Answer:
0.0276
Step-by-step explanation:
The computation of the probability that the next driver is texting while driving is shown below:
= Fourth pull failure × fifth pull success
where,
Fourth pull failure is (1 - 0.52)^4
And, the fifth pull success is 0.52
Now placing these values to the above formula
So,
= (1 - 0.52)^4 × 0.52
= 0.0276
Hence, the probability is 0.0276
Marcus played 3 different activities this week after school. The time he spent playing is described below. Swam forof an hour Played soccer for 9/10 2/3 2/4 of an hour Jogged forof an hour Which statement correctly compares the times of 2 of his activities?
Answer:
A
Step-by-step explanation:
We can find a common denominator for all of these fractions, compute, and then compare the values to find the right answer.
the sum of three consecutive numbers is 276. What is the smallest of these intengers?
Answer:
91
Step-by-step explanation:
Let x be the smallest one:
● x is the first number
● x+1 is the second number
● x+2 is the third number
The sum of these numbers is 276
● x+(x+1)+(x+2) =276
● x+x+1+x+2 = 276
● 3x + 3 = 276
Substract 3 from both sides:
● 3x+3-3 = 276-3
● 3x = 273
Divide both sides by 3
● (3x)/3 = 273/3
● x = 91
So the smallest one is 91
This diagram is a straightedge and compass construction. A is the center of one circle,
and B is the center of the other. Explain how we know triangle ABC is equilateral.
ABC is a equilateral triangle .
Proof :-
Let's assume both circles as C1 and C2 [ as shown in the figure ]
AB is the radius of circle C1 AB is the radius of Circle C2AC is the radius of circle C1.
BC is the radius of circle C2 .
AB and AC both are radius of circle C1 so both are equal ie AB = AC .
AB and BC both are radius of circle C 2 so both are equal ie AB = BC .
Hence we conclude that .
AB = BC = AC.
So the triangle is equilateral triangle.
The area of a circle is 16π cm2. What is the circle's circumference?
Answer:
C = 8 pi cm
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
16 pi = pi r^2
Divide each side by pi
16 = r^2
Taking the square root
4 = r
The circumference is
C = 2 * pi *r
C = 2* pi *(4)
C = 8 pi cm
Help anyone can help me do this question,I will mark brainlest.
Answer:
Hello,
Step-by-step explanation:
Loi d'Ohm: U=R*I
a) U=20*0.5=10 (amp)
b) I=U/R=50/0.5=100 (amp)
Solve for x : 2^(x-5) . 5^(x-4) = 5
Answer:
x = 5
Step-by-step explanation:
Notice that there is also a base 5 on the right hand side of the equation, therefore, let's move [tex]5^{x-4}[/tex] to the right by dividing both sides by it. and then re-writing the right hand side as 5 to a power:
[tex]2^{x-5}\,*\,5^{x-4}=5\\2^{x-5}=5/5^{x-4}\\2^{x-5}=5\,*\,5^{4-x}\\2^{x-5}=5^{5-x}[/tex]
Now apply log to both sides in order to lower the exponents (where the unknown resides):
[tex](x-5)\,log(2)=(5-x)\,log(5)[/tex]
Notice that when x = 5, this equation is true because it makes it the identity: 0 = 0
So, let's now examine what would be the solution of x is different from 5, and we can divide by (x - 5) both sides of the equation:
[tex]log(2)=\frac{5-x}{x-5} \,log(5)\\log(2)=-1\,\,log(5)\\log(2)=-log(5)[/tex]
which is an absurd because log(2) is [tex]\neq[/tex] from log(5)
Therefore our only solution is x=5
Answer:
if decimal no solution
if multiply x =5
Step-by-step explanation:
If this is a decimal point
2^(x-5) . 5^(x-4) = 5
Rewriting .5 as 2 ^-1
2^(x-5) 2 ^ -1 ^(x-4) = 5
We know that a^ b^c = a^( b*c)
2^(x-5) 2 ^(-1*(x-4)) = 5
2^(x-5) 2 ^(-x+4) = 5
We know a^ b * a^ c = a^ ( b+c)
2^(x-5 +-x+4) = 5
2^(-1) = 5
This is not true so there is no solution
If it is multiply
2^(x-5) * 5 ^(x-4) = 5
Divide each side by 5
2^(x-5) * 5 ^(x-4) * 5^-1 = 5/5
We know that a^ b * a^c = a^ ( b+c)
2^(x-5) * 5 ^(x-4 -1) = 1
2^(x-5) * 5 ^(x-5) = 1
The exponents are the same, so we can multiply the bases
a^b * c*b = (ac) ^b
(2*5) ^ (x-5) = 1
10^ (x-5) = 1
We know that 1 = 10^0
10^ (x-5) = 10 ^0
The bases are the same so the exponents are the same
x-5 = 0
x=5
The length of a rectangle is seven inches more than its width. Its area is 540 square inches. Find the width and
length of the rectangle.
