The value of measure of angle WPN is,
⇒ m ∠WPN = 108°
We have to given that;
Parallel lines EN, BH, and RK, with transversal PW are shown.
And, m ∠ BMV = 108° and m ∠KVS = 72°
Now, We get by definition of vertically opposite angle;
m ∠ BMV = m ∠PWN = 108°
Hence, By definition of alternate angle we get;
⇒ m ∠PWN = m ∠WPN = 108°
Thus, The value of measure of angle WPN is,
⇒ m ∠WPN = 108°
Learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ1
A ship headed due east is moving through the water at a constant speed of 8 miles per hour. However, the true course of the ship is 60°. If the currents are a constant 4 miles per hour, what is the ground speed of the ship? (Round your answer to the nearest whole number. )
The ground speed of the ship is approximately 10 miles per hour.
To calculate the ground speed, we need to use vector addition. The ship's velocity can be broken down into two components: its speed in the easterly direction and its speed in the northerly direction. The easterly component is 8 miles per hour (since the ship is moving due east), and the northerly component can be found using trigonometry: northerly component = 8 * sin(60°) ≈ 6.93 miles per hour
Now, we need to take into account the effect of the currents, which are moving in a southerly direction. Again using vector addition, we can find the resultant velocity (i.e., the velocity of the ship relative to the ground) by adding the ship's velocity vector to the current's velocity vector. Since the current is moving due south, its velocity vector has no easterly component, but its southerly component is 4 miles per hour. resultant velocity = (8, 6.93) + (0, -4) = (8, 2.93)
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity: |resultant velocity| = [tex]\sqrt{} (8^2 + 2.93^2)[/tex]≈ 8.6 miles per hour. Rounding to the nearest whole number, the ground speed of the ship is approximately 10 miles per hour.
Learn more about Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ4
The percentage of the moon's surface that is visible to a person standing on the Earth varies with the time
since the moon was full.
The moon passes through a full eyele in 28 days, from full moon to full moon. The
maximum percentage of the moon's surface that is visible is 50%. Determine an equation, in the form
P=Acos(Bt)+C for the percentage of the surface that is visible, P, as a function of the number of days, t,
since the moon was full. Show the work that leads to the values of A, B, and C
The equation is P = [tex]25cos(0.224t) + 50[/tex], where P represents the percentage of the moon's surface visible and t is the number of days since the moon was full.
How to derive equation for moon visibility?To determine an equation for the percentage of the moon's surface visible as a function of the number of days since the moon was full, we can use the cosine function [tex]P = Acos(Bt) + C[/tex], where P represents the percentage visible, t is the number of days since full moon, A is the amplitude, B is the frequency, and C is the vertical shift.
Given that the maximum percentage visible is 50%, we know that C = 50. The period of the function is 28 days, so we can calculate B using the formula B = 2π/period = 0.224. The amplitude A can be calculated as half of the maximum percentage visible, or A = 25.
Therefore, the equation for the percentage of the moon's surface visible as a function of the number of days since full moon is P = 25cos(0.224t) + 50.
Learn more about moon's
brainly.com/question/30427719
#SPJ11
An air temperature of 30°C is equal to
1. -1°F
2. 68°F
3. 83°F
4. 86°F
Answer:
86 degrees fahrenheit
Step-by-step explanation:
(30°C × 9/5) + 32 = 86°F
Find the standard matrix for the linear transformation T:R2 + R2 that shears horizontally, with T "((A)) = (-1,67)
The standard matrix for the linear transformation T that shears horizontally is T = [(1 1) (0 1)] [(1 0) (-6 1)] [(1 1) (0 1)]^(-1) = [(1 -6) (0 1)].
To find the standard matrix for the linear transformation T that shears horizontally, we need to determine the matrix that transforms the standard basis vectors e1 and e2 into the shear vectors s1 and s2. The shear vectors are obtained by applying the linear transformation T to the standard basis vectors e1 and e2, respectively.
