Answer:
16.6 ftStep-by-step explanation:
The height of the house, the ground and the ladder forms a right angle triangle, with the following parameters stated below.
1. the hypotenuse is the length of the ladder which is 30 feet
2.the opposite is the height of the house, which is 25 feet
3. the adjacent is the distance of the ladder away from the building, this is the parameter we are solving for.
Since we have two sides of the triangle given, we can employ Pythagoras theorem to solve for the third side of the triangle
let the the opposite be x
we know that
[tex]hyp^2= opp^2+adj^2\\\\ 30^2= x^2+25^2\\\\ 900= 625+x^2\\[/tex]
Solving for x we have
[tex]x^2= 900-625\\\\X^2= 275\\\\x=\sqrt{275} \\\\x= 16.58[/tex]
Hence the maximum distance away from house that he can place
the ladder is 16.6 ft to the nearest foot
Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?
Answer:
16
Step-by-step explanation:
1x to 2x ratio
total is 24 oz, aka 3x or 1x+2x
24oz=3x
do some math
x=8oz
raisins = 2x = 16 oz
Answer:
Step-by-step explanation: 2x-16 oz
HELP ASAP;The tree diagram represents an
experiment consisting of two trials.
Answer:
P(A) = 0.5
Step-by-step explanation:
Look from the tree root (left) and find A.
When you reach the first branch that shows A, the probability is on it's left, so
P(A) = 0.5
4. Starcraft 2 player Serral won 36 out of his last 45 matches in high-level play. Continuing with that level of competition, where each match ends in a win or a loss, answer the following queries. (a) If Serral is scheduled to play exactly 6 games, what is the probability that Serral will lose at most 2 games. (b) If the venue instead has players keep playing until their first loss, what is the probability that Serral will have a win streak of at least 4 games
Answer:
Starcraft
a) Probability of losing at most 2 games = 33%
b) Probability of winning at least 4 games = 67%
Step-by-step explanation:
a) To lose 2 out of 6 games, the probability is 2/6 x 100 = 33.333%
b) To win at least 4 games out of 6, the probability is 4/6 x 100 = 66.667%
c) Since Serral is playing 6 games, for her to lose at most 2 of the games is described as a probability in this form 2/6 x 100. This shows the chance that 2 of the games out of 6 could be lost by Serral. On the other hand, the probability of Serral winning at least 4 of the 6 games is given as 4/6 x 100. It implies that there is a chance, 4 out of 6, that Serral would win the game.
n ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?
Answer:
48.28 cmStep-by-step explanation:
Since the shape is a cube of side 20cm, then all the side of the cube will be 20cm since all the side of a cube are all equal.
The shortest path the ant can be take is to first travel along the diagonal of the square from point A to the other edge on the front face and then move to point B on its adjacent side on a straight line.
To get the total distance he will take, we will first calcuate the value of the diagonal distance of the square face using pythagoras theorem as shown.
hypotenuse² = opposite² + adjacent²
The opposite = adjacent = 20cm
The hypotenuse is the length of the diagonal that we need.
hyp² = 20²+20²
hyp² = 400+400
hyp² = 800
hyp = √800
hyp = 28.28 cm
The length of the diagonal is 28.28 cm.
Afterwards, the ant will move 20cm to point B from the stopping point.
Total distance will be 28.28 + 20 = 48.28 cm
Enter the range of values for x
Greetings from Brasil...
See the attached figure. The smaller the θ angle, the smaller the AB side will be. If the angle θ = 90º, then AB = 25. As θ < 90, then AB < 25
5X - 10 < 25
5X < 25 + 10
X < 35/5
X < 7
The AB side can be neither zero nor negative. So
5X - 10 > 0
5X > 10
X > 10/5
X > 2
2 < X < 7From 1985 to 2007, the number B B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 B(t)=-329.4t+13747 where t is the year and t=0 corresponds to 1985. How many federally insured banks were there in 1990?
Answer:
12100
Step-by-step explanation:
If the number B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 from 1985 to 2007 where t = 0 correspond to year 1985
In order to determine the amount of federally insured banks that were there in 1990, we will first calculate the year range from initial time 1985 till 1990
The amount of time during this period is 5years. Substituting t = 5 into the modeled equation will give;
B ( t ) = − 329.4 t + 13747
B(5) = -329.4(5) + 13747
B(5) = -1647+13747
B(5) = 12100
This shows that there will be 12100 federally insured banks are there in the year 1990.
Consider the function f(x) = 2 ^x.and the function g(x).
g(x) = f(x + 4)
= 2^(x+4)
How will the graph of g(x) differ from the graph of f(x)?
A.
The graph of g(x) is the graph of f(x) shifted 4 units to the left.
B.
The graph of g(x) is the graph of Ax) shifted 4 units upward.
C.
