Answer this math question for 10 points
Measure of angle:
∠A = 36.86°
∠B = 90°
∠C = 53.13 °
Measure of side ,
AB = 28
BC = 21
CA = 35
Given triangle ABC.
Right angled at B.
Now, using trigonometric ratios to find angle A , B , C .
Right angled at B : ∠B = 90°
Angle A,
SinA = 21/35
∠A = 36.86
Angle C,
SinC = 28/35
∠C = 53.13
Now measures of side.
To find the length of side use sine rule .
Sine rule:
a/sinA = b/sinB = c /sinC
a = opposite side of angle A .
b = opposite site of angle B .
c = opposite side of angle C.
AB = 28
BC = 21
CA = 35
Hence the sides and angles of the triangles are measured .
Know more about sine rule,
https://brainly.com/question/30339239
#SPJ1
-2x² - 6x =15
Atenderes form
Answer:
Step-by-step explanation:The solutions to the equation x^2=6x-15 are x=3+sqrt(6)i,x=3-sqrt(6)i
Answer:
\(\displaystyle x=-\frac{3}{2}\pm \frac{\sqrt{21}}{2}i\)
Step-by-step explanation:
\(\displaystyle -2x^2-6x=15\\0=2x^2+6x+15\\\\x=\frac{-6\pm\sqrt{6^2-4(2)(15)}}{2(2)}=\frac{-6\pm\sqrt{36-120}}{4}=\frac{-6\pm\sqrt{-84}}{4}=\frac{-6\pm2i\sqrt{21}}{4}\\\\=-\frac{3}{2}\pm \frac{\sqrt{21}}{2}i\)
a plumber charges
\( \frac{1}{4} \)
of the cost of materials as a labor free. if the materials dor the current job cost $130.00, how much will the plumber charge the client?
respuesta: $32,5
Step-by-step explanation:
Divide los $ 130,00 entre 4 y obtendrás cuanto cobra el fontanero como mano de obra
Present the descriptive statistics of the variables total_cases
and total_deaths. Comment on the means and measures of dispersion
(standard deviation, skewness, and kurtosis) of these two
variables.
The descriptive statistics of the variables tota The mean of total_cases represents the average number of reported COVID-19 cases, while the mean of total_deaths represents the average number of reported COVID-19 deaths.
The measures of dispersion, such as standard deviation, indicate the spread or variability of the data points around the mean.
The mean of total_cases reveals the average magnitude of the spread of COVID-19 cases. A higher mean suggests a larger overall impact of the virus. The standard deviation quantifies the degree of variation in the total_cases data. A higher standard deviation indicates a wider range of reported cases, implying greater heterogeneity or inconsistency in the number of cases across different regions or time periods.
Skewness measures the asymmetry of the distribution. Positive skewness indicates a longer right tail, suggesting that there may be a few regions or time periods with exceptionally high case numbers. Kurtosis measures the shape of the distribution. Positive kurtosis indicates a distribution with heavier tails and a sharper peak, which implies the presence of outliers or extreme values in the data.
Similarly, the mean of total_deaths provides an average estimate of the severity of the COVID-19 outbreak. A higher mean indicates a greater number of deaths attributed to the virus. The standard deviation of total_deaths indicates the variability or dispersion of the death toll across different regions or time periods. Skewness and kurtosis for total_deaths provide insights into the shape and potential outliers in the distribution of death counts.
The means of total_cases and total_deaths offer average estimates of the impact and severity of COVID-19. The standard deviations indicate the variability or spread of the data, while skewness and kurtosis provide information about the shape and potential outliers in the distributions of the variables. These descriptive statistics help us understand the overall patterns and characteristics of COVID-19 cases and deaths.
Learn more about statistics here:
brainly.com/question/31577270
#SPJ11
A project has an initial cost of $30 million.The project is expected to generate a cash flow of $2.85 million at the end of the first year.All the subsequent cash flows will grow at a constant growth rate of 3.85% forever in future.If the appropriate discount rate of the project is 11%,what is the profitability index of the project? a.1.917 b.1.328 c.1.387 d.1.114 ortcehov e. None of the above
Profitability index is 1.387. Thus, the correct option is (c) 1.387.
The formula for calculating the profitability index is:
P.I = PV of Future Cash Flows / Initial Investment
Where,
P.I is the profitability index
PV is the present value of future cash flows
The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.
The present value of cash flows can be calculated using the formula:
PV = CF / (1 + r)ⁿ
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
n is the number of periods
For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.
