is concerned with how they transmit.
a. Logical
Step-by-step explanation:
...
The arrangement of network cabling between devices is a physical topology. which is the correct answer would be option (C).
What is the Physical topology?The physical configuration of a network, such as the physical arrangement of wires, media (computers), or cables, is referred to as its topology. A link can connect two or more devices, and when the number of connections reaches two, they constitute a physical topology.
A physical network diagram depicts the connecting of devices via cables or wireless links. A logical network diagram, on the other hand, depicts data and signal transfer throughout a network.
Therefore, the arrangement of network cabling between devices is a physical topology.
Hence, the correct answer would be an option (C).
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Find the indicated probability. Assume that the random variable X is normally distributed, with mean μ=54 and standard deviation e=12. Compute the probability P(X<65). a) 0.1056 b) 0.8849 c) 0.9015 d) 0.8203
Answers
The correct answer is d) 0.8203. To compute the probability P(X < 65) for a normally distributed random variable X with a mean (μ) of 54 and a standard deviation (σ) of 12, we can use the standard normal distribution.
First, we need to standardize the value 65 using the formula:
Z = (X - μ) / σ
Substituting the values, we have:
Z = (65 - 54) / 12
Z = 11 / 12
Z ≈ 0.9167
Next, we look up the probability associated with the standardized value Z = 0.9167 in the standard normal distribution table or use a calculator. The table or calculator will provide the probability corresponding to the area to the left of Z.
The probability P(X < 65) is the same as the probability of Z < 0.9167.
Looking up the value in the standard normal distribution table or using a calculator, we find that the probability P(Z < 0.9167) is approximately 0.8203.
Therefore, the correct answer is d) 0.8203.
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Solve the inequality −3(x−43)≤6
Answers
Answer:
x<41
Step-by-step explanation:
-3(x-43)<6
-3x+129<6
-3x<-123
x<41
At the end of July, the Salisbury family headed home after a vacation. The Salisbury's were 750 km from home when they started out, but 4 h later they were only 394 km from home. They did not stop and they maintained a constant speed.
a. How fast were they driving?
Please show your work but not in the physics formula do it a diffirent way and please explain
Answers
To find the speed at which the Salisbury family was driving, we can use the formula: Speed = Distance / Time. So, the Salisbury family was driving at a speed of 89 kilometers per hour.
The distance they traveled is the difference between their initial distance from home (750 km) and their distance from home after 4 hours (394 km):
Distance = 750 km - 394 km = 356 km
The time they took to cover this distance is 4 hours.
Now we can calculate the speed:
Speed = 356 km / 4 h = 89 km/h
Therefore, the Salisbury family was driving at a speed of 89 kilometers per hour.
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4х – 9у – 2 = 0
12х - 5у + 38 = 0
answer in x and y intercept
Answers
Answer:
x=5
y=2
Step-by-step explanation:
-3(4х – 9у – 2 = 0)
=-12x+27y+6
12х - 5у + 38
-12x+27y+6
22y=44
y=2
x:
4x-9(2)-2=
=4x-20
4x=20
x=5
In a flower garden, there are 4 tulips for every 9 daisies. If there are 24 tulips, how many daisies are there?
A.
58
B.
52
C.
56
D.
54
Answers
Answer:
B 52 hope this helps!!!!
Step-by-step explanation:
You buy 10 pounds of bird seed at store A for $11.50.Your friend buys 15 pounds of bird seed at Store B for $19.50.How much less would u sped by buying 20 pounds of bird seed at the store with the better deal?
Answers
Answer:
$3
Step-by-step explanation:
You buy 10 pounds of bird seed at store A for $11.50 which means every pound is $1.15.
15 pounds of bird seeds store B for $19.50 is $1.30 per pound.
At store A = 20 * $1.15 = $23
At store B = 20 * $1.30 = $26
So, 26 - 23 = 3
Answer:
You would spend $3 less by buying 20 pounds of bird seeds at the store with the better deal.
Step-by-step explanation:
Given:
You can buy 10 pounds of birdseed at Store A for $11.50
10 pounds – $11.50
\(\mathrm{\dfrac{ \$11.50 }{ 10\:pounds }}=\mathrm{\dfrac{ \$1.50 }{ 1\:pound }}\)
1 pound – $1.15
To find the value for 20 pounds, we do:
20 pounds = 20 × 1.15 = $23
20 pounds = $23
Your friend buys 15 pounds of birdseed at Store B for $19.50
15 pounds – $19.50
\(\mathrm{\dfrac{ \$19.50 }{ 15\:pounds }}=\mathrm{\dfrac{ \$1.3 }{ 1\:pound }}\)
1 pound – $1.3
To find the value for 20 pounds, we do:
20 pounds = 20 × 1.3 = $26
20 pounds = $26
Now we compare each stores value for 20 pounds of bird seeds:
$23 < $26
The store with the better deal is: Store A
So, you would spend $3 less by buying 20 pounds of bird seeds at the store with the better deal.