The graph of g(x) is the graph of Ax) shifted 4 units to the right.
D.
The graph of g(x) is the graph of f(x) shifted 4 units downward.
Answer:
A.
Step-by-step explanation:
Hello,
g(x-4)=f(x) so the graph of g is the graph of f shifted 4 units to the left.
For any x, the point (x-4, g(x-4)) is 4 units to the left of the point (x,f(x)).
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
:) i just took the test and it was right
Two points on line p have
coordinates (2, 1) and (5, 3).
The slope of the line is?
A. 2
B. 3/2
C. 1
D. 2/3
E. 4
Answer:
D. 2/3Step-by-step explanation:
[tex](2, 1) (5, 3)\\x_1 =2 \\y_1 =1\\x_2=5\\y_2 =3\\m =\frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{3-1}{5-2} \\\\m = 2/3[/tex]
A restaurant operator in Accra has found out that during the partial lockdown, if she sells a plate of her food for GH¢20 each, she can sell 300 plates, but for each GH¢5 she raises the price, 10 less plates are sold.
Draw a table of cost relating to number of plates using 6 values of cost and its corresponding number of plates bought.
What price in GH¢ should she sell the plates to maximize her revenue?
Answer:
Step-by-step explanation:
First, note this parameters from the question.
We let x = number of $5 increases and number of 10 decreases in plates sold.
Our Revenue equation is:
R(x) = (300-10x)(10+5x)
We expand the above equation into a quadratic equation by multiplying each bracket:
R(x) = 3000 + 1500x - 3000x - 1500x^2
R(x) = -1500x^2 - 1500x + 3000 (collect like terms)
Next we simplify, by dividing through by -1500
= 1500x^2/1500 - 1500x/1500 + 3000/1500
= X^2 - x + 2
X^2 - x + 2 = 0
Next, we find the axis of symmetry using the formula x = -b/(2*a) where b = 1, a = 1
X = - (-1)/2*1
X = 1/2
Number of $5 increases = $5x1/2 = $2.5
=$2.5 + $20 = $22.5 ticket price gives max revenue.
Which of the following is the slope-intercept form of 6x + 2y = 28
a) y= 3x-4
b) y= 3x +4
c) y= -3x+4
d) y= -3x-4
Find the unknown side length x write your answer in simplest radical form
A.24
B.4squareroot37
C.2squareroot154
D.5squareroot117
Answer:
(B)[tex]4\sqrt{37}[/tex]
Step-by-step explanation:
First, we determine the height of the triangle which we label as y.
Using Pythagoras Theorem.
[tex]25^2=7^2+y^2\\y^2=25^2-7^2\\y^2=576\\y=\sqrt{576}\\y=24[/tex]
In the smaller right triangle with hypotenuse, x
Base = 7-3 =4 Units
Height, y= 24 Units
Therefore, applying Pythagoras Theorem.:
[tex]x^2=24^2+4^2\\x^2=592\\x=\sqrt{592}\\ x=4\sqrt{37}[/tex]
Select the correct option.
In a game, bonus points are awarded based on the number of the level that is cleared. The bonus points are calculated by a function
that is 15 times the cube root of the level cleared and rounded to the closest integer value.
Which of the following options represents the bonus points scored as the levels advance?
Answer:
Graph A.
Step-by-step explanation:
Need help with this, I don’t need an explanation, just the answer.
Answer:
-4
Step-by-step explanation:
give me brainliest please
Answer: x= 4.25 y= 12.75
Step-by-step explanation:
PLEASE HELP ASAP. Drag each tile to the correct box
Answer:
3 <1<4<2
hope it worked
pls mark me as
BRAINLIEST
plss
Answer:
3>1>2>4
Step-by-step explanation:
Solve the quadratic equation by factoring 9x^2 -16 = 0
Answer: x= - 4/3 and x = 4/3
Step-by-step explanation:
(3x-4) times (3x+4) = 0
What is the difference of the rational expressions below?
6/x - 5x/x+2
A.
5x + 6
2
O
B. 5x + 6x +12
** + 2x
O
c.
5x6
2x+2
D. 5x' +6x +12
2x + 2
The difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
To find the difference of the rational expressions, we need to subtract the second expression from the first expression.
Let's simplify the expressions first:
The first expression is 6/x - 5x/(x+2).
To combine the terms, we need a common denominator, which is (x)(x+2).
Converting the first term, 6/x, to have a denominator of (x)(x+2), we get (6(x+2))/(x(x+2)).
Now, we can combine the terms:
[(6(x+2))/(x(x+2))] - [5x/(x+2)]
To subtract the fractions, we need to have a common denominator, which is (x)(x+2).
