Step-by-step explanation:
Given :-
The length of the garden 8m greater than 2 times the width.
Area of the garden is 280 m²
Let us consider the length as x and width as y.
Sp, we can day length as :-
x = 8 + 2y ---(1)
Now, we know that:-
Area of Rectangle = Length × Breadth
280 = x * y
We can replace the value of x now,
280 = y × ( 8 + 2y)
280 = 8y + 2y²
2y² + 8y - 280 = 0
y² + 4y - 140 = 0
Factorise it.
(y -10)(y + 14)
Cancelling -ve value, we get the width as 10 metres.
Hope it helps :)
Answer:
Step-by-step explanation:
Width = w
Length = 2w + 8
Area of rectangular garden = 280 square meter
length * width = 280
(2w + 8 ) *w = 280
2w * w + 8*w = 280
2w² + 8w = 280
2w² + 8w - 280 = 0
Divide the whole equation by 2
w² + 4w - 140 = 0
w² + 14w - 10w - 14 *10 = 0
w(w + 14) - 10(w + 14) = 0
(w + 14)(w - 10)= 0
w - 10 = 0 {Ignore w + 14, as measurements will not be -ve}
w = 10 m
l = 2*10 +8
= 20 +8
l = 28 m
In the equation below, variables X and Y represent two matrices. Which property of matrix addition is illustrated below?
Answer:commutative property
Step-by-step explanation:
Did it on edge
A psychologist is interested in whether hypnosis affects brain dominance. Twelve college students from the freshmen class are randomly sampled for an experiment. The experiment has two conditions which are given on different days. In condition 1, the students are hypnotized and then given a test which measures the relative dominance of the right and left hemispheres. The higher the score, the more dominant is the right hemisphere. In condition 2, the same students are given the test again, only this time they are not hypnotized but are in their normal state of consciousness. The following scores are obtained:
Student 1 2 3 4 5 6 7 8 9 10 11
Condition 1 26 15 22 19 23 37 16 17 14 16 21
Condition 2 12 13 18 17 21 22 11 22 10 14 15
Answer the following questions and show your work for each mathematical question:
a. What is the (non-directional) alternative hypothesis?
b. What is the null hypothesis?
c. What is the p value?
Answer:
[tex](a)\ H_a : d_1 - d_2 \ne 0[/tex]
[tex](b)\ H_0 : d_1 - d_2 = 0[/tex]
[tex](c)\ p\ value = 0.0216[/tex]
Step-by-step explanation:
Given
The above data
The question says 12 college students were sampled. However, data for 11 students were provided.
So, I will solve this question using 11 students i.e. n = 11
Solving (a): The alternative hypothesis
Let the relative dominance of the hypnotized students (condition 1) be [tex]d_1[/tex] and the relative dominance of the non-hypnotized students (condition 2) be [tex]d_2[/tex], respectively
The alternative hypothesis is the difference between these relative dominance not equal to 0.
So:
[tex]H_a : d_1 - d_2 \ne 0[/tex]
Solving (b): The null hypothesis
The null hypothesis is the difference between these relative dominance equal to 0.
Using the same notation as (a), the null hypothesis is:
[tex]H_0 = d_1 - d_2 = 0[/tex]
Solving (c): The p value
Using paired samples t test:
First, calculate the difference in scores
[tex]i.e.\ Condition\ 1 - Condition\ 2[/tex]
The difference (d) is as follows:
[tex]d: 14, 2, 4,2, 2, 15, 5, -5, 4, 2, 6[/tex]
Next, calculate the mean of the differences:
This is calculated as:
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{14+ 2+ 4+2+ 2+ 15+ 5 -5+ 4+ 2+ 6}{11}[/tex]
[tex]\mu = \frac{51}{11}[/tex]
[tex]\mu = 4.6364[/tex]
Next, calculate the standard difference of the differences.