Answer: 20 is the width and 27 is length
Find the midpoint of the line segment whose endpoints are (2.6,5.1) and (3,4.7).
1. (0.2, 0.2)
2. (1.45, 4.9)
4. (2.8, 4.9)
Answer:
Mid point is: (2.8;4.9)
Step-by-step explanation:
To find midpoint of a line segment we can use the general equation:
[tex]Mid=\frac{x_1+x_2}{2} ;\frac{y_1+y_2}{2}[/tex]
Where the point of the line are: (x₁;y₁) and (x₂;y₂).
In the problem, x₁ = 2.6, y₁ = 5.1 and x₂ = 3 and y₂ = 4.7. Replacing in the equation:
[tex]Mid=\frac{2.6+3}{2} ;\frac{5.1+4.7}{2}[/tex]
Mid point is: (2.8;4.9)Answer:
(2.8, 4.9)
Step-by-step explanation:
What is the LCD of 1/2 and 3/5
Answer:
10
Step-by-step explanation:
How you find LCD (lowest common denominator) is that you have to look at the denominator (the bottom number) and try to find the lowest multiple between both of the numbers that is on the bottom (in this case it is 2 and 5). Sometimes you have to multiply both denominators together to get a LCD.
Example of multiplying two denominators together to get an LCD:
1/3 and 1/13 LCD is 39 because you multiply 3 and 13.
1/5 and 1/4 LCD is 20 because you multiply 5 and 4.
HELP !!! find the surface area of each figure. Round it to the nearest tenth.
Answer:
556
Step-by-step explanation:
Surface area=2*(lb+bh+lh)=2*(110+80+88)=556
Find the value of x to the nearest degree.
A. 35
B. 28
C. 51
D. 55
Answer:
A
Step-by-step explanation:
First, we are already given the sides adjacent and opposite to ∠x. Therefore, we can use the tangent function. Recall that:
[tex]\tan(x)=opp/adj[/tex]
The opposite side is 20 while the adjacent side is 14.
Plug in the numbers. Use a calculator:
[tex]\tan(x)=20/14=10/7\\x=\tan^{-1}(10/7)\\x\approx55.0080\textdegree\approx55\textdegree[/tex]
Edits: Improved Answer. Removed Wrong Answer.
Answer:
55
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan x = 20/14
Taking the inverse tan of each side
tan ^-1 tan x = tan ^ -1 (20/14)
x =55.0079798
To the nearest degree
x = 55
A man lends 12,500 at 12% for the first
year, at 15% for the second year and at 18%
for the third year. If the rates of interest are
compounded yearly; find the difference
between the C.I. of the first year and the
compound interest for the third year.
Answer: $1398
Step-by-step explanation:
Given , Principal (P) = $12,500
Rate of interest for 1st year [tex](R_1)[/tex]= 12% =0.12
Rate of interest for 2nd year [tex](R_2)[/tex]= 15% =0.15
Rate of interest for 3rd year [tex](R_3)[/tex]= 18% =0.18
Interest for first year = [tex]I=P\times R_1\times T[/tex]
= [tex]12500\times 0.12\times 1[/tex]
= $1500
Now, For second year new principal [tex]P_2 = \$12,500+\$1,500 =\$14,000[/tex]
Interest for second year = [tex]I=P_2\times R_2\times T[/tex]
= [tex]14000\times 0.15\times 1[/tex]
= $2100
Now, For third year new principal [tex]P_3 = \$14000+\$2,100 =\$16,100[/tex]
Interest for third year = [tex]I=P_3\times R_3\times T[/tex]
= [tex]16100\times 0.18\times 1[/tex]
= $2898
Difference between the compound interest of the first year and the compound interest for the third year. = $2898 - $1500 = $1398
Hence, the difference between the compound interest of the first year and the compound interest for the third year is $1398 .