Substituting the values, we get:
PV = 2.85 / (1 + 0.11)¹ = $2.56 million
To calculate the present value of all future cash flows, we can use the formula:
PV = CF / (r - g)
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
g is the constant growth rate
For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.
Substituting the values, we get:
PV = 2.85 / (0.11 - 0.0385) = $39.90 million
The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.
PV of future cash flows = $39.90 million + $2.56 million = $42.46 million
Profitability index (P.I) = PV of future cash flows / Initial investment
= 42.46 / 30
= 1.387
Therefore, the correct option is (c) 1.387.
Learn more about Profitability index
https://brainly.com/question/30641835
#SPJ11
Joan bought 2 cases of golf balls. Each case holds 12 boxes of 12 golf balls each. A different manufacturer of golf balls sells them
in packages of 18 golf balls. How many packages would Joan need to buy to have the same amount of golf balls?
(Ctrl)
Answer:
I believe the correct answer would be 16.
Step-by-step explanation:
There are 2 cases of golf balls that hold 12 boxes of 12 balls.
12(12) + 12(12) = 288
You need to find how many cases Joan can buy to equal the amount of 288 balls.
18(x) = 288
I simply divided 288 by 18 to get the answer of 16.
x = 16
The number of packages should need to buy is 16.
The calculation is as follows:There are 2 cases of golf balls that hold 12 boxes of 12 balls.
12(12) + 12(12) = 288
Now
18(x) = 288
x = 16
Learn more: https://brainly.com/question/10309631?referrer=searchResults
23. the difference between the number of customers in line at the express checkout and the number in line at the super-express checkout in exercise 3 is x1 2 x2. calculate the expected difference.
The expected difference is 0.17
What is super express market?A supermarket is a self-service store with various food, drink, and household goods options divided into categories. While this type of store is bigger and has a wider variety of products than older grocery stores, it is smaller and offers a smaller selection of goods than a hypermarket or big-box market. Fresh meat, produce, dairy, deli foods, baked goods, etc. may usually be found in the store.
Additionally, shelf space is set aside for canned and packaged goods as well as a variety of non-food items like pet supplies, cleaning supplies, cookware, and household cleansers.
The table is: 0 1 2 3
x1 0 0.08 0.06 0.04 0.00
1 0.05 0.18 0.05 0.03
2 0.05 0.04 0.10 0.06
3 0.00 0.03 0.04 0.07
4 0.00 0.01 0.05 0.06
Expected difference =
+(0.08*(0-0)) +(0.06*(0-1)) +(0.04*(0-2)) +(0.00*(0-3)) +(0.05*(1-0)) +(0.18*(1-1)) +(0.05*(1-2)) +(0.03*(1-3)) +(0.05*(2-0)) +(0.04*(2-1)) +(0.10*(2-2)) +(0.06*(2-3)) +(0.00*(3-0)) +(0.03*(3-1)) +(0.04*(3-2)) +(0.07*(3-3)) +(0.00*(4-0)) +(0.01*(4-1)) +(0.05*(4-2)) +(0.06*(4-3))
= 0.17
To know more about super express market please visit:
https://brainly.com/question/22416965
#SPJ4
Photo pasted below please check and show possible answers
Therefore, the set of values of c in the equation for which the curve and the line intersect at two distinct points is given by:
c > -4
What exactly is meant by the word "equation"?To show that two amounts or values are equivalent, an equation is employed, such as 6 x 4 = 12 x 2. Number able noun A situation where two or more factors must be considered in order to see or comprehend the overall situation is referred to as an equation.
To find the points of intersection between the curve and the line, we need to solve the system of equations:
y = x² + 2cx + 4
y + 4x = -c
Substituting the expression for y from the first equation into the second equation:
x² + 2cx + 4 + 4x = -c
x² + (2c + 4)x + (c + 4) = 0
For the curve and the line to intersect at two distinct points, the quadratic equation above must have two distinct real solutions for x. This means that the discriminant of the quadratic equation must be positive:
(2c + 4)² - 4(c + 4)(c) > 0
4c² + 8c + 16 - 4c² - 16c > 0
4c > -16
c > -4
Therefore, the set of values of c for which the curve and the line intersect at two distinct points is given by:
c > -4
To know more about equation visit:
brainly.com/question/29657992
#SPJ1
Given a curve $C$ defined by $\mathbf{r}(t)=\langle 3 t-3,3 t\rangle, 0 \leq t \leq 4$. The line integral $\int_C 2 x^2 \mathrm{~d} y$ is equal to
486
$-486$
None of the others
504
1512
The line integral of $2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486 according to the given information.
