Using proportions, it is found that 7% of the population has blue eyes without blonde hair.
10% of the population has blue eyes. These 10% are composed by:
75% of 4%(have blonde hair).x% of 96%(do not have blonde hair)Hence, the relation according to the proportion of 10% is:
[tex]0.75(0.04) + 0.96x = 0.1[/tex]
[tex]x = \frac{0.1 - 0.75(0.04)}{0.96}[/tex]
[tex]x = 0.0729[/tex]
Out of the entire population:
0.0729(0.96) = 0.07
7% of the population has blue eyes without blonde hair.
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In a parallelogram ABCD, prove that (AC)2 + (BD)2= 2[(AB)? +(BC)?].
Answer:
AC² + BD² = 2[AB² + BC²]
Step-by-step explanation:
Let the parallelogram be ABCD with sides AB, BC, CD and AD. It also has diagonals AC and BD.
Since the diagonals are perpendicular and bisect each other at their mid-point, and P is the point of intersection of the diagonals, we have that AP = AC/2, PC = AC/2, PB = BD/2 and PD = BD/2.
Since APB forms a right angled triangles with length of sides AP, PB and AB where AB is the hypotenuse side, using Pythagoras' theorem, we have
AB² = AP² + PB²
Since AP = AC/2 and PB = BD/2, we have
AB² = (AC/2)² + (BD/2)²
AB² = AC²/4 + BD²/4 (1)
Also, BPC forms a right angled triangles with length of sides BP, PC and BC where BC is the hypotenuse side, using Pythagoras' theorem, we have
BC² = BP² + PC²
Since PC = AC/2 and PB = BD/2, we have
BC² = (AC/2)² + (BD/2)²
BC² = AC²/4 + BD²/4 (2)
Adding equations (1) and (2), we have
AB² = AC²/4 + BD²/4 (1)
+
BC² = AC²/4 + BD²/4 (2)
AB² + BC² = AC²/4 + BD²/4 + AC²/4 + BD²/4
AB² + BC² = AC²/2 + BD²/2
Multiplying through by 2, we have
2[AB² + BC²] = AC² + BD²
So, AC² + BD² = 2[AB² + BC²] which proves our expression.
is (x-2) a factor of f(x) = x^3 − 2x^2 + 2x + 3, use either remainder theorem or factor theorem to explain your reasoning
Answer:
Step-by-step explanation:
x-2=0
x=2
f(2)=2³-2(2)²+2(2)+3=8-8+4+3=7≠0
so x-2 is not a factor of f(x).
HELP ASAP ILL GIVE BRAINLIST
t/f If substituting the test point produces a false solution, we shade on the opposite side of the line.
t/f Elimination will give you an exact answer to a system of equations.
Answer:
TRUE If substituting the test point produces a false solution, we shade on the opposite side of the line.
FALSE Elimination will give you an exact answer to a system of equations.
Step-by-step explanation:
Weird, I thought I already answer this xD
Helppppp meeeeeeeeeeeeeeeee
Answer:
A. 8/10
Step-by-step explanation:
(0.8 × 10) / (1 × 10) = 8/10 (since, multiplying 10 shifts the decimal point towards the right by one place)
Further, we can reduce fractions 8/10 by dividing the numerator and denominator by 2.
(8 ÷ 2) / (10 ÷ 2) = 4/5
Thus, 0.8 as a fraction is 8/10 or 4/5
Answer:
C
Step-by-step explanation:
https://socratic.org/questions/how-do-you-convert-0-8-8-repeating-to-a-fraction
Through (-1,2) parallel to the line x=5. Find an equation of a line that satisfies the given conditions.
Answer:
x= -1
Step-by-step explanation:
Since x= 5 is a vertical line, the unknown line would also be a vertical line with an equation of x=___ as they are parallel to each other.
Given that the line passes through (-1, 2), the equation of the line is x= -1.
Parallel lines have the same slope and will never meet.
applying the distributive property to the expression, 24x+18y will produce which equivalent expression.
1. 6(4+3y)
2. 6(4x+3y)
3. 3xy(8+6)
4. 3(8x+6y)
Answer:
6(4x + 2y)
Step-by-step explanation:
24x = 2 * 2 * 2 * 3 * x
18y = 2 * 3* 3 * y
Common factors = 2 * 3 = 6
24x + 18y = (6*4x) + (6*2y) {6 is common in both terms}
= 6*(4x + 2y)
Sally collected 22 pounds of cans to recycle
and plans to collect 1.8 more pounds each
week. In this situation, what is the value of
the y-intercept?
Step-by-step explanation:
this is an example u can see and write it yourself...
Lila uses craft sticks to make stars for an art project. She uses 5 craft sticks for each star,and she has 19 craft sticks. Lila makes as many stars as she can how many stars does Lila make?
Answer:
3
Step-by-step explanation:
5×3=15 she would have 4 left but can't make a full star
Figure ABCD is a parallelogram.
What is the perimeter of ABCD?
