Answer:
a:b = 14 : 15
Step-by-step explanation:
The equation is 2a−3b/5 = a+b/3
To find the ratio you will find the fraction of a/b. Therefore,
2a−3b/5 = a+b/3
(10a - 3b)/5 = (3a + b)/3
cross multiply
3(10a - 3b) = 5(3a + b)
30a - 9b = 15a + 5b
collect like terms
30a -15a - 9b - 5b = 0
15a - 14b = 0
15a = 14b
divide both sides by b
15a/b = 14
divide both sides by 15
a/b = 14/15
Therefore,
a:b = 14 : 15
Answer:
14:1
Step-by-step explanation:
this is right
What is the area of this figure?
Answer: 84
Step-by-step explanation: break down the parts and you multiply the sides and the answer to the square is 30 and the other half is 54 so 30 +54 =84
the average human hair measures about 90 micrometers wide which is 0.00009 correctly represent this in scientific notation
Answer:
90 micrometers / 1,000,000 = 0.00009 meters =
9 x 10^-5 meters
Step-by-step explanation:
Answer:
0.9 x 10^-4
Step-by-step explanation:
its pretty simple lol
A game advertises, EVERYONE IS A WINNER! It costs $2 to play. You get to choose a card from a standard deck of 52 playing cards. If you choose a red card, you win $3. If you choose a black card, you get $1. What is the expected value of playing this game?
$0
$1
$2
$3
Answer:
$2
Step-by-step explanation:
$2 because it's in between.
The total playing value will be $0.
What is probability?
Probability shows the possibility of any event to occur. The maximum value of probability can be 1 and shows the event will happen, and minimum can be 0, shows that event will not occur.
Given that,
Cost of playing the game= $2
There are total 52 playing cards,
Red cards=26
So, the probability to come red on card = 1/2.
Black cards=26
So, the probability to come black on card=1/2
If investor invests $2,
For red card, win $3,
The profit is $1
For black card, win $1,
The loss is $1
Total invest = $4
Total earning=$4
playing value = $4-$4=0.
So the total playing value will be $0.
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Bernardo heard that as a general rule, he should spend no more than one
week's pay on rent. If Bernardo's pay is $34,800 per year, what is the
maximum amount per month that he should spend on rent?
A. $2030
B. $2900
C. $1044
D. $669
Answer:
D. $669
Step-by-step explanation:
$34,800 yearly salary
34,800/52= $669 weekly salary
Find the exact values of sin 2x and cos 2x for cos x=3/7 on the interval 0
*view photo for choices*
Please help me . (Right now)
Answer:
The area of trapezoid is 39.6cm²
Step-by-step explanation:
Given that the formula of area of trapezoid is A = 1/2×(a+b)×h where a and b is the length and h is the height. So you have to substitute the values into the formula :
[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]
[tex]let \: a \: = 8.9 \\ let \: b \: = 5.5 \\ let \: h \: = 5.5[/tex]
[tex]area = \frac{1}{2} \times (8.9 + 5.5) \times 5.5[/tex]
[tex]area = \frac{1}{2} \times 14.4 \times 5.5[/tex]
[tex]area = \frac{1}{2} \times 79.2[/tex]
[tex]area = 39.6 {cm}^{2} [/tex]
Answer: The area is 39.6
Step-by-step explanation:
First multiply 5.5×5.5= 30.25
Then subtract 8.9 - 5.5=3.4
Then multiply 5.5 x 3.4=18.7
Divide 18.7/2=9.35
Add 30.25 + 9.35 =39.6
b x h ÷2
[tex]l *w=a[/tex]
Hope this helps.
Michael’s pencil box is shaped like a rectangular prism. It is 30.5 centimeters long, 20.3 centimeters wide, and 10 centimeters tall. He estimates that the surface area of the box is about 2,200 square centimeters. Is his estimate reasonable? Explain your reasoning.
Answer:
yes
Step-by-step explanation:
the approximate surface area is (30 × 20 × 2) + (30 × 10 × 2) + (20 × 10 × 2) or 2,200 cm2
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none,
then select none.