a box's volume set is 112 cubic inches. it has an open top. what is the length, width, and height?
hi
it a cube so it's height,length and width are the same.
if volume is 112 so one if this measure is : 112^(1÷3) =4,82
PLEASE HELP I WILL GIVE BRAINLIEST Complete the frequency table: Method of Travel to School Walk/Bike Bus Car Row totals Under age 15 60 165 Age 15 and above 65 195 Column totals 152 110 98 360 What percentage of students under age 15 travel to school by car? Round to the nearest whole percent. 11% 18% 41% 80%
Answer:
11%
Step-by-step explanation:
1. Fill out the table with the correct numbers.
2. After you fillout the numbers, you should notice that under the column car and in the first row, there should be the number 18.
3. We know the total number of students under the age of 15 is 165.
4. To find the percent:
18/165 * 100
= 11%
Answer:
41%
Step-by-step explanation:
Look at the column "Age 15 and above".
Notice how the row total for that column is 195.
Also, look at "Bus".
Notice how there is a gap between 60 and 110.
To calculate the answer, you need to fill in the blanks using the surrounding numbers.
60 + 50 = 110, so to the right of "65" on "Age 15 and above", there should be a 50.
The "195" at the end of the row is now on the same row as the numbers: 65, 50, and a blank spot.
Now, all we have to do is simply ask ourselves what 65 + 50 gets us, and what we need to add to that to get 195.
65 + 50 = 115, 115 + 80 = 195.
Although, notice that this does not mean the answer is not 80%.
We need to find what percentage is 80 out of 195.
80 out of 195 = 41.03%.
By rounding, we will get an answer of 41%.
Maria sold t-shirts at a festival. She made 6$ for each t-shirt she sold. Her expenses were 30$. If she made a profit of 84, how many t-shirts did she sell?
high reward low risk claim ur prize and help with math
the two lines are parallel, the angle they make should be equal and one angle is common so the triangles are similar by AAA.
Now the ratio of sides are [tex] \frac{20+8}{20}=\frac{x+18}{x}[/tex]
use divideno, [tex]\frac8{20}=\frac{18}x[/tex]
and then inverse the whole equation to get [tex]x=20\times\frac{18}{8} \implies x= 45[/tex]
Answer:
[tex]\Large \boxed{\mathrm{B) \ 45}}[/tex]
Step-by-step explanation:
We can solve the problem using ratios.
[tex]\displaystyle \frac{x}{20} =\frac{x+18}{20+8}[/tex]
Cross multiply.
[tex]20(x+18)=x(20+8)[/tex]
Expand brackets.
[tex]20x+360=28x[/tex]
Subtract 20x from both sides.
[tex]360=8x[/tex]
Divide both sides by 8.
[tex]45=x[/tex]
Find the area of the semicircle. diameter = 12
Answer:
[tex]\huge\boxed{\sf Area\ of \ Semicircle = 56.55 \ units^2}[/tex]
Step-by-step explanation:
Diameter = 12
Radius = 12/2 = 6
[tex]\sf Area\ of \ Semicircle =\frac{\pi r^2}{2} \\Area\ of \ Semicircle =\frac{\pi (6)^2}{2} \\Area \ of \ Semicircle = \frac{\pi (36)}{2}\\ Area \ of \ Semicircle = 18 \ pi[/tex]
[tex]\sf Area\ of \ Semicircle = 56.55 \ units^2[/tex]
Answer:
18π units²
Step-by-step explanation:
(see attached for reference)
Recall that the area of a whole circle is given by:
A = (π/4) D²,
where D is the diameter of the circle.
We know that the area of a semi-circle is half the area of a whole circle.
Therefore,
Area of Semi Circle
= (1/2) x area of whole circle
= (1/2) x (π/4) D² (Substitute D = 12 units)
= (1/2) x (π/4) (12)²
= 18π units²
HELLLLPPPPP PLZZZZ!!!!