A
4y - 2
B
14 units
VX
0 38 units
3x - 1
44 units
2x + 2
49 units
D
2y + 6
С
Answer:
3rd option, 44 units
Step-by-step explanation:
3x-1 = 2x+2
or, x = 3
so each side, 3×3-1 = 8
4y-2 = 2y+6
or, y = 4
so each side, 4×4-2 = 14
so perimeter
= 2(8+14)
= 44 units
Answered by GAUTHMATH
WHATS YOUR TIKTOKKK OMG I WANT MUTUALS
A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 feet below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 feet per second. At what rate is the person walking when s/he is 20 feet from being directly under the pulley
The image of this question is missing and so i have attached it.
Answer:
dd/dt = 4.47 ft/s
Step-by-step explanation:
From the image attached, let's denote the following;
d = horizontal distance beneath pulley
h = height of pulley
l = diagonal from the pulley to the head of the person
v = velocity of rope rising
Using pythagoras theorem;
l² = d² + h²
Differentiating with respect to time and considering h = c^(te) gives;
2l(dl/dt) = 2d(dd/dt)
We are given;
d = 20 ft
h = 10 ft
v = 4 ft/s
We know that velocity in this case is change in diagonal distance with time. Thus;
v = dl/dt = 4 ft/s
From earlier, we saw that;
2l(dl/dt) = 2d(dd/dt)
Thus, reducing it gives
(dl/dt)(l/d) = dd/dt
Now, l² = d² + h²
l = √(d² + h²)
Also, v = dl/dt = 4
Thus;
4(√(d² + h²))/d = dd/dt
4(√(20² + 10²))/20 = dd/dt
dd/dt = 4.47 ft/s
I need help with this someone help me out
Answer:
answer is 10 (very easy)
Answer:
380. 1
Step-by-step explanation:
A=π r2=π. 11^2= 380.13271
Write the equation of the graph shown below in factored form.
f(x) = (x − 2)2(x + 1)(x − 4)
f(x) = (x + 2)2(x − 1)(x + 4)
f(x) = (x + 2)2(x + 1)(x + 4)
f(x) = (x − 2)2(x − 1)(x − 4)
Answer:
(x+2)2(x+1)(x+4)
Because
x=-4. x=2. x=-1
(x+4). (x+2). (x+1)
If 5k = -25, then 5k - 1 = -25 - 1
Segment proof
Find the volume of this sphere please help
Answer:
Volume = 108 ft³
Step-by-step explanation:
Volume of a sphere is given by the expression,
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
Here, r = Radius of the sphere
From the picture attached,
Radius of the sphere = 3 ft
By substituting the value of r in the expression,
Volume = [tex]\frac{4}{3}\pi (3)^{3}[/tex]
= 36π
= 36×3
= 108 ft³
Step by step solution
Answer:
b is correct answer
Step-by-step explanation:
when we write logarithmic terms we change the result from number which is power of 3
4. Find f(x) - g(x)
4 options to chose from
Answer:
Last option
-10x³ + 2x - 8
is the answer
HOPE IT HELPS YOU
What are the zeros of the following quadratic equation: y = 6x2 - 17x - 3
Answer:
[tex]\displaystyle x=-\frac{1}{6}, 3[/tex]
Step-by-step explanation:
Hi there!
[tex]y = 6x^2 - 17x - 3[/tex]
Factor by grouping:
[tex]y = 6x^2 - 18x+1x - 3\\y = 6x(x- 3)+1x - 3\\y = 6x(x- 3)+(x - 3)\\y = (6x+1)(x- 3)[/tex]
Let y=0. Apply the zero product property:
[tex]0 = (6x+1)(x- 3)[/tex]
[tex]6x+1=0\\6x=-1\\\\\displaystyle x=-\frac{1}{6}[/tex]
AND
[tex]x-3=0\\x=3[/tex]
I hope this helps!
Pythagorean Theron can someone help me solve this
Find the present value that will grow to $24000 if interest is 3% compounded quarterly for 14 quarters. The present value is $ . (Round to the nearest cent as needed.)
Answer:
$21,616.26.
Step-by-step explanation:
24000 =P(1 + 0.03/4)^14
P = 24000 / (1 + 0.03/4)^14)
21,616.26.
=
The present value that will grow to $24000 if interest is 3% compounded quarterly for 14 quarters is $21,482.40
To find the present value that will grow to $24,000 at 3% interest compounded quarterly for 14 quarters, we use the formula for compound interest:
[tex]PV = FV / (1 + r/n)^{(n*t)}[/tex]
Where:
PV = Present Value
FV = Future Value ($24,000)
r = Annual interest rate (3% or 0.03 as a decimal)
n = Number of compounding periods per year (quarterly, so n = 4)
t = Number of years (14 quarters = 14/4 = 3.5 years)
Substitute the values into the formula:
PV = [tex]$24,000 / (1 + 0.03/4)^{(4*3.5)}[/tex]
PV = [tex]$24,000 / (1 + 0.0075)^{(14)}[/tex]
PV = [tex]$24,000 / (1.0075)^{14}[/tex]
PV ≈ $21,482.40 (rounded to the nearest cent)
Therefore, the present value required for it to grow to $24,000 in 14 quarters at 3% interest compounded quarterly is approximately $21,482.40.
In this explanation, we used the formula for compound interest to calculate the present value (PV). The formula accounts for the future value (FV), the annual interest rate (r), the number of compounding periods per year (n), and the time in years (t). By plugging in the given values and performing the calculations, we arrived at the present value of approximately $21,482.40.
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Given: x-5> -10.
I clicked it on accident so ignore the blue thing ! Help needed
Answer:
the first one
Step-by-step explanation:
[tex]x - 5 > - 10 \\ x > - 10 + 5 \\ x > - 5[/tex]
if two similar rectangles have a scale factor of 5:2 and the area of the smaller rectangle is 45 cm^2, what will be the area of the larger rectangle?
Answer:
281.25 cm^2
Step-by-step explanation:
Given that,
The scale factor of Two similar triangles = 5:2
Area of the smaller rectangle = 45 cm^2
To find,
The Area of the larger rectangle = ?
Procedure:
As we know, similar triangles have similar ratios of sides. Thus, this can be written in proportion with the sides' ratio to the left while ratio of areas on the right.
(5)^2/(2)^2 = a/45
∵ The area of the larger rectangle = 25/4 * 45
= 281.25 cm^2
WILL MARK BRAINLIST!!
Please help!!!
Answer:
the sum of total angles of triangle is 180°.
Martha and Dave have 99$. Martha has 3 more than seven times as much money as Dave. How much does each person have?
Answer:
x = 12 m = 87
Step-by-step explanation:
x = Dave
(7x + 3) + x = 99
8x + 3 = 99
-3 -3
8x = 96
---- ----
8 8
x = 12
7(12) + 3
84 + 3
87
Dave has 12 dollars, Martha has 87.
The volume of a rectangular prism with a cone shaped hole in it is approximately 163.22cm³ (as shown below).
✏️ What is the height of the cone?
Answer:
Height of the cone = 5 cm
Step-by-step explanation:
Volume of the rectangular prism with a cone shaped hole = Volume of the rectangular prism - Volume of the cone
Volume of the rectangular prism = Length × Width × Height
= 5 × 5 × 7
= 175 cm³
Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here, r = Radius of the cone
h = Height of the cone
Volume of the cone = [tex]\frac{1}{3}\pi (\frac{3}{2})^{2}(h)[/tex]
= 0.75πh cm³
Volume of the rectangular prism with a hole = 163.22 cm³
175 - 0.75πh = 163.22
0.75πh = 175 - 163.22
0.75πh = 11.78
h = 5 cm
The area of triangle PQR is 231 cm2 , and PQ = 21 cm. Find the altitude SR. Help me solve this
Answer:
SR = 22 cm
Step-by-step explanation:
area = bh/2
(21 cm)(h)/2 = 231 cm^2
21h = 462 cm
h = 22 cm
SR = 22 cm
(x+8)^2-2(x-8)(x-2)+(x+2)^2=15
find the value of x in the triangle.
Answer:
The answer is 36°.
Hope it helps.
Step-by-step explanation:
• • •
How many terms are in the following geometric sequence? Type your numerical answer only. Do not type any additional characters.
0.0625, 0,25, 1, 4194304
Given:
The given geometric sequence is:
0.0625, 0.25, 1, ..., 4194304
To find:
The number of terms in the given geometric sequence.
Solution:
We have,
0.0625, 0.25, 1, ..., 4194304
Here, the first term is 0.0625 and the common ratio is:
[tex]r=\dfrac{0.25}{0.0625}[/tex]
[tex]r=4[/tex]
The nth term of a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]a_n=4194304, a=0.0625, r=4[/tex] in the above formula, we get
[tex]4194304=0.0625(4)^{n-1}[/tex]
[tex]\dfrac{4194304}{0.0625}=(4)^{n-1}[/tex]
[tex]67108864=(4)^{n-1}[/tex]
[tex]4^{13}=(4)^{n-1}[/tex]
On comparing both sides, we get
[tex]13=n-1[/tex]
[tex]13+1=n[/tex]
[tex]14=n[/tex]
Therefore, the number of terms in the given geometric sequence is 14.
Kraig deposited money into a money market account. It has an interest of 12% and is compounded annually. Kraig thought 3% would be the equivalent quarterly interest rate. Is Kraig correct? If he is, explain why. If he is not correct, state what the equivalent quarterly interest rate. Explain.
Answer:
If the amount is P, with the interest rate of 12%, the interest over the year is:
P*(1.12) - P = 0.12PIn this case the quarterly interest rate is:
0.12P/4 = 0.03PWith the same amount and 3% quarterly rate, the yearly interest would be:
P*(1.03)^4 - P = 0.1255PThe quarterly interest rate in this case is:
0.1255P/4 = 0.031375PIf the quarterly interest rate is r, it should be little less than 3% to yield a 12% yearly rate.
So Kraig is wrong.