When m
8=m4
Answer:
b) AD || BC
Step-by-step explanation:
The missing options are:
a) AB || DC
b) AD || BC
c) none
The missing drawn is shown in the figure attached.
The only way that m∠8 = m∠4 is that segment AD and segment BC are parallel. Because in that case, they are alternate angles, and therefore, they are equal. Notice that angle 8 lies on side AD and angle 4 lies on BC
Answer:
b) AD || BC
Step-by-step explanation:
What is 588.75 to the nearest cubic inch?
Answer:
589
Step-by-step explanation:
To find the nearest cubic inch, round your volume measurement down to the nearest whole number if the number to the right of the decimal point is less than 0.5 . If the decimal point is 0.5 or greater, round up.
In this case, your decimal point is 0.75 , which is greater than 0.5 . This means we round up.
588.75 --> 589
Answer:
589
Step-by-step explanation:
588.75 rounded up would be 589!
If the base is 4, what is the value if the exponent is 2? What if the exponent is -2?
A) 16, 1/16
B)16, -16
C)8, -8
D)8, 1/8
The right answer is 16,1/16
Please see the attached picture for full solution
Hope it helps..
Good luck on your assignment
For the base value of 4, if the exponent is 2; the value will be 16.
For the base value of 4, if the exponent is -2; then value will be 1/16.
Base and ExponentA base number and an exponent are typically used to denote a power.
What is base value?The total number of digits required to express numbers in a number system is known as the base in mathematics. What number is being multiplied is revealed by the base number.
What is exponent?The exponent, a little number printed above and to the right of the base number, provides the multiplicative power of the base number.
Calculation for the exponent of 2:The base number is given as 4.
The exponent is given as 2.
So, the number becomes,
=> [tex]4^{2} =4[/tex]×[tex]4[/tex]
= 16
Thus, the base 4 with exponent 2 becomes 16.
Calculation for the exponent of -2:The base number is given as 4.
The exponent is given as -2.
So, the number becomes,
=> [tex]4^{-2} =\frac{1}{4^{2} }[/tex]
= [tex]\frac{1}{16}[/tex]
Thus, the base 4 with exponent -2 becomes 1/16.
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Given ( 12 -13 17 -22) (x y)= (7 -51), what is |A y|?
B.) | 12, 7, 17, -22 |
The complete question is attached below:
What is matrix ?A set of numbers arranged in rows and columns so as to form a rectangular array.
Given:
[tex]\left[\begin{array}{ccc}12&-13\\17&-22\end{array}\right]* \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}7\\-51\end{array}\right][/tex]
[ 12x - 13 y
17x - 22y ] = [tex]\left[\begin{array}{ccc}7\\-51\end{array}\right][/tex]
As we need to find Ay for that the matrix on RHS of equal sign [tex]\left[\begin{array}{ccc}7\\-51\end{array}\right][/tex] is to be putted in the matrix [tex]\left[\begin{array}{ccc}12&-13\\17&-22\end{array}\right][/tex]
Hence, Ay = [tex]\left[\begin{array}{ccc}12&7\\17 & -51\end{array}\right][/tex]
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Solve -3 1/2= 1/2x+ 1/2x+x
Answer:
-1 3/4
Step-by-step explanation:
1/2x + 1/2x + x
2x = -3 1/2
/2 /2
x = -1 3/4
Which is the best first step and explanation for solving this system of equations? 3x+4y=12 3x=2y-8
Answer:
Since it is a simultaneous equation,
Using elimination method, Multiply equation 1 by the co efficient of x in equation 2 and multiply equation 2 by the co efficient of x in equation 1.
Step-by-step explanation:
For further explanation , Please contact me through the comment section.
:)
Can someone help me with this?
You flip a coin 50 times. What is the probability that you will get tails exactly 35 times?
Answer:
35:50 would be the probability:)
There are 130 people in a sport centre.
73 people use the gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Thank you in advance. :)
Answer:
0
Step-by-step explanation:
the probability that this person doesn't use any facility = 0/130
= 0
hope it helps!