Answer:
width = 5 ft
Step-by-step explanation:
1.9 times of width = length
1.9*w = 9.5 ft
1.9w = 9.5
Divide both sides by 1.9
w = 9.5/1.9
w = 5 ft
Answer:
1.9w=9.5
w=width
1.9(w)=9.5
1.9(5)=9.5
Width(w)=5
Find the distance across the lake. Assume the triangles are similar.
80 m
х
у
20 m
60 m
Answer:
a
Step-by-step explanation:
Answer:
A. L = 240 m
Step-by-step explanation:
use similar triangle
L / 60 = 80 / 20
L = (80 * 60) / 20
L = 240 m
Doubling both the area of the bases and the height of a prism doubles its volume. T/F
Answer:
True.
Step-by-step explanation:
Answer: False
==========================================================
Explanation:
Let's consider a prism that has dimensions of
L = 3 ft W = 4 ft H = 5 ftand we'll say that the base is a rectangle with length L and width W. The area of the base is L*W = 3*4 = 12 sq ft. The volume of this prism is L*W*H = 3*4*5 = 60 ft^3
If we double the area of the base, then we go from 12 ft^2 to 24 ft^2. If we double the height, then we go from 5 ft to 10 ft.
The new volume of this larger prism is (area of base)*(height) = (24)*(10) = 240 ft^3
The jump from 60 ft^3 to 240 ft^3 is not "times 2". Instead, the multiplier is 240/60 = 4. This example shows that the volume has been quadrupled.
Geometry, please answer question ASAP
A 4-pack of greeting cards costs $7.40. What is the unit price?pls answer fast
Answer:
The unit price of the problem is that one pack of greeting cards costs $1.85
Step-by-step explanation:
In order to find the unit rate, you have to divide the price by the quantity of the product. So, we will divide 7.40 by 4 so we can see the price of one pack.
7.40 ÷ 4 = 1.85
So, one pack of greeting cards costs $1.85 which is also our unit price.
Answer:
1.85
Step-by-step explanation:
First, divided the money ( $7.40 ) by the whole number ( 4 )
Then, you will receive your answer
Helppppp!!!! Thank you
Greetings from Brasil...
In a triangle the sum of the internal angles is 180 °.... Thus,
Ô = 180 - 30
Ô = 60
The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60
A1 = area of the rectangle triangle
TG B = OA/AB
AB = OA / TG B
AB = 6 / TG 30
AB = 6√3
A1 = (AB . OA)/2
A1 = (6√3 . 6)/2
A1 = 18√3A2 = area of the circular sector
(rule of 3)
º area
360 ------------ πR²
60 ------------ X
X = 60πR²/360
X = 6π
So,
A2 = 6πThen the area shaded is:
A = A1 - A2
A = 18√3 - 6πEvaluate the expression for x=-5,y=-7, and z=9
Answer:
Is 11
Step-by-step explanation:
x+(-y)+z —> -5 +(+7)+9 = -5+7+9 = 11
Find the Area of the figure below, composed of a rectangle and one semicircle, with another semicircle removed. Round to the nearest tenths place.
I need help, please
Answer:
so you multiply the 13 by 12. Then divid 12 by 2 to get 6 as the radius then use a calculator and type in 2(PIE SYMBOL) R. R=radius then whatever number you get cut it in half then subtract it from 13x12.
help asap will give 10 points
Answer:
FALSE
Step-by-step explanation:
The properties of exponents tells us that
[tex]9^9\ \ *\,\,9^{-20}\,=\,9^{9-20}\,=9^{-11}[/tex]
Answer:
False
Step-by-step explanation:
[tex](9 {}^{9} ) \times (9 {}^{ - 20}) = 9 {}^{9 + ( - 20)} = 9 {}^{9 - 20} = 9 {}^{ - 11} [/tex]
Hope this helps ;) ❤❤❤
The graph of y=x^2 - 2x- 3 is shown above. What are the zeros and factors of y=x^2 - 2x -3
A. X=1 and x = -3;(x-1)(x+3)
B. X=-1 and x = -3;(x+1)(x+3)
C. X=1 and x = -3;(x-1)(x-3)
D. X=-1 and x = -3;(x+1)(x-3)
Answer:
zeros -1,3 and the factors ( x+1) (x-3)
Step-by-step explanation:
The zeros are where it crosses the x axis
It crosses at x=-1 and x=3
So the factors are ( x- -1) and ( x-3)
( x+1) (x-3)
Answer:
[tex]\boxed{x = -1, \ x = 3 \ \ ( x+1) (x-3)}[/tex]
Step-by-step explanation:
Zeros of the function:
The zeros of a function is when the y value is 0 or where the function crosses the x-axis.