The shear vector s1 is obtained by shearing the point (1,0) horizontally by -1 unit, and then vertically by 6 units. This gives us s1 = (-1,6). Similarly, the shear vector s2 is obtained by shearing the point (0,1) horizontally by -1 unit and leaving it vertically unchanged. This gives us s2 = (-1,1).
To obtain the standard matrix for the linear transformation T, we need to find the matrix A that transforms the standard basis vectors e1 and e2 into the shear vectors s1 and s2, respectively. We can express A as [s1 s2] [e1 e2]^(-1), where [s1 s2] is a 2x2 matrix whose columns are the shear vectors, and [e1 e2]^(-1) is the inverse of the 2x2 matrix whose columns are the standard basis vectors.
Substituting the values of s1, s2, e1, and e2, we get:
A = [(1 -1) (6 1)] [(1 0) (0 1)]^(-1) = [(1 -1) (6 1)] [(1 0) (0 1)] = [(1 -1) (6 1)]
Therefore, the standard matrix for the linear transformation T that shears horizontally is T = [(1 1) (0 1)] [(1 -1) (6 1)] [(1 1) (0 1)]^(-1) = [(1 -6) (0 1)].
For more questions like Matrix click the link below:
https://brainly.com/question/28180105
#SPJ11
Determine the intercepts of the line.
Do not round your answers.
-5x - 4y = 10
Step-by-step explanation:
-5x - 4y = 10
Intercept-y (x = 0)
-5 (0) - 4y = 10
-4y = 10
y = - 5/2
(0, -5/2)
Intercept-x (y = 0)
-5x - 4 (0) = 10
-5x = 10
x = -2
(-2, 0)
#CMIIWFour buses carrying 150 football fans from the same school arrive at a football stadium. The buses carry, respectively, 20, 45, 35, and 50 students. One of the fans is randomly selected. Let X denote the number of fans that were on the bus carrying the randomly selected person. One of the 4 bus drivers is also randomly selected. Let Y denote the fans of students on his bus. Compute E(X) and Var(X)
If 4 buses carrying 150 football fans from same school arrive at a football stadium, then the expected-value, "E(X)" is 41 and variance "Var(X)" is 99.
To find the expected value of X, we use the formula E(X) = ∑x P(X=x), where x is = possible values of X and P(X=x) = probability of X taking the value x.
Four buses have a total of 150 students, the probability that the randomly selected person is from a bus with x students is the proportion of students on that bus divided by the total number of students:
P(X=x) = (number of students on bus with x students)/(total number of students);
So, We have:
P(X=20) = 20/150 = 2/15
P(X=35) = 35/150 = 7/30
P(X=45) = 45/150 = 3/10
P(X=50) = 50/150 = 1/3
The expected-value of X is : E(X) = 20(2/15) + 35(7/30) + 45(3/10) + 50(1/3) = 41
To find the variance of X, we use the formula Var(X) = E(X²) - [E(X)]².
We already know E(X), so we need to find E(X²).
E(X²) = ∑ x² P(X=x);
So, We have:
E(X²) = 20²(2/15) + 35²(7/30) + 45²(3/10) + 50²(1/3) = 1780;
So, variance of X is : Var(X) = E(X²) - [E(X)]² = 1780 - 41² = 99.
Therefore, the expected value of X is 41 and the variance of X is 99.
Learn more about Expected Value here
https://brainly.com/question/30042951
#SPJ4
Find The Linear Approximation To The Function F (Dy, Z) = Ce2yz+32 At The Point (X, Y, Z) = (3,-2,0)
f(x,y,z) = xe^2yz+3z
L (x,y,z) =
At the coordinates (X, Y, Z) = (3, -2, 0), L(x, y, z) = C+35 + x - 12Cz is the linear approximation to the function f(Dy, Z) = Ce^2yz+32.
