Capacity of 1 thumb drives = 4 gigabytes.
Capacity of 1 compact disk = 2 gigabytes.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Let capacity of a thumb dives = x
And, Capacity of a compact disk = y
Then, For first condition;
''4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes.''
We can formulate;
4x + y = 18 .... (i)
And, For second condition;
'3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes.'
We can formulate;
4x + 3y = 22 .... (ii)
Solve the equation (i) and (ii) we get;
Subtract (ii) by equation (i) we get;
2y = 4
y = 2
And, 4x + 2 = 18
4x = 16
x = 4
So, Capacity of 1 thumb drives = 4 gigabytes.
Capacity of 1 compact disk = 2 gigabytes.
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Mr. Anderson decides to visit a childhood friend. His car gives him 24.23 miles to the gallon. Mr. Anderson has 4 gallons of fuel. Which of the following is true?
A: Mr. Anderson can travel 48.46 miles.
B: Mr. Anderson can travel 112.92 miles.
C: Mr. Anderson can travel 96.92 miles.
D: Mr. Anderson can travel 80.92 miles.
Answer:
C
Step-by-step explanation:
multiply 24.23 by 4
This table represents equivalent ratios. What are the values of a and b?
Ths values of a and b in the equivalent ratio illustrated on the table will be 6 and 12
How to calculate the value?It should be noted that from the information given, the relationship that exist between the numbers is illustrated as:
y = 0.8x
Therefore, when y is 4.8, the value of x will be:
y = 0.8x
x = 4.8 / 0.8
x = 6
When x = 15, the value of y will be:
y = 0.8x
y = 0.8 × 15
y = 12
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Multiply using the FOIL method.
(8z + 7)(9z-1)
Answer: [tex]72z^{2} +55z-7[/tex]
Step-by-step explanation:
We multiply each component with each other:
8z * 9z = 72z^2
8z * -1 = -8z
9z * 7 = 63z
7 * -1 = -7
We then add it all together, 63z + -8z = 55z and get
[tex]72z^{2} +55z-7[/tex]
Find the scale factor from triangle A to triangle B:
Answer:
Step-by-step explanation:
x=3?
Answer:
3
Step-by-step explanation:
If you multiply 1 by 3 it gives you 3, the side of triangle B. Using that scale factor. you can then take the side of triangle B that is 9 and divide it by 3. That gives you the missing side of triangle A.
Hope this helps! :)
find each angle measure
The measure of angle A in triangle ABC is 90 degrees.
What is the measure of angle A?An isosceles triangle is a triangle that has at least two sides of equal length.
Since side AC the same as side AB, this forms an isosceles triangle and angle C is the same as angle B.
Hence;
Angle A = 4xAngle C = 2xAngle B = 2xNote that, the sum of the interior angle of a triangle is 180°
Hence
Angle A + Angle B + Angle C = 180°
4x + 2x + 2x = 180
Solve for x
8x = 180
Divide both sides by 8
8x/8 = 180/8
x = 180/8
x = 22.5
Now, we find measure of angle A.
Angle A = 4x
Plug in x = 22.5
Angle A = 4( 22.5 )
Measure of angle A = 90°
Therefore, the measure of angle A in the isosceles triangle is 90°.
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I would appreciate it if anyone could help?
:)
The most appropriate choice for corrosponding angle will be given by-
x = 2 is the correct answer
What is corrosponding angle?
At first we need to understood what is angle, parallel lines and transversal
Angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Parallel lines
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal
Transversal is a line that intersects two or more parallel lines
Corrosponding angle
The angles formed in the same position on the same side of transversal when a transversal cuts two or more parallel lines
Here,
(7x + 3)° and (8x + 1)° are corrosponding angles.
Lines m and n are parallel.
So corrosponding angles are equals
By the problem,
(7x + 3) = (8x + 1)
8x - 7x = 3 - 1
x = 2
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0.867, 0.086, 0.008, and 0.870 smallest to largest
Answer:
Smallest to largest would be:
0.008, 0.086, 0.867, 0.870
Step-by-step explanation:
math.
A set of average city temperatures in April are normally distributed with a mean of 19.7 Celsius in a standard deviation of two Celsius the average temperature of Kabul is 15 Celsius what proportion of the average city temperatures are lower than that of Kabul?
Answer:
There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Step-by-step explanation:
In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.
Firstly, we shall calculate the z score
Mathematically;
z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35
so we are to calculate the probability of; P(z< -2.35) = 0.0094
This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Find the length of the third side. If necessary, write in simplest radical form.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{2}\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 2^2}\implies c=\sqrt{16 + 4}\implies c=\sqrt{20}[/tex]
Write an equation for the function graphed below. The y intercept is at (0,0.2)
Equation for the function graphed is f(x) = -0.6 (x - 1)² ÷ (x + 1)(x + 3)
Given, the y-intercept is at (0, 0.2).