Point Q is the centroid of △ABC. QE = _____
The median of [tex]\triangle ABC[/tex] are lines CD, AE and BF. These lines meet at point Q, makes Q the centroid. The length of QE is 9 units.
The centroid of a triangle divides the median of a triangle using the following ratio;
[tex]m:n = 2:1[/tex]
This means that:
[tex]BQ:QF=2:1[/tex]
[tex]AQ:QE=2:1[/tex]
[tex]DQ:QC=2:1[/tex]
To calculate QE, we make use of:
[tex]AQ:QE=2:1[/tex]
From the triangle;
[tex]AQ = 18[/tex]
So, we have:
[tex]18:QE=2:1[/tex]
Express as a fraction
[tex]\frac{18}{QE}=\frac{2}{1}[/tex]
Cross multiply
[tex]2 \times QE = 18 \times 1[/tex]
[tex]2 \times QE = 18[/tex]
Divide both sides by 2
[tex]QE = 9[/tex]
Hence, the length of QE is 9 units.
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A spinner has 4 equal-sized sections. To win the game, the pointer must land on a purple section.
Complete the statement.
favorable outcomes
?
P(purple) =
= ?
total number of possible outcomes 4
Click the icon to view the spinner.
favorable outcomes
P(purple) =
total number of possible outcomes
(Type integers or simplified fractions.)
4
Answer:
1/4
Step-by-step explanation:
In a spinner which has 4 equal-sized sections., the probability of pointer must land on a purple section to win the game is 1/4.
What is probability?
Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
A spinner has 4 equal-sized sections. To win the game, the pointer must land on a purple section. Thus, the number of favorable outcomes is,
[tex]P(\text {purple}) =1[/tex]
Total number of possible outcomes is 4 as there is 4 equal-sized sections. Thus, the probability of the pointer must land on a purple section is,
[tex]P=\dfrac{1}{4}[/tex]
Thus, in a spinner which has 4 equal-sized sections., the probability of pointer must land on a purple section to win the game is 1/4.
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benjamin writes an expression for the sum of 1 cubed, 2 cubed, and 3 cubed. What is the value of the expression
Answer:
14
Step-by-step explanation:
(1*1)+(2*2)+(3*3)
1+4+9
5+9
14
The height (h) of a fireball launched from a Roman candle with an initial velocity of 64 feet per second is given by the equation h(t) = -16t^2 + 64t, where t is time in seconds after launch. Use the graph of this function to answer the questions. Estimate the time when the fireball is at its maximum height.
A. 2.3 seconds
B. 2 seconds
C. 0 seconds
D. 4 seconds
Answer: C or 2 seconds.
Step-by-step explanation:
To find the vertex in a standard form equation: (-b/2a,f(-b/2a))
plug it in: -64/2*-32 = 2
Find the area of the circle given the following information. Give the exact answer and an approximation to the nearest tenth.
________________________________
Hey!!!!
Solution,Diameter=12 in
Radius=12/2 =6 inch
Now,
Area of circle=pi r ^2
=3.14*(6)^2
=3.14*36
=113.04 inches^2
So the area of circle is 113.04 inches^2.Hope it helps......
Good luck on your assignment
________________________________
Draw diagonals from one vertex to all of the non-adjacent vertices. Which polygon is constructed from four triangles?
Answer:
B
Step-by-step explanation:
Answer:
It is B Because of the non-adjacent vertices.
Kai was making pizza for lunch. They used 1/4 of a package of pepperoni and 1/6
of a package of sausage. How much more pepperoni than sausage did Kai use on
their pizza?
Answer:
1/12 more pepperoni than sausage
Step-by-step explanation:
to make 1/6 and 1/4 have the same denominator you multiply top and bottom by 6 and 4.
1/6*4 = 4/24
1/4*6 = 6/24
6/24 - 4/24= 2/24= 1/12
Which graph shows the solution to the inequality -3x-7 <20?
Answer:
x > -9
Step-by-step explanation:
The solution to the inequality is obtained as follows:
-3x -7 < 20
-3x - 7 + 7 < 20 + 7
-3x < 27
-3x/(-3) > 27/(-3)
x > -9
Notice that when you divide by a negative number, the inequality sign changes.