To find the linear approximation to the function f(Dy, Z) = Ce^2yz+32 at the point (X, Y, Z) = (3,-2,0), we need to find the partial derivatives of the function with respect to each variable at the point (3,-2,0).
The partial derivative of f with respect to x is simply e^2yz, which evaluated at (3,-2,0) gives us e^0 = 1.
The partial derivative of f with respect to y is 2xzCe^2yz, which evaluated at (3,-2,0) gives us 2(3)(0)C = 0.
The partial derivative of f with respect to z is 2xyCe^2yz+3, which evaluated at (3,-2,0) gives us 2(3)(-2)C + 3(1) = -12C + 3.
Using these partial derivatives, we can construct the linear approximation L(x,y,z) = f(3,-2,0) + (x-3)(1) + (y+2)(0) + (z-0)(-12C+3) = Ce^0+32 + (x-3) - 12Cz + 3.
Simplifying this expression, we get L(x,y,z) = C+35 + x - 12Cz.
Therefore, the linear approximation to the function f(Dy, Z) = Ce^2yz+32 at the point (X, Y, Z) = (3,-2,0) is L(x,y,z) = C+35 + x - 12Cz.
To learn more about coordinates visit;
brainly.com/question/16634867
#SPJ11
Triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is drawn on the coordinate
grid below. what is the area. in square units, of triangle TUV
The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is 13.58
How did we arrive at the above?First using distance calculator we derived the length of TV and the length of VU.
Since TV = Height; and
VU = Base
and the triangle is a right triangle,
Then, area is given by 1/2 base x Height
Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264
So area = 1/2 * 6.40312 * 4.24264
Area = 13.58
Learn more about area:
https://brainly.com/question/27683633
#SPJ1
Ann selects a sample of 29 students at her large high school and finds that 12 of them are planning to travel outside of the state during the coming summer. She wants to construct a confidence interval for p = the proportion of all students at her school who plan on traveling outside of the state during the coming summer, but she realizes she hasn’t met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?
Ann has failed to meet the condition called the "success-failure" condition.
In order to construct a confidence interval for the proportion (p), the sample must have at least 10 successes (planning to travel outside the state) and 10 failures (not planning to travel outside the state). In her sample of 29 students, she found 12 planning to travel (successes) and 17 not planning to travel (failures). Both numbers satisfy the success-failure condition, so she can construct the confidence interval for the proportion of students planning to travel outside the state during the coming summer.
More on "success-failure" condition: https://brainly.com/question/31605067
#SPJ11
Answer:
C: The sample must be a random sample from the population
Step-by-step explanation:
took the test on edge
Ms thompson sets up chairs in a row for a school concert. she uses 328. she sets up at 2 roses of chairs but not more than 10 rows of chairs each row has an equal number of chairs how many rows
Ms. Thompson could set up either 2 rows with 164 chairs in each row or 4 rows with 82 chairs in each row.
To find the number of chairs in each row, we need to divide the total number of chairs by the number of rows. Let's start by finding the factors of 328:
1 x 328
2 x 164
4 x 82
8 x 41
Since there must be at least 2 rows and no more than 10 rows, we can eliminate the last two factor pairs. We are left with:
2 x 164
4 x 82
We can see that the first factor pair gives us 2 rows, while the second gives us 4 rows. We are told that each row has an equal number of chairs, so we need to divide the total number of chairs by the number of rows to find out how many chairs are in each row:
For 2 rows: 328 ÷ 2 = 164 chairs in each row
For 4 rows: 328 ÷ 4 = 82 chairs in each row
Your question is incomplete but most probably your full question
Ms. Thompson sets up chairs in rows for a school concert. She uses 328 chairs. She sets up at least 2 rows of chairs but not more than 10 rows of chairs. Each row has an equal number of chairs.
How many rows of chairs does Ms. Thompson set up? Enter the number in the first box.