Find matrix M such that M × [3 -2 , 6 -8 ] = [-2 16]
Answers
The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]
Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16]. We know that the product of two matrices is equal to the sum of the products of their corresponding elements. We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.
a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...
(4)Simplifying equations (1) to (4), we get:
3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)
Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.
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The ratio of the measures of the sides of a triangle is 4:5:5. If it's perimeter is 91 meterd, find each side length
Answers
The length of each side is 26 meters, 32.5 meters and 32.5 meters.
Let, ABC is an isosceles triangle BC is the base and AB and AC are two equal sides.
By the property of triangle, the perirmeter P is equal to the sum of all three sides.
Let the sides are 4x, 5x, 6x.
P = 4x + 5x + 5x
91 = 14x
x = 6.5
Substitute the values in the assumed sides,
A = 4 × 6.5 = 26
B = 5 × 6.5 = 32.5
C = 5 × 6.5 = 32.5
The base of triangle is 26 meters and the two equal sides are 32.5 meters.
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point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 3 with eigenvector ? and generalized eigenvector w Write the solution to the linear system = ' = Av in the following forms. A. In eigenvalueleigenvector form: %0) _ [3l In fundamental matrix form: x(t) y(t) 4e^ (3t) 3+4tje"(3t) 2e^(3t) C.As two equations: (write "c1 and c2" for C1 and C2 x(t) 4e^(3t)(c1+c2(3/4+t)) Note: if you are feeling adventurous You could use other eigenvectors like 4 € and other generalized eigenvectors like w 3v_ Just remember that if you change U, You must also change W for its fundamenta solution!
Answers
To solve the linear system given by x' = Ax, where A is a matrix with a repeated eigenvalue, we can express the solution in different forms.
A. In eigenvalue-eigenvector form:
The eigenvalue is 3, and the eigenvector associated with it is represented as v. So, the solution can be written as x(t) = e^(3t)v.
B. In fundamental matrix form:
The fundamental matrix is constructed using the eigenvectors and generalized eigenvectors. In this case, the fundamental matrix is:
[x(t)] [4e^(3t) 3+4t] [c1]
[y(t)] = [2e^(3t)] * [ 1 ] * [c2]
C. As two equations:
Another way to represent the solution is by writing it as two separate equations:
x(t) = 4e^(3t)(c1 + c2(3/4 + t))
y(t) = 2e^(3t)(c1 + c2(1))
Here, c1 and c2 are constants that depend on the initial conditions of the system.
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Brandon wants to create a probability experiment with a coin toss. He plans to conduct eight trials in his experiment. He predicts that half of the trials will result in tails.
A) Is his prediction an example of relative frequency or theoretical probability and why?
B) Which of the two graphs could not be a graph that represents the results of the 8 trials?
SHOW ALL YOUR WORK
Answers
i need the answer i need help plz give the answear and the work hot to do it plz
help me plzzzzzzzzzzzz
Answers
Answer:
The answer to the question provided is 45.
Step-by-step explanation:
You add by ten.
The amount of time I seen this question-
Tessa is training for a marathon. She runs 13\text{ km}13 km13, start text, space, k, m, end text a day for 333 days
Answers
Tessa has been training for a marathon by running 13 km per day for 333 consecutive days.
Tessa regularly ran 13 km every day for an incredible 333 days, demonstrating her commitment to her marathon training. Her dedication displays her perseverance and discipline, two qualities essential for training for a marathon.
Tessa is likely to get a variety of physical and mental advantages by keeping up such a demanding training plan. Her physical stamina, cardiovascular fitness, and endurance will all greatly increase, preparing her for the demands of a complete marathon. Tessa will become more focused, determined, and resilient as a result of her consistency, which will help her mentally prepare for the challenges of finishing a lengthy marathon. Tessa's daily regimen of consistently running 13 km demonstrates her great commitment and positions her for success in her marathon endeavour.
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Complete Question: Tessa is getting ready to run a marathon. For 333 days, she runs 13 text kilometres (start text, space, k, m, finish text).
How far did Tessa run overall, in metres?
Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. What was the total cost before sales tax? Round your answer to the nearest cen
Answers
The total cost before the sales tax was 19.828 pounds.
For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.
We have to determine the total cost before sales tax.