In the picture attached, the graph of the solution s shown. Notice that -9 is not included in the solution.
A rectangular piece of cardboard that is 7 inches by 20 inches has squares of length x inches on a side cut from each corner.
(Assume that 0 < x < 3.) Represent the remaining area in the form of a polynomial function A(x).
Answer:
The remaining area in the form of a polynomial function [tex]A(x)= 140-4x^2[/tex]where 0 < x < 3.
Step-by-step explanation:
Breadth of rectangular piece of cardboard = 7 inches
Length of rectangular piece of cardboard = 20 inches
Area of cardboard = [tex]Length \times Breadth[/tex]
Area of cardboard = [tex]20 \times 7[/tex]
Area of cardboard =[tex]140 in^2[/tex]
Squares of length x inches on a side cut from each corner.
Length of square = x
Area of 1 square = [tex]Side^2 = x^2[/tex]
Area of 4 squares = [tex]4x^2[/tex]
Area of remaining portion [tex]A(x)= 140-4x^2[/tex]
So, the remaining area in the form of a polynomial function [tex]A(x)= 140-4x^2[/tex]where 0 < x < 3.
Answer the question. 20 points
-4/13 + 5/26
Answer:
erm
Step-by-step explanation:
-3/26
Answer:
Step-by-step explanation:
(-4/13)+(5/26)
So,now take the common denominator by taking least common multiple (LCM)..
LCM=26
= {(-4/13)x26} + {(5/26)x26}
= (-8+5)/26
= -3/26
Find the equation of a line passing through the point (6,−5) and parallel to the line y = 7x + 1. answers : y = 7x − 47 y = −17x + 41 y = −17x +477 y = 7x − 29
Answer:
y = 7x-47Step-by-step explanation:
[tex]y = 7x + 1.\\(6,-5)\\m= 7\\x1= 6\\y1 = -5\\y-y1=m(x-x1)\\y-(-5) = 7(x-6)\\y+5=7x-42\\y=7x-42-5\\y = 7x-47[/tex]
Look at the attached photo
Answer:
Step-by-step explanation:
radius of the circle=12 cm / 2=6 cm
Area of the square=side²=(12 cm)²=144 cm²
Area of the circle=πr²=(3.142)(6 cm)²≈(3.142)*36 cm²≈113.112 cm²
Area of the four sides between the square and the circle=
=Area of the square - area of the circle=144 cm²-113.112 cm²=30.888 cm²
shaded area =30.888 cm²/4=7.722 cm²
Answer =7.722 cm²
Elmo has two different part-time jobs, and he works 20 hours per week at each job. He earns $ 8 per hour at one job. Which expression represents how much Elmo earned last week if he earns d dollars per hour at his other job ?
Answer:
$160+20d
Step-by-step explanation:
$8*20=$160
$160+20d
Match the words with their definitions.
1.
denominator
symbol with three parts: a horizontal bar, a whole number
above the bar, and a whole number below the bar
number with a value less than 1, written in place value
notation, using a decimal point
2.
numerator
3. of a fraction, the number above the horizontal bar
fraction
4. of a fraction, the number below the horizontal bar
percent
5. number with a whole number part and a fraction part
decimal fraction
6. per hundred; out of every hundred; hundredths
improper fraction
7.
fraction with a numerator greater than its denominator, giving
it a value greater than 1
mixed number
Answer:
denominator-of a fraction the number below the horizontal bar
numerator-of a fraction the number above the horizontal bar
fraction- ??? I don't see the definition
decimal fraction-symbol with three parts: a horizontal bar, a whole number above the bar, and a whole number below the bar number what's up value less than one, written place value notation, using a decimal point
percent-per hundred; out of every hundred; hundredths
improper fraction - fraction with a numerator greater than its denominator, giving it a value greater than 1
mixed number - number with a whole number part and a fraction part
10. You are given the equation 2(1/2t+3)=1to solve as part
of a homework assignment.
PART A
Describe the first step needed to solve
the equation.
PART B
Solve the equation for t.