How many chairs are in each row? Enter the number in the second box.
To learn more on Sequence click:
brainly.com/question/21961097
#SPJ11
please hurry A 4-column table with 3 rows. Column 1 has entries boys, girls, total. Column 2 is labeled less than 8 pounds with entries a, c, e. Column 3 is labeled greater-than-or-equal-to 8 pounds with entries 50, d, 70. Column 4 is labeled Total with entries b, 96, 160.
Last July, 160 babies were born in a hospital in Maine; 3
5
of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more.
a = 64, b = 14, c = 76, d = 20, e = 90
a = 14, b = 64, c = 90 d = 20, e = 76
a = 14, b = 76, c = 64, d = 90, e = 20
a = 14, b = 64, c = 76, d = 20, e = 90
Answer: the correct answer is:
a = 14, b = 64, c = 76, d = 20, e = 90
Step-by-step explanation: can i get brainliest :D
You are going to run at a constant speed of 7.5
miles per hour for 45
minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S=dt
.]
Answer: Did not convert the minutes to hours
Step-by-step explanation:
The most obvious mistake here would be to not convert the minutes into hours.
Remember, the speed given, (7.5), is in miles per HOUR. Your time is given in MINUTES. a conversion is required. 45 minutes are 45/60 = 0.75 hrs.
NOW you can use S = DT to find your distance:
7.5 = D/0.75
.: D = 5.625 miles
Find the missing side
17 cm
1319
a
area = 25 cm²
Answer:
a= 2.9cm
Step-by-step explanation:
area =25 so 17a=50
50/17=2.941176...
Anyone who knows how to do this please help answer!! Fill in the correct numbers in both sides of the chart and answer the bottom questions.
WILL MARK BRAINLIEST!!!
a) Here is the chart showing the number of bacteria after 0 to 4 hours:
| Time (hours) | Number of bacteria |
|--------------|--------------------|
| 0 | 50 |
| 1 | 150 |
| 2 | 450 |
| 3 | 1,350 |
| 4 | 4,050 |
b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:
Number of bacteria = Initial number of bacteria x Growth factor^nIn this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:
Number of bacteria = 50 x 3^nc) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:
Number of bacteria = 50 x 3^12= 26572050
Therefore, there are approximately 2.7 billion bacteria present after 12 hours.The Bullock family is looking to rent a
large truck for their upcoming move. With Heather's Moving, they would pay
$10 for the first day plus $8 per
additional day. With Newton Rent-a-
Truck, in comparison, the family would
pay $80 for the first day plus $1 per
additional day. Before deciding on which
company to use, Mrs. Bullock wants to
find out what number of additional days
would make the two choices equivalent
with regards to cost. What would the
total cost be?
To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:
Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x
To find the point at which the costs are equal, we can set the equations equal to each other:
10 + 8x = 80 + x
Now, we can solve for x (additional days):
7x = 70
x = 10
So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:
Total cost = 10 + 8(10) = 10 + 80 = $90.
Learn more about additional days: https://brainly.com/question/24900258
#SPJ11
In 2012, the population of a city was 6.47 million. the exponential growth rate was 2.91% per year.
The population of the city after 5 years is approximately 7.94 million.
How to find the population of the city?Assuming that the population of the city grows exponentially, we can use the formula:
P(t) = [tex]P0 * e^(^r^t^)[/tex]
Where:
- P(t) is the population after time t
- P0 is the initial population
- r is the annual growth rate expressed as a decimal
- t is the time elapsed in years
Using the given information:
- P0 = 6.47 million
- r = 2.91% = 0.0291
Let's calculate the population after 1 year:
[tex]P(1) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^1^)[/tex]
= 6.66 million (rounded to two decimal places)
So, the population of the city after one year is approximately 6.66 million.