From the given graph, it can be deduced the vertical asymptotes are at x = -1, x = 1 and x = -3.
Which implies denominator is 0 and the function is undefined for x = -1, x = 1 or x = -3.
So, -1 and -3. are the roots of the denominator. As a result, the denominator equation has the form: (x + 1)(x + 3).
For finding the equation of the function f(x) = a(x - 1)² ÷ (x + 1)(x + 3)
Put f(0) = 0.2
f(0) = a(0 - 1)² ÷ (0 + 1)(0 + 3) = 0.2
a = - 0.6
∴ Equation is f(x) = -0.6(x - 1)² ÷ (x + 1)(x + 3) for y-intercept is at (0,0.2).
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What 2 2/4 x 3 5/6
I need an answer quick because i need this answer.
[tex] \frac{10}{4} \times \frac{23}{6} \\ = \frac{230}{24} \\ = \frac{115}{12} \\ = 9 \frac{7}{12} [/tex]
ATTACHED IS THE SOLUTION
You are one of the retirement counselors at the Valley View Bank. You have been asked to give a presentation to a class of high school seniors about the importance of saving for retirement. Your boss has designed an example for you to use in your presentation. The students are shown five retirement scenarios and are asked to guess which yields the most money. Note: All annuities are ordinary annuities. Also, although some people stop investing, the money remains in the account and receives 10% interest compounded annually. Look over each scenario and make an educated guess as to which investor will have the largest accumulation of money invested at 10% over the next 40 years. Then for your presentation, calculate the final value for each scenario, how much each person actually contributed, and how much interest was earned. • Adam invests $1,200 per year and stops after 15 years (remember, the balance will remain in this account, earning 10% interest compounded annually for the remaining 25 years. • Becky waits 15 years, invests $1,200 per year for 15 years, and then stops (balance will earn int • Clare waits 15 years, then invests $1,200 per year for 25 years. • David waits 10 years, then invests $1,500 per year for 15 years, and then stops (balance will earn interest for the remaining 15 years). • Ellen waits 10 years, then invests $1,500 per year for 30 years.
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
[tex](1+10)^{15}[/tex]Venus invests $1,200 per year and stops after 15 years.
He can get money : [tex]1200*[/tex] [tex](1+10)^{15}[/tex] at the first year,
We can use ,
Compound interest formula, S = [tex]P*(1+i)^{n}[/tex]
Where,
P means the Principal
I means the interest
n means the year
S means the principal and interest
At the second year he can get,
= 1200 * [(1+[tex]\frac{10degrees}{1}[/tex]) + ([tex]1+[\frac{10degrees}{1} ]^{2}[/tex])
The money of first year has two years interest,
The money of second year has one year interest.
So, we can calculate the 15th year he can get :
= 1200 * [[tex](1+\frac{10degrees}{1}] ^{1}) +(1+(\frac{10degrees}{1} )^{2} )+......(1+(\frac{10degrees}{1})^{15} )[/tex]
= 1200 * [tex]\frac{(1*1)*(1-1*1^{15} )}{1-1*1}[/tex]
The sum of geometric progression,
[tex]S_{n} =\frac{a*(1-q)^{n} }{1-q}[/tex] , q≠1
= $ 41939.67
The rest of years he can get money :
= 41939.67 * ([tex](1+10percent))^{40-15}[/tex]
= $ 454404.053
Kevin can get money 1200* [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{15} )[/tex]
= 41939.67 at 30th year
Finally he can get money = 41936.67 [tex](1+\frac{10degrees}{1}) ^{40-15*0}[/tex]
= $ 108780.71
Rafael can get money : 1200 * [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{25} )[/tex]
= $ 129818.11
$454404.05 > $129818.11 > $108780.71
Therefore,
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
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State the slope of each line-without rewriting the equation in y = mx + b form:
a. Given the expression of the form Ax + By + C = 0, the slope is
[tex]\text{slope}=\frac{-A}{B}[/tex]In this case: A = -2 and B = 3.
[tex]\text{slope}=\frac{-(-2)}{3}=\frac{2}{3}[/tex]Answer: 2/3
b. A = -4 and B = 1, so
[tex]\text{slope}=\frac{-(-4)}{1}=4[/tex]Answer: 4
c. A = 5 and B = -7, so
[tex]\text{slope}=\frac{-5}{-7}=\frac{5}{7}[/tex]Answer: 5/7
d. A = 5 and B = -8, so
[tex]\text{slope}=\frac{-5}{-8}=\frac{5}{8}[/tex]Answer: 5/8
Need help for this
Answer:
[tex]1. a=-10[/tex]
[tex]2. b=-0.2[/tex]
[tex]3. c=0.25[/tex]
Step-by-step explanation:
1. 1/5a = -2
a=-10
2. 8+b=7.8
b=-0.2
3.-0.5=-2c
c=0.25
:]
(Brainliest would help a lot) Tell me if this is incorrect!
