Answer:
$15
Step-by-step explanation:
Let bushes = b and trees = t.
We can write:
12b + 15t = 600 (Equation 1)
8b + 20t = 680 (Equation 2)
24b + 30t = 1200 (Equation 3 -- Multiply Equation 1 by 2)
24b + 60t = 2040 (Equation 4 -- Multiply Equation 2 by 3)
30t = 840 (Subtract Equation 3 from 4)
t = 28 (Divide by 30)
12b + 15 * 28 = 600 (Substitute t = 28 into Equation 1)
12b = 180 (Simplify)
b = 15 (Divide by 12)
2. Points A, B and C are all on the
circumference of the circle.o
represents the centre.
DA and DB are tangents to the
circle. Angle BDO = 31
Work out the size of angle.
Question
Points A, B and C are all on the
circumference of the circle. O represents the centre. DA and DB are tangents to the circle. Angle BDO = 31°
Work out the size of angle x
Answer:
62°
Step-by-step explanation:
To solve for the above question, we would be using circle theorems.
Step 1
Angle OBD = 90° This is because a radius and a tangent meet at 90°
Step 2
The sum of Angles in a triangle = 180°
180° = Angle OBD + Angle BDO + Angle BOD
180° = 90° + 31° + Angle BOD
Angle BOD = 180° - (90° + 31°)
= 180° - 121°
Angle BOD = 59°
Step 3
Angle BOD = Angle AOD because they are congruent ,therefore, Angle AOD = 59°
Step 4
The sum of angles of a straight line = 180°
Angle BOD, Angle AOD and Angle x are angles on a straight line
Hence,
180° = Angle BOD + Angle AOD + Angle x
180° = 59° + 59° + x
x = 180° - ( 59 + 59)°
x = 180° - 118°
x = 62°
Therefore Angle x = 62°
In how many ways can you put seven marbles in different colors into two jars? Note that the jars may be empty.
Answer:
128
Step-by-step explanation:
You have two jars and seven marbles.
You do [tex]2^{7}[/tex].
That is 128
Given the following three arithmetic sequences : 1, 3, ... and 1, 4, ... and 1, 5, ... A number is randomly selected from 1 to 1000, inclusive. What is the probability that the selected number is not a term of any of the given sequences?
Answer:
0.333
Step-by-step explanation:
The first sequence starts at 1 and has a common difference of 2. It will include every odd number in the range.
__
The second sequence starts at 1 and has a common difference of 3. It will include odd numbers and the even numbers 4, 10, 16, .... That is, all even numbers of the form 6n -2 will be included. The last one corresponds to the largest value of n such that ...
6n -2 ≤ 1000
6n ≤ 1002
n ≤ 167
That is, 167 even numbers will also be excluded.
__
The third sequence starts at 1 and has a common difference of 4. Every number in this sequence is also a number in the first sequence.
__
So the numbers in these sequences include all 500 odd numbers and 167 even numbers, for a total of 667 numbers. The probability that a randomly chosen number is not in one of these sequences is ...
(1000 -667)/(1000) = 333/1000 = 0.333 . . . . p(not a sequence term)
Answer:
1/3
Step-by-step explanation:
If a cow has a mass of 9×102 kilograms, and a blue whale has a mass of 1.8×105 kilograms, which of these statements is true?