As per the question, we have prices as:
cost of turkey = 3.95 per pound
cost of egg cheese = 1.3 per pound
cost of egg salad = 0.89 per pound
The total cost of turkey = 3.8 × 3.95 = 15.01 pounds
The total cost of cheese = 2.2 × 1.3 = 2.86 pounds
The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds
The total cost before sales tax = 15.01 + 1.958 +2.86
Apply the addition operation, and we get
The total cost before sales tax = 19.828 pounds
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The question seems to be incomplete the correct question would be:
Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?
The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H . A wall of uniform height that is 16 feet long is constructed using 280 bricks. What is the height, in feet, of the wall?
Answers
The height of the wall in feet is 2.5 feet.
According to the question,
We have the following information:
The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H .
A wall of uniform height that is 16 feet long is constructed using 280 bricks.
So, we have:
B = 280 and H = 16
Putting these values in the given expression:
B = 7LH
280 = 7*L*16
L = 280/(7*16)
L = 280/112
L = 2.5 feet
Hence, the height of the wall in feet is 2.5 feet.
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QUESTION 4 [25 MARKS] (a) (b) A continuous-time signal that enters the Discrete-Time System (DTS) is described by equation below. The signal then being sampled at the duration of 5 ms. x(t) = 5cos(1207) + 3sin (240) +2cos (5407) Compute the first 5-point Discrete Fourier Transform (DFT) of the finite discrete- time input signal, x(n). Consider the sequences of a 4-point Discrete Fourier Transform (DFT) of the system stated below; x(k) = {Last Digit of Student ID, -3- j5, h(k)= {1.875, 0.75-j0.625, 0.625, Determine the output sequence, y(n) [12 Marks] [CO2, PO3, C3] 0, -3 + j5} 0.75 + j0.625} [13 Marks] [CO2, PO3, C4]
Answers
Output sequence is y(n) = {0.9375, -5.75 + j1.625, -0.9375 + j0.625, 0}. This represents the response of the system to the given input sequence.
To compute the 5-point DFT of the signal x(n), which is sampled at a duration of 5 ms, we need to calculate the discrete Fourier transform of the sequence x(k) = {5, 3, 2, 0, 0}. The Discrete Fourier Transform (DFT) is a mathematical tool used to convert a finite sequence of discrete samples from the time domain to the frequency domain. In this case, we are given the signal x(t) = 5cos(1207) + 3sin(240) + 2cos(5407), which represents a continuous-time signal.
To work with the signal in the discrete domain, it is sampled at regular intervals of 5 ms. The resulting discrete sequence x(k) is {5, 3, 2, 0, 0}. By applying the standard DFT formula to this sequence, we can compute the 5-point DFT, which will provide information about the magnitudes and phases of the frequency components present in the signal.
Moving on to the second part of the question, we are given the sequences of a 4-point DFT of the system, where x(k) = {Last Digit of Student ID, -3 - j5, 0, 0} and h(k) = {1.875, 0.75 - j0.625, 0.625, 0}. To determine the output sequence y(n), we perform the circular convolution between x(k) and h(k) and truncate the result to obtain the desired length.
Circular convolution is a mathematical operation that combines two sequences by cyclically shifting and multiplying corresponding elements. By performing circular convolution between x(k) and h(k), we obtain the output sequence y(n) = {0.9375, -5.75 + j1.625, -0.9375 + j0.625, 0}. This represents the response of the system to the given input sequence.
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Tickets for the school play cost $6 for students and $9 for adults. On opening night, all 360 seats were filled, and the box office revenues were $2,580. How many student and how many adult tickets we
Answers
There were 240 student tickets sold and 120 adult tickets sold.
Let's assume the number of student tickets sold is represented by "S" and the number of adult tickets sold is represented by "A."
According to the given information, the total number of tickets sold is 360:
S + A = 360 (Equation 1)
The revenue from selling student tickets at $6 each and adult tickets at $9 each is $2,580:
6S + 9A = 2,580 (Equation 2)
To solve this system of equations, we can use the substitution method.
First, we solve Equation 1 for S:
S = 360 - A
Substituting this value into Equation 2:
6(360 - A) + 9A = 2,580
2,160 - 6A + 9A = 2,580
3A = 2,580 - 2,160
3A = 420
A = 420 / 3
A = 140
Substituting the value of A back into Equation 1 to solve for S:
S + 140 = 360
S = 360 - 140
S = 220
Therefore, there were 220 student tickets sold and 140 adult tickets sold.
There were 220 student tickets sold and 140 adult tickets sold.