Expanding the numerators, we get:
[(6x + 12)/(x(x+2))] - [5x/(x+2)]
Now, we can subtract the fractions:
[(6x + 12 - 5x)/(x(x+2))]
Simplifying the numerator, we have:
(6x - 5x + 12)/(x(x+2))
Combining like terms, we get:
(x + 12)/(x(x+2))
Therefore, the difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).
Thus, the correct option would be:
C. (x + 12)/(x(x+2))
For similar question on rational expressions.
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Eight less than four times a number is less than 56. What are the possible values of that number?
Answer:
The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15
Step-by-step explanation:
Eight less than four times a number is less than 56 . The expression can be written below
let
the number = a
4a - 8 < 56
add 8 to both sides
4a - 8 + 8 < 56 + 8
4a < 64
divide both sides by 4
a < 64/4
a < 16
The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15
Which is true about the polynomial 9x²y – 6x - 5y^2
Answer:
D
Step-by-step explanation:
It is a trinomial with a degree of 3.
This is the correct answer on the exam.
plzz help brainliest thanks and 20 points Look at the cups shown below (images are not drawn to scale): A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches. How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth. 18.8 cubic inches 21.9 cubic inches 25.1 cubic inches 32.6 cubic inches
Answer:
18.8 cubic inches
Step-by-step explanation:
1. Solve for the volume of Cup A. (volume of a cone = 1/3πr² · h)
1/3 · 3.14 · 1² · 3 = 3.14 in³
2. Solve for the volume of Cup B (volume of a cylinder = πr² · h)
3.14 · 1² · 7 = 21.98 in³
3. Subtract the volume of Cup A from Cup B
21.98 - 3.14 = 18.84
4. Round 18.84 to the nearest tenth
18.84 → 18.8 in.³
Answer:
18 .8
Step-by-step explanation:
got it right on test
Two similar triangles have perimeters of 45 cm and 75 cm respectively. What scale factor would relate these two triangles?
Answer:
1 2/3
Step-by-step explanation:
Well we divide 75 by 45 which is 1.6 repeating and that as a fraction is 1 2/3.
Thus,
the scale factor that relates the 2 triangles is 1 2/3.
Hope this helps :)
The quotient of a number and -5 has a result of 2. What is the number?
Type the correct answer in the box. Use numerals instead of words.
Answer:
-10
-5 * 2 = -10
Hope this is right
Please I need your help, if i get wrong will get f in class, just one question
Answer:
(D) 56
Step-by-step explanation:
x/y = 2/7
x = 2/7 y
S = x + y
S = 2/7 y + y
S = 9/7 y
y is a multiple of 7, so S is a multiple of 9.
So S cannot be 56.
Find the area of the shaded regions.
Answer:
[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]
Step-by-step explanation:
The area of the shaded region can be calculated as the area of the semicircle less the area of the right triangle.
The area of the right triangle can be calculated as:
[tex]A_t=\frac{b*h}{2} =\frac{LM*MN}{2}[/tex]
Where LM and MN have the same length because the internal angles are L=45°, M=90°, and N=45°. So the area is:
[tex]A_t=\frac{4*4}{2}=8[/tex]
The diameter of the circle can be calculated using the Pythagorean theorem as:
[tex]D=\sqrt{(LM)^2+(MN)^2} =\sqrt{4^2+4^4}=4\sqrt{2}[/tex]
So, the radius is [tex]r=2\sqrt{2}[/tex]
Finally, the area of the semicircle is:
[tex]A_c=\frac{\pi*r^2 }{2}=\frac{\pi*(2\sqrt{2})^2 }{2}=4\pi[/tex]
So, the area of the shaded region is:
[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]
Find the linear correlation coefficient using only the four points in the lower left corner (for women). Will the four points in the upper right corner (for men) have the same linear correlation coefficient? The correlation coefficient for the points in the lower left corner is requals nothing.
Answer:
Yes, because the four points in the upper right corner from the same pattern as the four points in the lower left corner.
Step-by-step explanation:
The correlation coefficient for the points in the lower left corner equals zero.
The four points in the upper right corner have the same correlation coefficient because the four points in the upper right corner from the same pattern as the four points in the lower left corner.
Compare the following pairs of decimals. Use to indicate their relationship. a. 0.7 _______ 0.52 b. .52 _______ .045 c. 0.49 _______ 0.94 d. 0.302 _______ .23 e. 0.9 _______ 0.6 f. 2.36 _______ 3.19
Answer:
a)0.7 is greater than>0.52
b)0.52 is greater than>0.045
c)0.49 is less than<0.94
d)0.302 is greater than>0.23
e)0.9 is greater than>0.6
f)2.36 is less than<3.19
Which of the following steps indicates the distributive property when solving –3(x + 2) = 21?
Question 4 options:
A)
–3x + 2 = 21
B)
–3x – 6 = 21
C)
D)
–3x – 6 = –63
Answer:
B) –3x – 6 = 21
Step-by-step explanation:
Well the distributive property is the multiplying of a number by more numbers in parenthesis.