Answer:
The mass of the Blue whale is 200 times the mass of the cow
Step-by-step explanation:
Given
Mass of Cow = 9 * 10² kg
Mass of Blue Whale = 1.8 * 10⁵ kg
Required
Determine the relationship between both weights
Represent the mass of the cow with C and the mass of the whale with B
[tex]C = 9 * 10^2kg[/tex]
[tex]C = 9 *100kg[/tex]
[tex]C = 900kg[/tex]
[tex]B = 1.8 * 10^5kg[/tex]
[tex]B = 1.8 * 100000kg[/tex]
[tex]B = 180000kg[/tex]
Divide the bigger weight by the smaller weight
[tex]\frac{B}{C} = \frac{180000kg}{900kg}[/tex]
[tex]\frac{B}{C} = \frac{180000}{900}[/tex]
[tex]\frac{B}{C} = {200}{}[/tex]
Multiply both sides by C
[tex]C * \frac{B}{C} = {200}{} * C[/tex]
[tex]B = {200}{} * C[/tex]
[tex]B = 200}C[/tex]
From the expression above, it can be concluded that the mass of the Blue whale is 200 times the mass of the cow
• How many 5 inch pieces of wood can
you cut* from a board that is 4 feet
long
Answer:
9
Step-by-step explanation:
To find the answer, first convert 4 ft. to inches. 4 ft.= 48 in. Now, you divide 48÷5. 48÷5=9 3/5, or 9.6, but you can't cut a sixth of a board. Therefore, the answer is 9.
Hope this helps!
Answer: 9 pieces
Step-by-step explanation:
First, convert 4 feet to inches. 4 ft = 48 in.
Then, divide 48 in by 5 in. 48/5 is 9.6 in
But since you can't cut the board into sixths the answer is 9.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
Valid
Step-by-step explanation:
No calculations, but,
Def. of isosceles triangle= two congruent sides.
yes is isosceles
Step-by-step explanation:
valid
GPAs at CCSU are normally distributed with a mean of 2.38 and a standard deviation of 0.45. Find the z-score for a GPA of 3.06. and discuss the significance of the z-score.
Step-by-step explanation:
Z-score = (score-mean)/standard deviation
= (3.06-2.38)/0.45
= +1.51
The significance of z-score will be "1.5111".
Given values are:
Mean,
[tex]\mu = 2.38[/tex]
Standard deviation,
[tex]\sigma = 0.45[/tex]
GPA,
[tex]\bar x = 3.06[/tex]
Now,
→ The z-score will be:
= [tex]\frac{\bar x - \mu}{\sigma}[/tex]
By putting the given values, we get
= [tex]\frac{3.06-2.38}{0.45}[/tex]
= [tex]\frac{0.68}{0.45}[/tex]
= [tex]1.5111[/tex]
Learn more about standard deviation here:
https://brainly.com/question/5778359
The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through (0, negative 2) and (2, 4). What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)
Answer:
(–1, –5)
Step-by-step explanation:
Two linear equations are represented by using the tables below. A 2-column table with 4 rows titled Equation A. Column 1 is labeled x with entries negative 2, 0, 3, 4. Column 2 is labeled y with entries negative 8, negative 2, 7, 10. A 2-column table with 4 rows titled Equation B. Column 1 is labeled x with entries negative 3, negative 1, 1, 5. Column 2 is labeled y with entries negative 9, negative 5, negative 1, 7. The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through (0, negative 2) and (2, 4). What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)
Answer: To find the equation of line A, we can use any two points. Let us use points (-2, -8) and (0, -2). Therefore, the equation of line A can be gotten using the equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ Substituting:\\y-(-8)=\frac{-2-(-8)}{0-(-2)}(x-(-2))\\y+8=3(x+2)\\y+8=3x+6\\y=3x+6-8\\y=3x-2[/tex]
To find the equation of line B, we can use any two points. Let us use points (-3, -9) and (-1, -5). Therefore, the equation of line B can be gotten using the equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ Substituting:\\y-(-9)=\frac{-5-(-9)}{-1-(-3)}(x-(-3))\\y+9=2(x+3)\\y+9=2x+6\\y=2x+6-9\\y=2x-3[/tex]
To find the solution to the system of equations, we solve them simultaneously
y = 3x - 2 . . . 1)
y = 2x - 3 . . . 2)
Subtracting equation 2 from 1:
x + 1 = 0
x = -1
Put x = -1 in equation 1)
y = 3(-1) - 2
y = -3 - 2
y = -5
Therefore the solution to the equation is (-1, -5)
the correct answer is B (–1, –5)
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
Step-by-step explanation:
eq. of any line parallel to y=1/2 x-4 is
y=1/2 x+a,where a is constant.