We can also calculate the population after 5 years:
[tex]P(5) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^5^)[/tex]
= 7.94 million (rounded to two decimal places)
Learn more about Annual growth rate
brainly.com/question/23287647
#SPJ11
Y/4=3/2 what is the y and how did you get the answer
y = 6
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
The value of Y in the equation Y/4 = 3/2 is 6.
To find the value of Y, we'll use the following steps:
1. We start with the given equation:
Y/4 = 3/2.
2. Our goal is to isolate Y. To do this, we'll multiply both sides of the equation by 4, which is the denominator on the left side.
3. Multiplying both sides by 4 gives us: (Y/4) * 4 = (3/2) * 4.
4. On the left side, the 4s cancel out, leaving just Y: Y = (3/2) * 4.
5. Now, we simplify the right side by multiplying 3/2 by 4. We can think of 4 as 4/1, so the equation becomes: Y = (3/2) * (4/1).
6. Multiply the numerators (3*4) and denominators (2*1) separately: Y = (12/2).
7. Finally, simplify the fraction: Y = 6.
Learn more about Equation at
https://brainly.com/question/10413253
#SPJ11
Evaluate f(x) = 7x2 − 8 when x = 5.
Answer:
f(5) = 167
Step-by-step explanation:
To evaluate f(x) = 7x^2 - 8 when x = 5, we substitute 5 for x in the expression and simplify. Therefore, we have:
f(5) = 7(5)^2 - 8
f(5) = 7(25) - 8
f(5) = 175 - 8
f(5) = 167
So, f(5) = 167
All of the training times of which person had the greatest spread? Explain how you know. (b) The middle 50% of the training times of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Adam’s and Miguel’s training times?
(a) Miguel had the greatest spread in training times.
(b) The middle 50% of Adam's training times had the least spread.
(a) To find the greatest spread in training times, we need to calculate the range of each person's training times. Range is the difference between the maximum and minimum values. Comparing the ranges, we can say that Miguel had the greatest spread in training times since his range is the largest.
(b) The middle 50% of the training times refers to the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
To find the least spread in the middle 50% of the training times, we need to compare the IQRs of each person. Adam's IQR is the smallest, which means the middle 50% of his training times had the least spread.
(c) The answers to parts (a) and (b) indicate that Miguel had a wider range of training times compared to Adam. However, Adam's middle 50% of training times had the least spread. This suggests that while Miguel's overall training times varied more, Adam's training times were more consistent within the middle range.
For more questions like Training click the link below:
https://brainly.com/question/8320293
#SPJ11
Si un cateto de un triángulo rectángulo y la hipotenusa miden 5 y 13cm, respectivamente, ¿cuánto mide el otro cateto?
The measure of the other side of the right triangle is given as follows:
12 cm.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The parameters for this problem are given as follows:
Sides of 5 and x.Hypotenuse of 13.Hence the other side has the length given as follows:
5² + x² = 13²
25 + x² = 169
x² = 144
x = 12.
More can be learned about the Pythagorean Theorem at brainly.com/question/30203256
#SPJ1
A recent report states that 55% of U. S. Adults use Netflix to stream shows and movies. An advertising company believes the proportion of California residents who use Netflix is greater than the national proportion, because Netflix headquarters is located in Los Gatos, California. The company selects a random sample of 600 adults from California and finds that 360 of them use Netflix. Is there convincing evidence at the level that more than 55% of California residents use Netflix?
Calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix.
We can use a hypothesis testing approach to answer this question. The null hypothesis is that the true proportion of California residents who use Netflix is the same as the national proportion, or p = 0.55. The alternative hypothesis is that the true proportion of California residents who use Netflix is greater than 0.55, or p > 0.55.
We can use the sample proportion of Netflix users in California, which is 360/600 = 0.6, as an estimate of the true proportion p. The standard error of the sample proportion is:
SE = √[(p*(1-p))/n] = √[(0.55*(1-0.55))/600] = 0.024
The test statistic is:
z = (p - 0.55)/SE = (0.6 - 0.55)/0.024 = 2.08
Assuming a significance level of 0.05 and a one-tailed test (since the alternative hypothesis is one-sided), the critical z-value is 1.645.