-4+8=
-23+-1=
help me guys
Step-by-step explanation:
-4+8=4
-23+-1=-24
this is correct answer
i needed help with the problem. didn't understand it.
Answer:
a
Step-by-step explanation:
as all the other points had inflection
In the figure below, G is between E and H, and F is the midpoint of EG. If EH = 10 and FG = 4, find GH.
Answer:
GH = 2
Step-by-step explanation:
since F is the midpoint of EG , then EF = FG = 4
EF + FG + GH = EH , that is
4 + 4 + GH = 10
8 + GH = 10 ( subtract 8 from both sides )
GH = 2
match the lettered entries in matrices a, b, and ab to their values.
Given:
The matrics
[tex]\begin{gathered} A=\begin{bmatrix}{a} & {2} & {3} \\ {4} & {b} & {6} \\ {c} & {8} & {-7}\end{bmatrix} \\ B=\begin{bmatrix}{5} & {1} & {-2} \\ {-1} & {3} & {4} \\ {2} & {d} & {e}\end{bmatrix} \\ AB=\begin{bmatrix}{14} & {-1} & {f} \\ {20} & {22} & {70} \\ {-27} & {44} & {-1}\end{bmatrix} \end{gathered}[/tex]Required:
Match lettered entries in the matrices A, B and AC to their values.
Explanation:
First multiply matrices A with B
[tex]\begin{gathered} AB=\begin{bmatrix}{a} & {2} & {3} \\ {4} & {b} & {6} \\ {c} & {8} & {-7}\end{bmatrix}\begin{bmatrix}{5} & {1} & {-2} \\ {-1} & {3} & {4} \\ {2} & {d} & {e}\end{bmatrix} \\ \begin{bmatrix}{5a-2+6} & {a+6+3d} & {-2a+8+3e} \\ {20-b+12} & {4+3b+6d} & {-8+4b+6e} \\ {5c-8-14} & {c+24-7d} & {-2c+32-7e}\end{bmatrix}=\begin{bmatrix}{14} & {-1} & {f} \\ {20} & {22} & {70} \\ {-27} & {44} & {-1}\end{bmatrix} \end{gathered}[/tex]Now we can find values of a, b, c, d, e and f from equating two matrices as:
[tex]\begin{gathered} 20-b+12=20 \\ b=12 \end{gathered}[/tex][tex]\begin{gathered} 5a-2+6=14 \\ a=2 \end{gathered}[/tex][tex]\begin{gathered} a+6+3d=-1 \\ 2+6+3d=-1 \\ 3d=-9 \\ d=-3 \end{gathered}[/tex][tex]\begin{gathered} -8+4b+6e=70 \\ -8+48+6e=70 \\ 6e=30 \\ e=5 \end{gathered}[/tex][tex]\begin{gathered} 5c-8-14=-27 \\ 5c=-5 \\ c=-1 \end{gathered}[/tex][tex]\begin{gathered} -2a+8+3e=f \\ -2(2)+8+3(5)=f \\ -4+8+15=f \\ 4+15=f \\ f=19 \end{gathered}[/tex]Answer:
The values are a = 2, b = 12, c = -1, d = -3, e = 5 and f = 19.
The midpoint of AB is M(-3, 5). If the coordinates of A are (-4, 6), what are the
coordinates of B?
Answer:
(-2, 4)
Step-by-step explanation:
Midpoints
x = (x1 + x2)/2
y = (y1 + y2)/2
so
-3 = (-4 + x2)/2
x2 - 4 = -6
x2 = -2
5 = (6 + y2)/2
y2 + 6 = 10
y2 = 4
The area of a rectangular pool is 8217m2. If the Length of pool is 99m, what is its width
The width of rectangle is 83 meter.
What is the area of rectangle?
By dividing the rectangle's length by its breadth, we may determine the area of a rectangle.
Formulas for rectangles.
Formula for the perimeter of a rectangle. Rectangle Area Formula: P = 2 (l + b). A = l × b, where l is length of rectangle and b is width of rectangle.
Given area of rectangle is 8217m^2
length l = 99 m
Let width of rectangle be b meter
Therefore,
99 x b = 8217
=> b = 8217/99
=> b = 83
Therefore, the width of rectangle is 83 m.
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help meeeeeeeeeeeeee
Answer:
74.44
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]
Kari wins 1,282 tickets at an arcade. For each group of 65 tickets, she will receive a prize. Kari solves the problem 1,282 ÷ 65 and determines that she has enough tickets right now for 19 prizes. What is the least number of additional tickets that Kari needs to win to have enough tickets for a 20th prize?and i need a step by step explanation.