∵ it passes through (4,5)
5=1/2(4)+a
5=2+a
a=5-2=3
so reqd. eq. is y=1/2 x+3
Answer:
Equation of the line is
y = 1/2x + 3Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
[tex]y = \frac{1}{2} x - 4[/tex]
comparing this equation with the above formula
Slope or m is 1/2
Since the lines are parallel their slope are also the same
That's
m = 1/2
Equation of the line using point (4,5) is
[tex]y - 5 = \frac{1}{2} (x - 4) \\ y - 5 = \frac{1}{2} x - 2 \\ y = \frac{1}{2} x - 2 + 5 \\ y = \frac{1}{2} x + 3[/tex]
Hope this helps you.
Which is equivalent to (4 x y minus 3 z) squared, and what type of special product is it?
[tex]
(4xy-3z)^2=16x^2y^2-24xyz+9z^2
[/tex]
Hope this helps.
Find the value of the trigonometric ratio, tan C.
Answer:
4/3
Step-by-step explanation:
TanC = opposite/adjacent
TanC = 40/30 ➡ 4/3
pppppplzzz HELPS ME!!!!
The answer is B)
Explanation:
In the equation 7(2B + J), the 7 indicates the seven days in a week, and the J indicates the money spent on juice. Thus, the B must represent the money spent on granola bars.
the volumes of two similar solids are 729m^3 and 125m^3. the surface area of the larger solid is 324m^2. what is the surface area of the smaller solid? A. 56m^2 B. 100m^2 C. 500m^2 D. 200m^2
Answer:
B. Is the Answer 100 m²
Step-by-step explanation:
The ratio of the two solid is 729/125
The ratio of the surface area = (729/125)^(2/3)=81/25
Surface area = 25 * 324 / 81 = 100 m²
Beth wrote a system of equations to determine when a referee will earn the same salary working the East Conference and West Conference games. y = 40x − 25 and y = 35x − 5 (x = total games and y = amount earned) Beth determined that at 135 games, the referee would earn the same salary for each conference game. Is she correct?
Answer:
She is incorrect
Step-by-step explanation:
Step 1: substitute
135 into x in both equations
Step 2: Solve the equations. Once you do this you will get y = 5375 for the first one and y = 4720 for the second one, therefore she is incorrect
If a(x) = 3x + 1 and b(x) = sqrt x-4 what is the domain of (b•a)(x)
Answer:
[4, infinity)
Step-by-step explanation:
(b·a)(x) = (sqrt(x - 4)·(3x + 1). The domain of 3x + 1 is "all real numbers," but the presence of the sqrt function limits the input to (b·a)(x) to [4, infinity); recall that the argument of the sqrt function must be zero or greater.
Find the missing side of each triangle.
A) 17 ft
B)9ft
C)8ft
D) 19 ft
10 POINTS !!!
Answer:9ft
Step-by-step explanation:15 times 15 = 225
225-12 times 12= 81
81sqrt
what is the slope of the line through (-3,3) and (-1,-1)
Answer:
-2
Step-by-step explanation:
Well we have to use the following formula [tex]\frac{y^2-y^1}{x^2-x^1}[/tex].
This formula is used to find slope with only two points.
So y2 is -1 and y1 is 3 so -1 - 3 is -4.
-1 - -3 is 2.
So the slope is -4/2 and is simplified to -2.
So the slope is -2.
A gambler loses $100 Saturday night and wins $65 on Sunday. What is the gambler’s total loss or gain? Express your answer as an integer.
Answer:
-35 dollar net loss
Step-by-step explanation:
Since the gambler won $65 but still lost $100, we can see that we would still have a negative net loss.
y
5
One of the solutions of the system of equations shown in
the graph has an x-value of -4. What is its corresponding
integer y-value?
4+
UCAT
ETEN
2
1
3
5 4 3 2
1
2
3
4
5
X
HERE
-2 +
-3
3
-4
-5
Answer:
-3
Step-by-step explanation:
IN URGENT NEED OF HELP. PLEASE HELP.
Answer:
533 sq. ft.