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n-1}}[/tex]
So:
[tex]\sigma = \sqrt{\frac{(14 - 4.6364)^2+ (2- 4.6364)^2+ (4- 4.6364)^2+ ............ (6- 4.6364)^2}{11-1}}[/tex]
[tex]\sigma = \sqrt{\frac{318.54545456}{10}}[/tex]
[tex]\sigma = \sqrt{31.854545456}[/tex]
[tex]\sigma = 5.64398[/tex]
Next, calculate the standard error of the mean difference.
This is calculated as:
[tex]SE = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]SE = \frac{5.64398}{\sqrt{11}}[/tex]
[tex]SE = \frac{5.64398}{3.3166}[/tex]
[tex]SE = 1.70173[/tex]
Next, calculate the degree of freedom (df)
[tex]df = n -1[/tex]
[tex]df = 11 -1[/tex]
[tex]df = 10[/tex]
Lastly, calculate the test statistics (t)
This is calculated as:
[tex]t = \frac{\mu}{SE}[/tex]
[tex]t = \frac{4.6364}{1.70173}[/tex]
[tex]t = 2.72452[/tex]
[tex]t \approx 2.72[/tex]
From the t distribution table:
Where [tex]df = 10[/tex] and [tex]t = 2.72[/tex]
We have:
[tex]P(t > 2.72) = 0.0108[/tex]
For a two-tailed test, the p value is
[tex]p\ value = 2 * P(t > 2.72)[/tex]
[tex]p\ value = 2 * 0.0108[/tex]
[tex]p\ value = 0.0216[/tex]
Pleaseeeeee helpppppp meeeeeee
Below is the graph of equation y=−|x−2|+2. Use this graph to find all values of x such that
1. y > 0
2. y < 0
3. y = 0
Of nine executives in a business firm, four are married, three have never married and two are divorced. Three of the executives are to be selected for a promotion. Let Y1 denote the number of married executives and Y2 be the number of never-married executives among the three selected for promotion. Assuming that the three are randomly selected from the nine available.
a. Find the joint PMF for y1 and y2
b. Find the marginal probability distribution of y1
c. If we let y3 denote the number of divorced executives among the three selected for promotion. Find P(y3 =1 | y2 = 1)
d. Are Y1 and Y2 independent? Why?
e. Find cov(Y1,Y2). Does the sign surprise you? Why?
Answer:
werere
Step-by-step explanation:
were
Find the equation of the line with the given properties: passes
through (0,-9) and (-2,-9).
Answer:
I WRITE THE STEPS
Step-by-step explanation:
Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line.
Each face of a small cube has a surface area of 0.25 square meters. A larger cube has edges that are six times as long as the edges of the small cube. What is the volume of the larger cube?
Answer:
1534
Step-by-step explanation:
34 35 baby you might need a seatbelet
There are 230 calories in 4 ounces of ice cream. How many calories are in 6 ounces of that ice cream?
Answer:
345 calories
Step-by-step explanation:
The easiest way to do this is to find out how many calories there are for 1 ounce. So 230 divided by 4, equals 57.5. So if 57.5 calories are in one ounce, then you just multiply by 6 to get your answer.
57.5 x 6 = 345 calories
Please help will give brainlist
Answer:
Sum
Step-by-step explanation:
Remember that the plus sign (+) always means to add.
Answer:
It would be the sum of a number and eight.
A kite flying in the air has a 78-string attached to it, and the string is pulled taut. The angle of elevation of the kite is 52°. Find the height of the kite. Round
your answer to the nearest tenth.
Answer:
sine 52 degrees = height / 78
height = 78 * sine 52
height = 78 * 0.78801
height = 61.46478 feet
rounded to nearest tenth 61.5 feet
Step-by-step explanation:
The game of Scrabble has 100 tiles. The diagram shows the number of tiles for each letter and the letter's point value. One tile is drawn from Scrabble's 100 tiles. Find the probability of selecting an O or a V.