The function crosses the x-axis at x = -1 and x = 3.
Factors of the function:
[tex]y=x^2 - 2x- 3[/tex]
Factor the right side.
[tex]y=x^2 +1x-3x- 3[/tex]
[tex]y=x(x +1) -3(x+1)[/tex]
Take (x + 1) common.
[tex]y=(x+1)(x-3)[/tex]
The factors are (x + 1) and (x - 3).
PLZ HELP MEH:(
Mean, Median, and Mode
quenage
Find the mean, median, mode and range for each set of data.
1. 6. 9, 2, 4, 3, 6,5
2. 25, 18, 14, 27, 25, 14, 18, 25, 23
3. 453, 345, 543, 345, 534
4. 13, 6, 7, 13,6
5. 8, 2,9, 4, 6, 8,5
6. 13, 7, 17, 19, 7, 15, 11, 7
7. 1, 15, 9, 12, 18, 9, 5, 14, 7
8. 28, 32, 23, 43, 32, 27, 21, 34
9. 3,9, 4, 3, 9, 4, 2, 3, 8
10. 42, 35, 27, 42, 38, 35, 29, 24
11. 157, 124, 157, 124, 157, 139
Answer:
to find the mean add all numbers the divide by the ammount of numbers given
Step-by-step explanation:
ex: 1 , 2 , 3
add:
1+2+3=6
divide:
6 / 3 = 2
your mean is 2
all good?
Answer: to find the mean add up all numbers and divide them by the amount of numbers there and to find the median that is the middle number write it on a piece of paper and cross out the beginning and end till you get the to the middle that is your median
Step-by-step explanation:
A jet ski rental company charges h dollars for the first hour its jet skis are rented and k
dollars per hour for each hour rented after the first. If a jet ski is rented for t total hours,
where t is an integer greater than 2, which of the following represents the total rental cost
of the jet ski?
h+t+k
B
h+ tk
h+k(t-1)
h+k(t + 1)
h+
Answer:
C. h + k (t - 1)
Step-by-step explanation:
If we use an example, you can plug in the numbers and test out which equation works. Say the first hours costs $10 and each hour after that is an additional $5. If someone rents a jet ski for 4 hours, how much did it cost?
The first hour = $10
The 3 additional hours (totaled) = $15
Cost = $25
So now that we know the cost, we can plug in our numbers to these equations to find which one comes out with $25.
h = 10
k = 5
t = 4
A. 10 + 4 + 5 = 19
B. 10 + (4 · 5) = 10 + 20 = 30
C. 10 + 5 (4 - 1) = 10 + 5 (3) = 10 + 15 = 25
D. 10 + 5 (4 + 1) = 10 + 5 (5) = 10 + 25 = 35
E. 10 + (4/5 - 1) = 10 + (-0.2) = 9.8
C is the only problem that comes out as $25, therefore it must be the correct answer.
Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are (–1, 0). What are the coordinates of B? B( , )
Answer:
-2, 3
Step-by-step explanation:
To find the coordinates of B, we need to understand the translation that has taken place. In a translation, each point of a figure is moved the same distance and in the same direction.
In this case, point A(5, 1) has been translated to point A'(6, -2). To find the distance and direction of the translation, we subtract the coordinates of A from the coordinates of A': Translation Vector [tex]= (6 - 5, -2 - 1) = (1, -3)[/tex] The translation vector represents the change in x and y coordinates between the original figure and its translated image.
Since B' has coordinates (-1, 0), we can apply the translation vector to find the coordinates of B as follows: B = B' - Translation Vector B [tex]= (-1, 0) - (1, -3)[/tex] B [tex]= (-1 - 1, 0 - (-3)) B = (-2, 3)[/tex] So, the coordinates of B are (-2, 3).
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