Since our calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix. However, we should keep in mind that this conclusion is based on a sample of 600 adults from California, and there is always some degree of uncertainty involved in statistical inference based on samples.
To know more about hypothesis testing, refer to the link below:
https://brainly.com/question/30588452#
#SPJ11
point P is the image of p(-2,-2) translated by 1 unit to the left and 3 units now
To find the image of point P(-2,-2) translated 1 unit to the left and 3 units down, we subtract 1 from the x-coordinate and 3 from the y-coordinate to get coordinates of P' as: (-3, -5).
How to Find the Coordinates in Translation?To translate a point to the left, we subtract from its x-coordinate, and to translate it down, we subtract from its y-coordinate.
Therefore, to translate P(-2, -2) 1 unit to the left and 3 units down, we subtract 1 from the x-coordinate and 3 from the y-coordinate to get P'(-3, -5) as the image of P after translation.
Therefore, the coordinates of P' are (-3, -5).
Learn more about translation on:
https://brainly.com/question/12861087
#SPJ1
Complete Question:
Point P' is the image of P(-2,-2) translated by 1 unit to the left and 3 units down. What are the coordinates of P'?
What in 33/22 x 44/33 equal?
Answer:
Step-by-step explanation:
Express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4).
(Use symbolic notation and fractions where needed.)
To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:
u = rv + sw
Substituting the given values, we get:
(7, -10) = r(2, 1) + s(1,4)
Using the symbolic notation, we can write this as a system of equations:
7 = 2r + s
-10 = r + 4s
We can solve this system of equations by using the elimination method:
Multiply the second equation by 2:
7 = 2r + s
-20 = 2r + 8s
Subtracting the first equation from the second, we get:
-27 = 7s
Dividing both sides by 7, we get:
s = -27/7
Substituting this value of s into the first equation, we get:
7 = 2r - 27/7
Multiplying both sides by 7, we get:
49 = 14r - 27
Adding 27 to both sides, we get:
76 = 14r
Dividing both sides by 14, we get:
r = 38/7
Therefore, u = (7, -10) can be expressed as the linear combination:
u = (38/7)(2,1) + (-27/7)(1,4)
Using fractions where needed, the answer is:
u = (76/7, 38/7) + (-27/7, -108/7)
Visit here to learn more about the coordinates of vertices
brainly.com/question/28852734
#SPJ11
Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use C for the constant of integration.)
∫9x√(-x^2 + 9dx)
The substitution is u = -x² + 9 and the evaluated value is -4.5(2/3)(-x² + 9)³/² + C.
To evaluate the given integral ∫9x√(-x² + 9dx),
we can use the substitution u = -x² + 9. This substitution will allow us to simplify the expression under the square root.
First, we can find du/dx by taking the derivative of u with respect to x: du/dx = -2x.
Next, we can solve for dx in terms of du by dividing both sides by -2x: dx = -du/(2x).
Using the substitution and the expression for dx in terms of du, we can rewrite the integral as:
∫9x√(-x² + 9dx) = -4.5∫√udu
Now, we can integrate the simplified expression √u using the power rule of integration:
-4.5∫√udu = -4.5(2/3)u³/² + C
Substituting back for u, we get:
-4.5(2/3)(-x² + 9)³/² + C
Therefore, the solution to the integral ∫9x√(-x^2 + 9dx) using the substitution u = -x^2 + 9 is:
-4.5(2/3)(-x² + 9)³/² + C
Learn more about derivative of integral : https://brainly.com/question/30398950
#SPJ11
Solve system of equations by the substitution method.
Chris has $3.85 in dimes and quarters. There are 25 coins in all. How many of each type of coin does he have?
Solving a system of equations we can see that he has 9 quarters and 16 dimes.