Answer:
18 more tickets
Step-by-step explanation:
What we know:
We know that 65 Tickets is 1 Prize.
We know we have 1,282 tickets.
So if 65 tickets is one prize
then to figure out how many for twenty then we:
65 x 20 = 1300
Now to figure out how many more she needs at the least we:
1300 - 1282 = 18
So for 1 more prize she needs 18 more tickets.
express the final answer in terms of log x, and log y
log x^3y^2
The logarithmic function log ( x³ y² ) when expressed in terms of log x and log y is 3 log ( x ) + 2 log( y).
The opposite of exponentiation is the logarithm. In other words, the exponent to which a fixed number, the base a, must be raised in order to create a specific number x, is represented by the logarithm of that number.
Consider the logarithmic function log x³ y⁴
Using the logarithmic formula,
log ( a b ) = log (a) + log (b)
We have,
log( x³ y² ) = log ( x³ ) + log( y² )
By applying the logarithmic property:
log ( xⁿ ) = n log x
We have,
log x³ y² = log ( x³ ) + log( y² )
log x³ y² = 3 log ( x ) + 2 log( y)
Therefore, the function log ( x³ y² ) in terms of log x and log y is 3 log ( x ) + 2 log( y).
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log 2 8 = 3 can be written in the form 2 A = B where
The equation written in exponential form is (a) 2³ = 8
What are exponents?A symbol used to denote the action of raising to a power that is written above and to the right of a mathematical phrase.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given equation is
㏒₂ 8 = 3
㏒ₐx = b
x = aᵇ
㏒₂8 = 3
8 = 2³
Hence, (a) 2³ = 8
Therefore, the equation written in exponential form is (a) 2³ = 8.
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BAсThe sum of m AB and mBC is equal to:O 360° - MAC240" - MAC180т АС120
The sum of mAB and mBC is equal
360 - mAC
which makes otion A the correct answer
If (8^7)^2 = 2^y, what number is y?
For the given expression (8^7)^2 = 2^y , the number equals to y is 42.
As given in the question,
Given expression :
(8⁷)² = [tex]2^{y}[/tex]
Simplify the given expression by using law of exponents :
Here the law of product of exponents or product law of exponents (power or index) has been applied under which [tex](8^{7})^{2} = 8^{7times2} = 8^{14}[/tex]
( 8¹⁴ ) = [tex]2^{y}[/tex]
⇒ (2³)¹⁴ = [tex]2^{y}[/tex]
⇒ 2⁴² = [tex]2^{y}[/tex]
Comparing the exponents i. e. power (or index), since the base is common, Also when two exponential numbers with common base are equal, their exponents (power or index) can be equated.
Number equals to represent the value of y is 42
Therefore, for the given expression (8^7)^2 = 2^y , the number equals to y is 42.
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Write an equation in slope-intercept form for the line with slope -4/3 and y-intercept 3
I got that but I’m not sure if it’s right.
Answer:
[tex]y=-\frac{4}{3}x+3[/tex]
Jane wants to rent a boat and spend less than $75. The boat costs $8 per hour, and Jane has a discount coupon for $5 off. What are the possible numbers ofhours Jane could rent the boat?Use t for the number of hours.Write your answer as an inequality solved for t.
Jane wants to rent a boat and spend less than $75.
The boat costs $8 per hour, and Jane has a discount coupon for $5 off
Let t for the number of hours
Then we can write the following inequality
[tex]8t-5<75[/tex]The discount coupon is being subtracted since it was off.
Let us solve the inequality for t
Step 1: Add 5 to both sides of the inequality
[tex]\begin{gathered} 8t-5+5<75+5 \\ 8t<80 \end{gathered}[/tex]
Step 2:
Divide both sides of the inequality by 8
[tex]\begin{gathered} \frac{8t}{8}<\frac{80}{8} \\ t<10 \end{gathered}[/tex]This means that Jane could rent the boat for less than 10 hours
[tex]t<10[/tex]How many
inches are in 3.5 miles
Answer:
221 760 inches
Step-by-step explanation:
So, 3.5miles * 63360= 221760 inches.
Formula: multiply the value in miles by the conversation factor '63360'.
1) Draw a small graph on your paper, and graph the following line: y = 2x + 3
The equation y = 2x + 3 is in its slope-intercept form in which slope = 2 and y-intercept is 3.
If the slope is 2, then this means that the rise = 2 and the run = 1.
[tex]slope=\frac{rise}{run}=\frac{2}{1}=2[/tex]Knowing the slope and the y-intercept, let's now graph the line.
Let's remove the indication of the slope, here is the graph of the line y = 2x + 3.