To calculate the line integral $\int_C 2x^2 \mathrm{~d}y$, we need to parameterize the curve $C$ and express $x$ and $y$ in terms of the parameter $t$. The given curve is defined as $\mathbf{r}(t) = \langle 3t-3, 3t \rangle$, where $0 \leq t \leq 4$.
Differentiating $\mathbf{r}(t)$ with respect to $t$, we have $\mathbf{r}'(t) = \langle 3, 3 \rangle$. Integrating $2x^2$ with respect to $y$ along the curve $C$ gives us:
$\int_C 2x^2 \mathrm{~d}y = \int_0^4 2(3t-3)^2 (3 \mathrm{~d}t) = 2 \int_0^4 (27t^2 - 54t + 27) \mathrm{~d}t$.
Evaluating the integral, we get $\int_C 2x^2 \mathrm{~d}y = [9t^3 - 27t^2 + 27t]_0^4 = 486$.
Therefore, the line integral $\int_C 2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486.
Learn more about line integral here: brainly.com/question/30763905
#SPJ11
Melanie and noah are baking a birthday cake for franceca. The recipe call for 3/4 meauring cup and noah ha a 1/8 meauring cup. Which cup hould they ue
They should use 6 cup of Noah's measuring cup
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Recipe call = 3/4Noah's cup = 1/8Number of cup = ?Calculating the number of cup the should use:
Number of cup = Recipe call / Noah's cup
Number of cup = (3/4) / (1/8)
Number of cup = 3*8 / 4*1
Number of cup = 24/4
Number of cup = 6
Learn more about algebraic operations at: brainly.com/question/3927786
#SPJ4
Correctly written question:
Melanie and Noah are baking a birthday cake for Francesca. The recipe call for 3/4 measuring cup and Noah has a 1/8 measuring cup. Which cup should they use?
Reflect the triangle over the y-axis and find the coordinate of the image of point K.
K’(2, 1)
K’(–2, 1)
K’(–2, –1)
K’(2, –1)
K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.
Therefore, the coordinate of the image of point K is K’(-2, 1).
To know more about triangle click-
brainly.com/question/17335144
#SPJ1
The 99% confidence interval of a population mean is (1,7). One of the following is the 95% confidence interval. Which is it?
(a) (2,6)
(b) (1,6)
(c) (0,8)
(d) (2,7)
Given that, The 99% confidence interval of a population mean is (1,7). We need to find the 95% confidence interval.As the confidence interval becomes wider as the confidence level increases. Hence, the 95% confidence interval will have a greater range than the 99% confidence interval.Confidence interval can be calculated by the formula:Confidence Interval = $\overline{X}$ ± Zα/2 (σ/√n)Where, $\overline{X}$ is the sample mean.Zα/2 is the critical valueσ is the population standard deviationn is the sample sizeNow, Zα/2 for 99% confidence interval is 2.576 as per the normal distribution table.In the same way, Zα/2 for 95% confidence interval is 1.96.Converting the above formula for 95% confidence interval:1.96 = (1,7 - $\overline{X}$)/(σ/√n)On solving the above equation, we get: σ/√n = 0.2039σ = 0.2039 √n.....(1)Also, (1,7 - $\overline{X}$)/σ = 1.96....(2)Substituting equation (1) in equation (2), we get:(1,7 - $\overline{X}$)/ (0.2039√n) = 1.96On solving this equation, we get:$\overline{X}$ = 1.47 √n + 1.7...........(3)Now, for option (a), (b), (c) and (d), we need to verify which option satisfies the equation (3).Let's check for option (a):(2+6)/2 = 4............taking the average1.47 √n + 1.7 = 4n = 19.22 squaring both sidesn = 363.6Hence, option (a) is the correct answer.Write the answer in main part:The 95% confidence interval is (2,6).Explanation:On solving the equation, we get that the option (a) is correct. Therefore, the 95% confidence interval is (2,6).Conclusion:Therefore, option (a) (2,6) is the correct 95% confidence interval.
The 95% confidence interval for the population mean is given as follows:
c) (2,6).
How to obtain the 95% confidence interval for the population mean?The 99% confidence interval for the population mean is given as follows:
(1,7).