Answer:
10%
Step-by-step explanation:
In the image attached below, we can see that there are
8 tiles of letter O
2 tiles of letter V
This means that there are 10 total tiles of the letters that you want to get (O and V). Since there are a total of 100 tiles we need to divide this value by 100 to get the probability of getting one of these tiles.
10 / 100 = 0.10 or 10%
Finally, we can see that the probability of selecting a O or a V is 10%
Answer: 8% of O, 2% of V
Step-by-step explanation: There are 8 O tiles and 2 V tiles
Answer Choices
A. -0.01
B. 2
C. 0.01
D. 10,000
Answer:I hink its B if its not im sorry
Step-by-step explanation:
CAN BOTS JUST PLEASE STOP REPOSTING THE SAME RESPONSE AND SOMEONE PLEASE HELP ME
Answer:
y=-5x+-3
Step-by-step explanation:
the slope is negative and its rise over run so 5/1 which is five and the y intercept is -3
What type of quadrilateral is quadrilateral ABCD if AB=4x-2, BC=2x+12, DC=3x+5, AD=6x-16, AC=4x+12, DB=8x-10, and x=7? Explain and use the properties of the types of quadrilaterals as proofs.
Answer:
The quadrilateral ABCD is a square.
Step-by-step explanation:
According to the statement, AB, BC, CD and DA are the sides of the quadrilateral, whereas DB and AC are its diagonals. If we know that [tex]x = 7[/tex], [tex]AB = 4\cdot x - 2[/tex], [tex]BC = 2\cdot x + 12[/tex], [tex]DC = 3\cdot x +5[/tex], [tex]AD = 6\cdot x -16[/tex], [tex]AC = 4\cdot x + 12[/tex] and [tex]DB = 8\cdot x -10[/tex], the lengths of each line segment are respectively:
Sides
[tex]AB = 4\cdot (7) -2[/tex]
[tex]AB = 26[/tex]
[tex]BC = 2\cdot (7) +12[/tex]
[tex]BC = 26[/tex]
[tex]DC = 3\cdot (7) +5[/tex]
[tex]DC = 26[/tex]
[tex]AD = 6\cdot (7) -16[/tex]
[tex]AD = 26[/tex]
Diagonals
[tex]AC = 4\cdot (7) +12[/tex]
[tex]AC = 40[/tex]
[tex]DB = 8\cdot (7) - 10[/tex]
[tex]DB = 40[/tex]
This information indicates that this quadrilateral is a square because of these characteristics:
1) All sides have the same length.
2) The ratio of any diagonal to any side is [tex]\sqrt{2}[/tex].
Find the area in square inches of the figure shown.
Answer:
96 [tex]in^2[/tex]
Step-by-step explanation:
48+12+36 (I divided it into 3 rectangles and added them up)
= 96 [tex]in^2[/tex]
Feel free to mark it as brainliest :D
Which shape have both parallel and perpendicular sides?
Answer:
a square
Step-by-step explanation:
all the sides are either perpendicular or parallel
pls help help me plssss i need real answers :( asap its maths I will give the brainliest whoever's answer the real question pls
Answer:
13.34 pm
22.43 pm
16.22 pm
i cant see the last one clearly
I need work shown as well
Answer:
A
Step-by-step explanation:
area of the triangle is 5 x 2/ 2 which is 5
area of the square is 25
area of the semi circle is 1/2 * 3.14 * 2.5^2 which is 9.8125
9.8125. + 25 + 5 = 39.8125
Calculator display for
1/9
Answer:
Here ya go :)
Step-by-step explanation:
Hope this helps!
Have a nice day <3
What is the probability the spinner will land on red or white?