For example -3(x + 2) by using the distributive property we get,
-3x - 6
Thus,
the answer is B) -3x - 6 = 21 because it shows the aftermath of the distributive property.
Hope this helps :)
When distributive property applies on 3(x + 2) = 21 expression than it changes as 3x + 6 = 21.
What is distributive property?Distributive property explains us how to solve expressions in the form of a(b + c).
After apply distributive property this term convert as ab+ac.
The given expression is,
3(x + 2) = 21
To solve the expression, use distributive property,
According to distributive property,
a(b + c) changes in the form of ab+ac.
Solve for the given expression,
3x + 2×3 = 21
3x + 6 = 21
Solve for the value of x,
3x = 21 - 6
3x = 15
x = 5
Hence, option (C) is correct.
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Can you figure out the missing number in this sequence? Type your answer below!
88511,16351,?,10251
Answer:
731`55
Step-by-step explanation:
*Step-by-step explanation:*
The given sequence:
88511, 16351, ?, 10251
To find, the missing number (?) = ?
The pattern follow:
1. To Add the first 2 digits in the number .
2. Subtract digit 3 from Digit 2 .
3. The multiply digit 3 and 4 .
4. To divide digit 4 by 3.
16351 ⇒ 8 + 8 = 16, 8 - 5 = 3, 5 × 1 = 5 and \dfrac{1}{1} =111=1
= 16351
? ⇒ 1 + 6 = 7, 6 - 3 = 3, 3 × 5 = 15 and \dfrac{5}{1}15 = 5
= 73155
10251 ⇒ 7 + 3 = 10, 3 - 1 = 2, 1 × 5 = 5 and \dfrac{5}{5}55 = 1
= 10251
∴ The missing number of the given sequence = 73155
Thus, the missing number of the given sequence is 73155.
The third number in the sequence is : 73155
The given sequence is:
88511, 16351, ?, 10251
Now the pattern to find the missing value is:
Add, subtract, multiply and then divide.
These patterns are applied on the previous number's double digits to get the next number of the sequence.
Example:
Take 88511.
First pair (8,8): Add them: 16
Second pair (8,5): Subtract them: 8-5 = 3
Third pair: (5,1): Multiply them: 5
Fourth pair(1,1): Divide them: 1/1 = 1
Thus the next number of the sequence we get is 16351.
Similarly, doing it on 2nd term (16351) to find the missing third term:
Add (1,6): 7
Subtract (6,3): 3
Multiply (3,5): 15
Divide (5,1): 5
Thus the third number in the sequence is : 73155
Learn more here:
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The shape of a garden is rectangular at the center and semicircular at the ends. Find the area and perimeter of this garden { length of the rectangle is 20 - (3.5+3.5) meters} The First, correct answer gets BRAINLIEST
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Plane Figure: A figure which lies in a plane is called a plane figure.
For e.g: a rectangle, square, a rhombus, a parallelogram, a trapezium.
Perimeter:
The perimeter of a closed plane figure is the total length of its boundary.
In case of a triangle or a polygon the perimeter is the sum of the length of its sides.
Unit of perimeter is a centimetre (cm), metre(m) kilometre(km) e.t.c
Area: The area of the plane figure is the measure of the surface enclose by its boundary.
The area of a triangle are a polygon is the measure of the surface enclosed by its sides.
A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.
Circumference of a circle is the perimeter of a circle.
In a circle the radius is half of the diameter.
The approximate value of π( Pi) is= 22/7
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For the population {0, 1, 2, 3, 5, 7},
(a) List all the simple random samples of size 5.
(b) Give an example of a systematic sample of size 3 where the elements are listed
in the order : 0, 1, 2, 3, 5, 7.
(c) Give an example of a proportional stratified sample of size 3 where the strata are
{0, 1, 2, 3}, {5, 7}.
(d) Give an example of a cluster sample size of 2 where the clusters are {0, 1}, {2,3},
{5, 7}.
What is the five-number summary for this data set?
12, 15, 17, 20, 22, 25, 27, 30, 33, 37
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.
Answer: min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .
Step-by-step explanation:
The five-number summary for this data set consists of min, Q1,
median, Q3, max.
Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.
Minimum value = 12
Maximum value = 37
since , number of observations = 10 (even)
So , Median = Mean of middle most terms
Middle most terms = 22, 25
Median =[tex]\dfrac{22+25}{2}=23.5[/tex]
First quartile ([tex]Q_1[/tex])= Median of first half ( 12, 15, 17, 20, 22)
= middle most term
= 17
Third quartile ([tex]Q_3[/tex]) = Median of second half (25, 27, 30, 33, 37)
= middle most term
= 30
Hence, five-number summary for this data set :
min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .