4 total numbers, 2 are odd
probability of getting odd = 2/4 = 0.50 =50%
Answer: 50%
Rahul drives 10 miles in 20 minutes. If he drove three hours in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Rahul drive in total?
Answer: 180 minutes
90 miles in 3 hours
Step-by-step explanation:
60 minutes = 1 hour
60 mins/20 mins = 3
60*3 = 180
30 miles per hour for 3 hours is 90 miles
Complete the long division problem on your own sheet of paper. Then, fill in the digits. 2 ÷ 694
Answer:
Here!! Hope i helped.
PLEASE HELP For what value of x is the parallelogram a rectangle. The arrows point to the entire diagonal, not just a segment.
Mike is working on solving the exponential equation 37x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.
Use the change of base formula: log base b of y equals log y over log b.
[tex]~~~~~37^x = 12\\\\\implies \ln\left( 37^x \right) = \ln(12)\\\\\implies x \ln (37) = \ln(12)\\\\\implies x = \dfrac{\ln(12)}{\ln(37)}\\\\\implies x \approx 0.689[/tex]
As a single logarithm, 2log2 6- log29+ 1/3log2 27 = log2 12.
Answer:
true
Step-by-step explanation:
2log2 6- log2 9+ 1/3log2 27 =
= log2 6² - log2 9 + log2 27^(1/3)
= log2 36 - log2 9 + log2 3
= log2 [(36 × 3)/9]
= log2 12
The statement is true.
Find the amount accumulated after investing m principal P for t and an internet rate compounded annually P=40500 r=3.8% t=20 k=12
The amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
What is an interest in banking?Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formula for calculating compound interest is expressed as;
A = P(1 + r/k)^(k*t)
Where A is final amount, P is initial principal balance, r is interest rate, k is number of times interest applied per time period and t is number of time periods elapsed.
Given that;
Initial principal balance P = $40500Interest rate r = 3.8= 3.8/100 = 0.038Time t = 20 yearsNumber of times interest applied per time period = 12 (annually) = 12/12 = 1 Amount accumulated A = ?A = P(1 + r/k)^(k*t)
A = 40500(1 + 0.038/1)¹ˣ²⁰
A = 40500 × (1.038)²⁰
A = 40500 × 2.10837
A = $85389
Therefore, the amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
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On a recent survey, 35% of those surveyed indicated that they preferred running. If 540 people were surveyed, how many people preferred running?
Answer: 189 people preferred running.
Step-by-step explanation: 35% is equal to 35/100. Since 540 people were surveyed, we can multiply 35/100 by 540 to find that 189 people out of 540 preferred running. Hope this helps!
PLeaseeeee Help
6. Given the order pairs (2, 3), (4, 5), (4, 7), (5, 10), and (6, 8) find the following. Round all final answers to three decimals places. Be careful not the round to early.
Express the line of best fit in the form of y = mx+b.
(a) The line of best fit. =
(b) Find the coefficient of linear correlation. =
Answer:
B
Step-by-step explanation:
answer is based on results from the Cartesian plane
Given the function f(x) = (1/4)^x , how will g(x) = (1/4) ^x-3 + 5 be translated
See
x is decreased by 3 .
and y is increased by 5
So translation is
f(x)=(1/4)^xHence
f(x)=(1/4)^x-3+5So
x will go 3 units right
y will go 5units up
Graph attached
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]
Translated 3 units to the right:
[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]
Translated 5 units up:
[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]
[tex]\implies g(x)=f(x-3)+5[/tex]
Therefore:
[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]
If 5 times a certain number is 40, and 9 times the same number is 72, how would you find 59 times that number? A)400 + 72 B)40 + 72 C)40 × 72 D)400 + 720 pls tell answer urgently.
Answer:
A) 400 + 72
Step-by-step explanation:
Let the certain number be denoted by x.
⇒ 5x = 40 [Equation 1]
⇒ 9x = 72 [Equation 2]
Multiply Equation 1 by 10 :
⇒ 10(5x) = 40(10)
⇒ 50x = 400 [Equation 3]
Finding the sum of Equation 2 and Equation 3 :
⇒ 50x + 9x = 400 + 72
⇒ 59x = 400 + 72
Hence, 59 times a certain number is represented by : 400 + 72
Help me with the 2 problems
Answer:
9) Vincent will not get the correct answer because the + 484 is unneccesary, as he already subtracted it.
10a) 310,000 + x = 465,000; so x = 155,000
10b) 930,000/310,000 = 3 times more
Step-by-step explanation:
Which of these numbers are relatively prime to 51? Select all that apply. da) 84 Ob) 70 Oc) 62 0d) 30
Answer:
b) 70
c) 62
Step-by-step explanation:
Numbers are relatively prime when they have no factors in common.
__
The factors of 51 are ...
51 = 3×17
The factors of the other numbers are ...
84 = 2²×3×7 . . . . . has a factor of 3 in common with 51
70 = 2×5×7 . . . . . . no factors in common
62 = 2×31 . . . . . . . no factors in common
30 = 2×3×5 . . . . . has a factor of 3 in common with 51
The numbers 70 and 62 are relatively prime to 51.
Given: 1 = 2
If AB = 10, AC = 6, and BC = 6, find AD:
The length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.
What is Angle Bisector?The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts.
Here, Let the lenght of AD be x
AB = 10 , AC = 6 and BC = 6
by Angle-Bisector theorem which states that
if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.
So, CD/BD =AC/AB
CD/(BC-CD) = 6/10
10. CD = 6.BC - 6.CD
16 CD = 6 X 6
16 CD = 36
CD = 36/16
CD = 2.25
Now, AD = AC - CD
AD = 6 - 2.25
AD = 3.75
Thus, the length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.
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Angle θ is in standard position. if sin(θ) = − 1/3, and π < θ < 3π/2 , find cos(θ).
A. -(2√2)/3
B.4/3
C.2√2/3
Answer:
Step-by-step explanation:
[tex]sin^2({ \theta})+cos^2({ \theta})=1\\cos({ \theta})=-/+\sqrt{1-sin^2({ \theta})} \\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} \\ --- > sin({ \theta})=\frac{1}{3} (known)\\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} =-\sqrt{1-(-\frac{1}{3})} =-\sqrt{\frac{9-1}{9}} =-\frac{2x^{2} }{3}[/tex]
City A is 300 km due east of city B. City C is 200 km on a bearing of 123° from city B. How far is it from C to A?
Answer:
500 km
Step-by-step explanation:
300 plus 200 is 500km this is how far it is
The distance between City A & City C is approximately 171.3km
Given that, city A is 300 km due east of city B.
City C is 200 km on a bearing of 123° from city B.
We need to find the distance between the cities A and C,
Here we will use the concept of Cosine rule,
{Refer to the figure attached}
From ∆ABC, to find |AC|,
The cosine rule will be used.
|AC|² = |BC|² + |AB|² - 2(|BC|)(|AB|)cosB
Let |AC| = x
x² = 200² + 300² - 2(200)(300)cos33
x² = 40000 + 90000 - 120000cos33
x² = 130000-100644
x² = 29356
x = √29356
x = 171.3359
x ≈ 171.3km
Therefore, the distance between City A & City C is approximately 171.3km
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Need help thank you
Answer: [tex]i\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{-5}=\sqrt{(-1)(5)}=\sqrt{-1} \sqrt{5}=\boxed{i\sqrt{5}}[/tex]
PLEASE HELP WILL MARK BRSINLIEST!!!!!pleaseeee
Answer:
[tex]x(3x-7)=3x^2-7x[/tex]
Step-by-step explanation:
[tex]\Large \begin{array}{| c | c | c |}\cline{1-3} \textsf{x} & 3x & -7\\\cline{1-3} x & 3x^2 & -7x\\\cline{1-3}\end{array}[/tex]
[tex]\textsf{Therefore,}\quad x(3x-7)=3x^2-7x[/tex]
Tosha received a 9.5 for vault, a 9.1 for bars, a 9.625 for beam, a 9.25 for her floor exercise at her last gymnastics meet. What was her combined (or total) score?
Answer:
9.500+9.100+9.625+9.250=
18.600+18.875=
37.475
Hope this helps!
Solve for x. Round to the nearest tenth.
Answer:
x = 27.19
Step-by-step explanation:
Sin(54) =22/x
0.81=22/x
x0.81= 22
x = 27.19
Simplify: (5 + i)(5 − i)
A) −12
B) 24i
C) 26
D) 8i
Answer:
C) 26
Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.
5 × 5 = 25 + positive 1(i) = 26
Answer:
option c, 26
Step-by-step explanation:
(5 + i)(5 - i)
Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2
a = 5, b =1
(5)^2 + (1)^2
(5)^2 = 25
(1)^2 = 1
25 + 1
can anyone help plssss??
Answer:
42 degrees
Step-by-step explanation:
48+90=138
180-138=42
Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to indicate exponents. For example, type a2 as a∧2. (Hint: Let s be a length of each side and x be the angle measure; then use these variables in the law of cosines.)
The algebraic proof shows that the angles in an equilateral triangle must equal 60° each
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.
Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are
cos A = (b² + c² - a²)/2bc
cos B= (a² + c²- b²)/2ac
cos C = (a²+ b²- c²)/2ab
Now, given that the triangle is equilateral, with each of the side lengths equal to s
That is, a = b = c = s
Then, we can write that
cos A = (s² + s² - s²)/(2s×s)
cos A = (s² )/(2s²)
cos A = 1/2
cos A = 0.5
∴ A = cos⁻¹(0.5)
A = 60°
Also
cos B = (s² + s² - s²)/(2s×s)
cos B = (s²)/(2s²)
cos B = 1/2
cos B = 0.5
∴ B = cos⁻¹(0.5)
B = 60°
and
cos C = (s² + s² - s²)/(2s×s)
cos C = (s² )/(2s²)
cos C = 1/2
cos C = 0.5
∴ C = cos⁻¹(0.5)
C = 60°
Thus,
A = 60°, B = 60° and C = 60°
Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.
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Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of PQ. P(1,4), Q(3,-2)
Answer:
a) 6.3; b) (2;1).
Step-by-step explanation:
[tex]a) \ |PQ|=\sqrt{(X_P-X_Q)^2+(Y_P-Y_Q)^2}=\sqrt{4+36}=\sqrt{40} =6.3;[/tex]
[tex]b) \ (\frac{X_P+X_Q}{2};\frac{Y_P+Y_Q}{2}); \ = > \ (2;1).[/tex]
Find the standard deviation of the data, 12, 19, 9.
Answer:
4.19
Step-by-step explanation:
Find the mean:
[tex]\text{Mean}=\frac{12+19+9}{3}=\frac{40}{3}[/tex]
Find the standard deviation:
[tex]\text{Standard Deviation}=\sqrt{\frac{(12-\frac{40}{3})^2+(19-\frac{40}{3})^2+(9-\frac{40}{3})^2}{3}}=\sqrt{\frac{158}{9}}\approx4.19[/tex]
Find the factor of each ff.
6z²+12z+18
Answer:
Step-by-step explanation:
6z² + 12z +1 8
= 6(z^2 + 2z + 3).
That's it.
1/5 is 60% of what number
1/5 = 60/100 * x
1/5 * 100/60 = x
100/300 = x
1/3 = x
Answer:
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
According to what we know, one-fifth is 60% of a number. Let us call that unknown number x. Since
[tex] \frac{1}{5} = 60\% \: \\ then \\ x = 100\%[/tex]
60% as a fraction is 6/10 or 3/5, in that case 100% as a fraction would be 5/5.
Recall: 60% = 3/5 and 100% = 5/5
therefore:
1/5 = 3/5
x = 5/5
note in order to find the value of x we cross multiply*
[tex] \frac{1}{5} ( \frac{5}{5}) = \frac{3}{5} x[/tex]
[tex] \frac{1}{5} = \frac{3}{5} x \\ \\ \frac{ \frac{1}{5} }{ \frac{3}{5} } = \frac{ \frac{3}{5} }{ \frac{3}{5} } x \\ \\ \frac{1}{5} \times \frac{5}{3} = x[/tex]
[tex] \frac{1}{3} = x[/tex]
This window is designed in the shape of a right trapezoid.
Answer: 128°
Step-by-step explanation:
There are 360° in a trapezoid. Since this is a right trapezoid, two of those angles will be equal to 90°. We will set up the following equation, and solve.
360° = 90° + 90° + 52° + x°
360° = 90° + 90° + 52° + x°
360° = 232° + x°
128° = x
x = 128°
The obtuse angle has a measure of 128°.
is 3/2 = to square of 2
Answer:
No, it will not
Step-by-step explanation:
as square of 2 is 4
May I please get help to this question.
Answer: 3
Step-by-step explanation:
Sandy baked two dozen cookies. She gave ten cookies to the neighbours and ate three cookies.
How many cookies are left?
Answer:
11
Step-by-step explanation:
2 dozen = 24
24-10=14
14-3=11
Answer:
11
Step-by-step explanation:
two dozens is 24 because one dozen is 12. 24-10=14-3=11