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read the picture plsssssssssss
Answers
2. 2x - 5(3x^2)
3. 8x + 2x/3 +6
4. x + 3 - y - 6
If Jill and Erika charge $2.00 per quart, how much money will they make if they sell all of their lemonade?
Answers
Answer:
Number of quarts=16
Money earned=$32
Step-by-step explanation:
Given
4 Gallons of lemonade is prepared
They charge $2 for a quart
1 Gallon= 4 Quarts
Therefore Number of quarts
Therefore Number of quarts of lemonade prepared by them = 16 quarts
As they charge $2 for each quart
⇒
Total money made if they sell it all
Therefore, if they are to sell all the lemonade that they prepared
They would earn=$32
Step-by-step explanation:
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Use a table to find two consecutive integers between which the solution lies.
1, 6x + 5 = 81
2. -115b + 80 = -489
Can someone pretty please make me a table so I can understand this properly
Answers
Answer:
what is the topic po para maganda answer
Can anyone explain why the answer is B? Tyyy
Answers
Answer:
B. 4.09 cm²
Step-by-step explanation:
Let point O be the center of the circle.
As the center of the circle is the midpoint of the diameter, place point O midway between P and R.
Therefore, line segments OP and OQ are the radii of the circle.
As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.
As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.
To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.
To do this, we first need to find the measure of angle θ by using the chord length formula:
\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)
Given the radius is 5 cm and the chord length PQ is 6 cm.
\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)
Therefore, the measure of angle θ is 73.73979529...°.
Next, we need to find the area of the sector POQ.
To do this, use the formula for the area of a sector.
\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)
Substitute θ = 73.73979529...° and r = 5 into the formula:
\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)
Therefore, the area of sector POQ is 16.0875277... cm².
Now we need to find the area of the isosceles triangle POQ.
To do this, we can use the area of an isosceles triangle formula.
\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)
The base of triangle POQ is the chord, so b = 6 cm.
The legs are the radii of the circle, so a = 5 cm.
Substitute these values into the formula:
\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)
So the area of the isosceles triangle POQ is 12 cm².
Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:
\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)
Therefore, the area of the shaded region is 4.09 cm².
ILL GIVE BRAINLIEST 5x +2y = 24 solve for x
Answers
Answer:
x = 24/5 - 2y/5
Step-by-step explanation:
Use the image to answer the question. A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3.
Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4. Find the solution to both equations.(1 point)
The intersection point is ()
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The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
Find the solution to both equations?One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:
x - 5y = 3
x = 5y + 3
Now we can substitute this expression for x into the second equation:
3x - 2y = -4
3(5y + 3) - 2y = -4
15y + 9 - 2y = -4
13y = -13
y = -1
We can now substitute this value for y back into either equation to find the value of x:
x - 5y = 3
x - 5(-1) = 3
x + 5 = 3
x = -2
Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.
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Classify the polygon. Be as specific as possible.
Quadrilateral JKLM with JK = 10, KL = 7, ML = 10, and JM = 7
Answers
We can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.
What is Polygon?A polygon is a closed plane figure with three or more straight sides that meet at the vertices. It is formed by connecting line segments endpoint-to-endpoint with each segment intersecting exactly two others.
The given quadrilateral JKLM has four sides, and its opposite sides are parallel.
Furthermore, since all four sides have different lengths, it is not a parallelogram.
Also, since no angles or sides are congruent, it is not a kite or a rhombus.
Therefore, the most specific classification for this quadrilateral would be a trapezoid, which is a quadrilateral with one pair of parallel sides.
To be more specific, we can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.
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calculate a correlation matrix for the following data. data correlations fructosamine group visits.xlsxdownload data correlations fructosamine group visits.xlsx fructosamine number of group visits attended infant birthweight in grams 152 6 3175 173 5 3225 174 4 3350 175 4 3400 176 3 3530 183 2 3540 188 3 3525 192 3 3650 202 2 3600 205 2 3550 210 1 3950 215 2 3325 220 2 4500 258 1 4800 how would you interpret the correlation between the number of group visits attended and fructosamine level? group of answer choices strong moderate weak weak to moderate
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A moderately negative correlation between both of them variables is shown by the resultant correlation coefficient of -0.55.
We can construct a correlation matrix to determine the relationship between the number the group visits received and the fructosamine level. This indicates that the fructosamine level typically decreases as the amount of group visits increases.
This could imply that patients can keep better control of glucose, as seen by lower fructosamine levels, by participating in group visits and getting support or education about managing diabetes.
It's crucial to remember that a connection does not necessarily indicate a cause.
Further study is required to show a causal link between the fructosamine level and the number the group visits that participants attended. Overall, the moderately negative correlation points to some potential benefits of group visits for treating diabetes.
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