Hence the sample mean is given as follows:
(1 + 7)/2 = 4.
Meaning that the mean of the two bounds in the interval must be of 4.
The 95% confidence interval is narrower than the 99% confidence interval, hence, considering the mean of the bounds of 4, option c is the correct option for this problem.
More can be learned about the confidence intervals at https://brainly.com/question/25890103
#SPJ4
Solve the system graphically and check x+2y the solution.2x+5y=0. X+6y=14
Given:
The system of the equation is,
\(\begin{gathered} 2x+5y=0 \\ x+6y=14 \end{gathered}\)Draw the lines on the graph, the point at which the lines intersects. That point will be the solution of the system.
The points on the line 2x+5y=0 are,
\(\begin{gathered} 2x+5y=0 \\ x=0\Rightarrow y=0 \\ x=5\Rightarrow y=-2 \\ x=-10\Rightarrow y=4 \end{gathered}\)And the points on the line x+6y=14
\(\begin{gathered} x+6y=14 \\ x=0\Rightarrow y=\frac{7}{3} \\ x=14\Rightarrow y=0 \\ x=-10\Rightarrow y=4 \end{gathered}\)The graph of the lines is,
As the point of intersection is ( -10,4).
The solution of the given system of equation is x = -10, y = 4.
(19,-9) (-7,-15) in slope intercept form
Answer:
\(y=\frac{3}{13}x-\frac{174}{13}\)
Step-by-step explanation:
slope:
\(m=\frac{-15-(-9)}{-7-19} =\frac{-15+9}{-26} =\frac{-6}{-26} =\frac{3}{13}\)
Equation, with the point (19, -9):
\(y-(-9)=\frac{3}{13} (x-19)\)
\(y+9=\frac{3}{13} x-\frac{57}{13}\)
\(y=\frac{3}{13} x-\frac{57}{13} -9\)
\(-9=-9(\frac{13}{13} )=-\frac{117}{13}\)
\(y=\frac{3}{13}x-\frac{174}{13}\)
Hope this helps
A line intersects the points
(1,6) and (3, 14).
Answer:
y=4x+13
Step-by-step explanation:
Answer:
y=4 x+ 13
Step-by-step explanation:
I have had that same question before gussed and got it right.
the barrel of a fountain pen, cylindrical in shape , is 7cm long and 5mm in diameter .a full barrel of ink in the pen will be used up in writting up 310 words on an average . how many words would use up on a bottle of ink containing one-fifth of a litre ?answer correct to the nearest 100 words.
Answer:
44 words
Step-by-step explanation:
Step one:
given data
The dimension is
7cm long and = 0.07mm
5mm in diameter
radius= 2.5mm
The volume = πr^2h
Volume= 3.142*2.5^2*0.07
Volume= 3.142*6.25*0.07
volume= 1.4 mm^3
If 1.4 mm^3 will write 310 words on an average
1/5(0.2mm^3) liter will write x
cross multiply we have
x= 0.2*310/1.4
x=62/1.4
x=44 words
Give the function y=5+2x, what is the output (y) when the input, x=4?
Answer:
13
Step-by-step explanation:
y=5+2(4)
Answer:
c y would equal 13 your answer is C
1- In Euclidean space, the locus of points equidistant from the origin of a plane is a circle What is the locus of points equidistant (in the spacetime distance seme) from the origin of a spacetime plane? 151 2. A ruler of length L. In at rest in with its left and at the origin. O moves from left to right with speed relative to o along the length of the ruler. The two origins coincide ut time zero for both, at which time a photon is emitted toward the other end of the rulut. What are the coordinates in Olof the event at which the photon maches the other end? (10) 3. The Earth and Alpha Centauri are 43 light years apart. Ignore their relative motion Events A and B occur att on Earth and at 1 year on Alpha Centauri, respectively. (a) What is the time difference between the events according to an observer moving at B - 0.98 from Earth to Alpha Centauri? (b) What is the time difference between the events according to an observer moving at 3 = 0.98 from Alpha Centauri to Earth? (c) What is the speed of a spacecraft that makes the trip from Alpha Centauri to Earth in 2.5 years according to the spacecraft clocks? (d) What is the trip time in the Earth rest frame? [5+5+5+51 + Plane polar coordinates are related to cartesian coordinates by x=rcos and y = rsin. Describe the transformation matrix that maps cartesian coordinates to polar coordinates, and write down the polar coordinate basis vectors in terms of the basis vectors of cartesian coordinates. [51 5- suppose that we are given a basis ei, es consisting of a pair of vectors making a 45° angle with one another, such that ei hus length 2 and ez has length 1. Find the dual basis vectors for the case of covariant components of the vectors. [101
1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.