Answer:
I think either 1/10 or 2/5
Step-by-step explanation:
On Mother’s Day, 86 children were interviewed, and 15 said they were going to buy a chocolates for their mother, 25 said they were going to take their mother for vacation and 18 said they were going to buy their mother roses. Of these, 8 said they were going to buy a chocolate and take their mother for vacation. Five said they were going to buy both chocolate and roses, and eleven said they were going to buy their mother roses and take their mother for vacation. Only two children said they were going to treat their mother to all three, but chocolates, roses and take for vacations.
i. Illustrate the situation above with the Venn diagrams.
ii. How many children are going to buy chocolates and take their mother for vacation but not
buy them roses.
Answer:
do you need the answer?
Step-by-step explanation:
?
Geometry help!! I don’t know how to do this
9514 1404 393
Answer:
659.52 cm^2
Step-by-step explanation:
In order to find the surface area of this figure, we need to know the dimensions of the base. If we assume the base is square, then the distance from its center to the center of one edge is half the dimension of one side of the base.
That center-to-edge distance (x) can be found from the given dimensions using the Pythagorean theorem.
x^2 + (15.4 cm)^2 = (17 cm)^2
x^2 = (289 -237.16) cm^2 = 51.84 cm^2
x = √51.84 cm = 7.2 cm
This means the edge length of the prism base is 2×7.2 cm = 14.4 cm.
__
The total surface area of the square prism is ...
A = b^2 +2bs . . . where b is the edge length of the base, s is the slant height
A = (14.4 cm)^2 + 2(14.4 cm)(17 cm) = 659.52 cm^2
The total surface area of this square pyramid is 659.52 cm^2.
Find the slope, or rate of change, from the following ordered pair: (-2, 17) and (-1,5)
Answer:
Slope, m = -12
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (-2, -1)
Points on the y-axis (y1, y2) = (17, 5)
To find the slope, m;
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {5 - 17}{-1 - (-2)} [/tex]
[tex] Slope, m = \frac {-12}{-1 + 2} [/tex]
[tex] Slope, m = \frac {-12}{1} [/tex]
Slope, m = -12
what is the probability that Sonny rolls a number on the number cube that is greater or equal to 5 and the spinner lands on Section labeled a
Answer:
your mom and do it yourself iinstead of getting it online
Step-by-step explanation:
btw im Purp
First grey box options:
1)reflection
2) rotation
3)translation
Second grey box options:
1) reflection
2) rotation
3) translation
Answer:
1) reflection
2) translation
Step-by-step explanation:
Figure 0 is first reflected across the x-axis, and then moved 4 spaces to the left, although it could also be seen the other way around.
The only options that aren't possible are any influcing rotation, since the two shapes aren't translated, and rotation-rotation and translation-translation.
Is There only one way to solve a equation, and if so please support your thinking.
Answer:
No
Step-by-step explanation:
Theirs always multiple ways to solve something, even if their is only one way to solve it. We all think things through differently
Find the length of are ab
Answer:
20.97?
Step-by-step explanation:
Use the Sine rule!
What expression is equivalent to 5(4x+3)-2x
Answer:
18x+15
Step-by-step explanation:
This is basically asking you to simplify the expression.
5(4x+3)-2x
Distribute the 5
20x+15-2x
Combine like terms (x values)
18x+15
Choose the best description of an angle.
A. An angle is formed where two rays meet at a common endpoint.
B. An angle is the point where two rays meet.
C. An angle is part of a line that has one endpoint and extends forever in one direction.
D. An angle extends forever in both directions.
Answer:
A. An angle is formed...
Answer:
An angle is formed where two rays meet at a common endpoint.
Step-by-step explanation:
David invests $7000 in two different accounts. The first account paid 2 %, the second account paid 5
% in interest. At the end of the first year he had earned $182 in interest. How much was in each
account?
Answer:
3,990
Step-by-step explanation:
y''+2y'+y=e^2x how to solve it?
Answer:
[tex]y=C_1e^{-x}+C_2xe^{-x}+\frac{1}{5}e^{2x}.[/tex]
Step-by-step explanation:
all the details see in the attached picture.