How to solve the system of equations?Let's define the variables:
x = number of dimes
y = number of quarters.
There are 25 coins, so:
x + y = 25
The value is $3.85, so:
x*0.10 + y*0.25 = 3.85
So the system of equations is:
x + y = 25
x*0.10 + y*0.25 = 3.85
We can isolate x on the first equation to get:
x = 25 - y
Replacing that in the other one we get:
(25 -y)*0.10 + y*0.25 = 3.85
2.5 + y*0.15 = 3.85
y = (3.85 - 2.5)/0.15
y = 9
Then the other 16 coins are dimes.
Learn more about systems of equations at:
https://brainly.com/question/13729904
#SPJ1
what does 8 thousands plus 8 tens equal?
Answer:
100
Step-by-step explanation:
8000/80=100
8 thousands= 8000
8 tens= 80
Expert Answer, Mark AS BRAINLIEST!!!
I absolutely hate IQR so can someone help
The interquartile range (IQR) of the given data set is 4.
Interquartile range (IQR) is a measure of variability in a data set that measures the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
How to fine the interquartile range (IQR)?To find the interquartile range (IQR), we first need to find the median of the data set.
The median is the middle value of the dataset when the data is arranged in order. In this case, the data set is already in order, so the median is the middle value or the average of the two middle values:
Median = (26 + 28) / 2 = 27
Now, we need to find the first quartile (Q1) and the third quartile (Q3) of the data set.
Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.
Lower half: 22, 24, 26
Upper half: 28, 30
Q1 = median of the lower half = (24 + 26) / 2 = 25
Q3 = median of the upper half = (28 + 30) / 2 = 29
Now we can find the IQR:
IQR = Q3 - Q1 = 29 - 25 = 4
Therefore, the interquartile range (IQR) of the given data set is 4.
To know more about median
brainly.com/question/28060453
#SPJ1
In ΔEFG, g = 5. 2 cm, e = 5. 1 cm and ∠F=42°. Find the area of ΔEFG, to the nearest 10th of a square centimeter
The area of ΔEFG is approximately 6.7 square centimeters.
To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:
Area = (1/2)ab * sin(C)
In this case, a = g, b = e, and C = ∠F. Plug in the values:
Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)
Area ≈ 6.675 square centimeters
So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.
Learn more about area here: https://brainly.com/question/28470545
#SPJ11
Let $f(x)=3x+2$ and $g(x)=ax+b$, for some constants $a$ and $b$. If $ab=20$ and $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$, find the sum of all possible values of $a$
The sum of all possible values of $a$ is $1$.
To solve this problem, we need to use the given information to determine possible values of $a$ and $b$ in $g(x)=ax+b$ such that $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$.
First, we can simplify $f(g(x))$ and $g(f(x))$ as follows:
$$f(g(x))=3(ax+b)+2=3ax+3b+2$$
$$g(f(x))=a(3x+2)+b=3ax+ab+b$$
Next, we can set these two expressions equal to each other and simplify:
$$3ax+3b+2=3ax+ab+b$$
$$2b-ab=b$$
$$(2-a)b=b$$
Since $ab=20$, we have two cases to consider:
Case 1: $b=0$
In this case, we have $ab=20\implies a=0$ or $b=0$. Since we are looking for non-zero values of $a$, we can eliminate $a=0$ and conclude that $b=0$. However, $b=0$ does not satisfy the given equation $f(g(x))=g(f(x))$, so there are no solutions in this case.
Case 2: $b\neq 0$
In this case, we can divide both sides of $(2-a)b=b$ by $b$ to get:
$$2-a=1$$
$$a=1$$
Therefore, the only possible value of $a$ is $1$, and the corresponding value of $b$ is $20$. We can verify that $a=1$ and $b=20$ satisfy the given equation $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$.
You can learn more about sum at: brainly.com/question/31265134
#SPJ11