In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:
ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,
where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.
To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:
-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.
If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:
-c^2*dt^2 + dx^2 = k^2.
This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.
Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.
(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)
To know more about equidistant, refer here:
https://brainly.com/question/29886221#
#SPJ11
Can someone please help me with this?
Answer:
about 8.5, -8.5
Step-by-step explanation:
NEEEEEEED HEEEEEEEELP !!!!!!!!!!!!!!!!! 13 POINTSSSSSS
the answer will be thirty three cm.
what is the result of 2.130 x 10³ - 6.6 x 10² =
Answer:
The answer you're looking for is 1470.
Step-by-step explanation:
The method I used was PEMDAS
Since there was no parenthesis, I simplified the exponents.
2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?
After that, I multiplied all terms next to each other.
2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?
The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.
1470 = ?
I hope this was helpful!
If Macy had 198 apples and Jerry had 105 Apples Macy gave Jerry 75 apples Jerry gave Macy 75 apples to Macy gave Jerry 70 apples and Jerry took 20 apples for Macy How many apples woulD Macy have
Macy has 148 apples.
\(198 - 75 = 123\)
\(123 + 75 = 198\)
\(198 - 70 = 128\)
\(128 + 20 = 148\)
Therefore, your correct answer would be 148.
What is the rule of parallel lines?.
The rule of parallel lines: they never intersect each other.
We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.
Parallel lines are always equidistant from each other.
Also, the parallel lines are coplanar.
Mathematically, the parallel lines are represented by the symbol, ‘||‘.
If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.
Two lines parallel to a third line are parallel
As we know, the slopes of parallel lines are equal.
Let us assume that m₁ be the slope of line l₁ and m₂ be the slope of line l₂.
If line l₁ and l₂ are parallel to each other then m₁ = m₂
Learn more about parallel lines here:
brainly.com/question/16701300
#SPJ4
How do you fully simplify (3)/(2x+12) - (x-15)/(x^2-2x-48)?
Answer:
Step-by-step explanation:
4564. 2 75444214///4222.-112
The fully simplified form of the expression is \(\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}\)
What do you mean by quadratic equation?A quadratic equation is a type of polynomial equation that has the general form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is an unknown variable. The equation has two solutions, which can be found using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where the ± symbol indicates that there are two possible solutions.
Quadratic equations are used to model a variety of real-world phenomena, such as the motion of objects under the influence of gravity, the path of a projectile, and the growth of a population over time. They are also used to describe the parabolic shape of curves and to solve optimization problems, such as finding the maximum or minimum value of a function
We can simplify the expression as follows:
\(\frac{3}{2x+12} =\frac{x-15}{x^{2} -2x-48}\)
First, we'll simplify the denominators. To do this, we can factor the quadratic expression x² - 2x - 48:
x² - 2x - 48 = (x - 8)(x + 6)
Now we can rewrite the denominators:
\(\frac{3}{2x+12}-\frac{x-15}{(x-8)(x+6)}\)
Next, we'll simplify the fraction in the second term using partial fraction decomposition:
\(\frac{x-15}{(x-8)(x+6)} =\frac{A}{x-8}+\frac{B}{x+6}\)
where A and B are constants that we can find by multiplying both sides by (x - 8)(x + 6) and equating the numerators:
x - 15 = A(x + 6) + B(x - 8)
Expanding both sides:
x - 15 = Ax + 6A + Bx - 8B
Comparing coefficients:
-15 = Ax + 6A + Bx - 8B
1 = A + B
8B = Ax + 6A + 15
-6A = -15 - Ax - 8B
-6A = -15 - (A + B)x - 8B
-6A = -15 - x + 7x
-6A = -15 - x + 7x
-6A = -15 + 6x
Solving for A and B, we have:
A = -3
B = 4
So, the second term can be written as:
\(\frac{x-15}{(x-8)(x+6)} =\frac{-3}{x-8}+\frac{4}{x+6}\)
Putting everything together, we have:
\(\frac{3}{2x+12} -\frac{x-15}{(x-8)(x+6)} =\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}\)
which is the fully simplified form of the expression.