Step-by-step explanation:
First find the area of the rectangle on the bottom:
22*13=286
Then in your head move the triangle on the right to the other side to create a triangle (if this doesn't make sense tell me in a comment)
It will turn into a rectangle that is 13 by 19 so find the area of that:
13*19=247
Then add the areas together:
286+247=533
pls i need it aaaaaaaahg
Answer:
5.1
Step-by-step explanation:
Answer:
1.7√9.18
= 5.4
Hope it helps
Points A,B,C and D are midpoints of the sides of the larger square. If the smaller square has area 60, what is the area of the bigger square? HELP ASAP!!! Will give brainiest if u get it right!
Answer:
120
Step-by-step explanation:
The area of the smaller square is half of the area of the larger square because it's formed by joining the midpoints. Therefore, the area of the big square is 60 * 2 = 120.
Answer:
120
Step-by-step explanation:
Rewrite the equation by completing the square
In the diagram, OP = 2 and OP’ = 8. Find the scale factor of the dilation. a) 1/4 b) 1/2 c) 4 d) 6
Answer:
c
Step-by-step explanation:
Consider the ratio of image to original, that is
scale factor = [tex]\frac{OP'}{OP}[/tex] = [tex]\frac{8}{2}[/tex] = 4 → C
The scale factor of the dilation will be option C; 4.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Since the scaling is done by multiplication of some constant, that constant is called scale factor.
Dilation of a figure will leave its sides get scaled (multiplied) by same number.
Let suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.
Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Consider the ratio of image to original, that is;
Scale factor = OP'/OP
OP'/OP = 8/2 = 4
Hence, the scale factor of the dilation will be option C; 4.
Learn more about scale factors here :
https://brainly.com/question/8765466
#SPJ2
2(x+3)=x-4 i really need help on this plss
Answer:
X = -10Step-by-step explanation:
[tex]2(x + 3) = x - 4[/tex]
Multiply each term in the parenthesis by 2
[tex]2 x + 6 = x - 4[/tex]
Move variable to L.H.S and change its sign
[tex]2x - x + 6 = - 4[/tex]
Move constant to R.H.S and change its sign
[tex]2x - x = - 4 - 6[/tex]
Calculate
[tex]x = - 10[/tex]
Hope this helps...
Good luck on your assignment...
A rectangular field is twelve times as long as it is wide. If the perimeter of the field is 1690 feet, what are the dimensions of the field?
The width of the field is __ feet.
The length of the field is __ feet.
Answer:
The width of the field is 65 feet.
The length of the field is 780 feet.
Hey guys! I need help ASAPPPP thanks, if u do :)
20 POINTS! An 85-foot wire is tied from the top of a utility pole to the top of the building as shown. Find d, the distance from the pole to the building.
Answer:
d = 78.810 feetStep-by-step explanation:
To find the distance d we use sine
sin∅ = opposite / hypotenuse
d is the opposite
the hypotenuse is 85ft
∅ = 68°
sin 68 = d / 85
d = 85 sin 68
d = 78.810 feet
Hope this helps you
A school typically sells 500 yearbooks each year for $50. The economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. The revenue for yearbook sales is equal to the number of yearbook sold times the price of the yearbook. Let x represent the number of $5 decreases in price. If the expression that represents the revenue is written in the form R(x) = (500 + ax)(50-bx). Find the value of a and b.
Answer:
a is 100 b is 5
Step-by-step explanation:
a is 100 because if you substitute 100 for a and 1 for x (decrease of 5 dollars) you get 600 yearbooks sold which is a curate according to the economics class prediction
b is 5 because substituting 5 into b and 1 to x gives you 45 dollars per year book. this is accurate because a 5.dollar decrease in price makes the year books 45 dollars instead of 50
{5,9,13,17,21,25,...}
How to write condition?
Answer:
Step-by-step explanation:
is an arithmetic progression with ratio=4
a1=5
a2=a1+4=5+4=9
a3=a2+4=9+4=13
...............
a n+1 = a n+4
the condition can be written as the set of sequence of numbers from 5 to infinite which are written from nth term 4n + 1.