To know more about expression visit:
https://brainly.com/question/29176690
#SPJ4
in a group of 900 students, 612 like football and
540 like volleyball. If all the students like at least one
game, find the following by using Venn diagramHow
many students like both game ?
How many students like only football?
Answer: Let's use a Venn diagram to solve this problem.
First, we know that 612 students like football, 540 students like volleyball, and all students like at least one game. This means that there is some overlap between the two groups in the Venn diagram.
Let x be the number of students who like both games. Then, the number of students who like only football is 612 - x, and the number of students who like only volleyball is 540 - x.
Since all 900 students like at least one game, we can add up the number of students in each of these three groups and set the sum equal to 900:
(612 - x) + x + (540 - x) = 900
Simplifying the left side of the equation gives:
1152 - 2x = 900
Subtracting 1152 from both sides gives:
-2x = -252
Dividing both sides by -2 gives:
x = 126
Therefore, 126 students like both football and volleyball.
To find the number of students who like only football, we can substitute x = 126 into the expression 612 - x:
612 - 126 = 486
Therefore, 486 students like only football.
Step-by-step explanation:
HELP! If the area of a rectangle is 10x^2+3x-4 and the width is 2x-1, what is the side length of the rectangle?
Answer:
5x+4
Step-by-step explanation:
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 8 cubic feet and the volume of each large box is 21 cubic feet. A total of 20 boxes of paper were shipped with a combined volume of 264 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
Answer:14
Step-by-step explanation: so if you add 21 and 264 and 20 u would get 14 hehehehhehehe im da best your not :)
Triangle ghj with vertices g(-2, 4), h(3, 6), and j(3, "-2)" is dilated by a factor of centered at the origin. What are the coordinates of after the dilation?.
The coordinates of G after dilation is ( -2/3, 4/3).
Dilation:
Dilation is a transformation, which is used to resize the object. Dilation is used to make objects larger or smaller. This transformation produces an image that is the same as the original shape.
Here the three vertices of the triangle are given:
G = ( -2, 4)
H = ( 3, 6)
J = ( 3, -2)
The scale factor is given as, k = 1/3
So the image of G is calculated as:
G' = kG
= 1/3( -2, 4)
= ( -2/3, 4/3)
So the coordinate of G' after dilation is (-2/3, 4/3).
Therefore the coordinate after dilation is (-2/3, 4/3)
To know more about the dilation refer to the link given below:
https://brainly.com/question/10253650
#SPJ4
On a coordinate plane, line D F goes through points (negative 1, negative 3) and (2, 3). Point G is at (negative 4, negative 4).
Which point on the y-axis lies on the line that passes through point G and is parallel to line DF?
(–2, 0)
Answer:
4
Step-by-step explanation:
D (-1, -3) and F( 2, 3)
G (-4, -4)
Which point on the y-axis lies on the line that passes through point G and is parallel to line DF?
If the line is parallel to DF then they have the same slope.
slope of line DF is m= difference in y/ difference in x = (-3-3)/( -1-2) = -6/-3 = 2
so slope of line that passes trough G and is ║ with DF is also m= 2
From point G (-4, -4) we go with a slope of 2 until we get to the y-axis
So we go up 2 and 1 left, 2up and 1 left, ... until we get to the point (0, 4), because the slope = rise/run = rise 2/run 1
Let f be a function such that lim h->0 ( f(2+h)-f(2) / h ) = 5. Which of the following are true?
I) f is continuous at x=2
II) f is differentiable at x=2
III) The derivative of f is coninuous at x=2
I) f is continuous at x=2
II) f is differentiable at x=2
These both f (function ) are true
The given limit can be recognized as the definition of the derivative of f at x=2. Specifically, it states that the derivative of f at x=2 is equal to 5.
Using this information, we can make the following conclusions:
I) We cannot say for sure whether f is continuous at x=2 based on the given limit alone. While a function being differentiable at a point implies that it is also continuous at that point, the converse is not necessarily true. Therefore, we would need additional information to determine whether f is continuous at x=2.
II) The given limit implies that f is differentiable at x=2, since the limit exists and is finite. Specifically, we can say that the derivative of f at x=2 exists and is equal to 5.
III) The given limit also implies that the derivative of f is continuous at x=2. This is because the limit defines a continuous function at x=2, and it is well-known that if a function is differentiable at a point, then it is also continuous at that point.
Therefore, the correct answers are II and III.
To know more about differentiable and continuous equation , refer here :
https://brainly.com/question/30039201#
#SPJ11