Answer:
1:2
Step-by-step explanation:
Because 10/20 = 1/2
Answer: 10,20
Step-by-step explanation:
what is 7x+14 = to 7(1+x), 7x-7 or 7(x+2)
Answer:
7(x + 2)
Step-by-step explanation:
7x + 14 =
7 can be factored out of each term.
= 7 * x + 7 * 2
= 7(x + 2)
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Answer:
3/1
Step-by-step explanation:
think in this question we have to find the ratio .
Question:
There are 9 tennis balls in 3 cans. What is the RATIO of number of tennis balls to number of cans?
Solution:
Given:
Number of tennis ball= 9
Number of cans = 3
Ratio of number of tennis balls to number of cans= tennis ball : cans
= 9/3 = 3/1
Hence, Ratio of number of tennis balls to number of cans= tennis ball : cans= 3:1
==================================================================
Hope this will help you....
Mario has a fish tank with 70 goldfish in it. One of the goldfish has unique pelvic fins, which are located on the bottom of the fish. He wants to show his friend the pelvic fins. What is the probability that Mario will randomly catch the right goldfish on the first 5 attempts?
0.034
0.049
0.069
0.091
Answer:
The probability that Mario will randomly catch the right goldfish on the first 5 attempts = 0.069
Step-by-step explanation:
From geometric distribution.
If the probability of success on each trial = P,
then the probability that the Nth trial is the first success
Pr (X = N) = [tex](1 - P)^{N - 1}[/tex] P
Now,
P = [tex]\frac{1}{70}[/tex]
Maximum attempt = 5
Probability that Mario will randomly catch the right goldfish on the first 5 attempts
= [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{1}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]
= [tex]\frac{1}{70}[/tex] + [tex]\frac{69}{70}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]
= 0.069
Answer: 1. A) 0.14
2. C) 46%
3. D) 86%
4. B) 0.513
5. A) 0.003
6. C) 0.069
7. C) 0.25%
8. D) 0.03
9. C) 71%
10. A) 10%
Step-by-step explanation: 100% :)
You want to use square tiles to cover the top of a stepping stone you're making. The top is 24 inches by 20 inches. What is the side measure of the largest-sized square tile you can use to cover the stepping stone without any overlap or cutting?
The side measure of the largest-sized square tile will be 4 in.
What is the greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Given that, The top of a stepping stone is 24 inches by 20 inches.
GCF of 24 and 20 = 4
Hence, The side measure of the largest-sized square tile will be 4 in.
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Calculate the measure of angle x
Answer:
x =56.4 degrees
Step-by-step explanation:
For right triangles, we know that the sin x = opposite/ hypotenuse
sin x = 20/24
Taking the arcsin of each side
arcsin (sin x) = arcsin (20/24)
x = 56.44269024 degrees
To the nearest tenth
x =56.4 degrees
x + 2y = 5
x - 3y = 7
What is the value of the y-determinant?
-2
-1
2
Answer:
y-determinant = 2
Step-by-step explanation:
Given the following system of equation:
x + 2y = 5 x - 3y = 7Let's represent it using a matrix:
[tex]\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] = \left[\begin{array}{ccc}5\\7\end{array}\right][/tex]
The y‐numerator determinant is formed by taking the constant terms from the system and placing them in the y‐coefficient positions and retaining the x‐coefficients. Then:
[tex]\left[\begin{array}{ccc}1&5\\1&7\end{array}\right] [/tex]
y-determinant = (1)(7) - (5)(1) = 2.
Therefore, the y-determinant = 2
The coordinates of a triangle are given as A(3, 2), B(-4, 1), C(-3, -2). What are the coordinates of the image after the triangle is reflected in the line y = x? A'( a0, a1) B'( a2, a3) C'( a4, a5)
Look at the picture.
[tex]A(3,\ 2)\to A'(2,\ 3)\\\\B(-4,\ 1)\to B(1,\ -4)\\\\C(-3,\ -2)\to C'(-2,\ -3)[/tex]
Which expression is equivalent to 9(w+8)?
72W
9W+72
9W+8
17W
Answer:
9W + 72
Step-by-step explanation:
using the distributive property, you would multiply both the w and the 8 by 9 to obtain 9*w and 9*8. 9*w + 9*8 = 9w + 72.
This works because if you have 9 of (w+8), you have 9 w's and 9 8's. Adding these up is simply multiplying 9 by w (since there are 9 w's) and 9 by 8 (since there are 9 8's).
Answer:
I’m patty’s urge in 9W + 8
Step-by-step explanation:
I just got the question right on Edge!
For what value of p will the pair of linear equations have infinitely many solutions (p-3)x + 3y = p , px+ py = 12
Answer: p = 6
Step-by-step explanation:
HI !
px + 3y - ( p-3)=0
a₁ = p , b₁ = 3 , c₁ = - (p-3)
=====================
12x + py - p=0
a₂ = 12 , b₂ = p , c₂ = -p
since , the equations have infinite solutions ,
a₁/a₂ = b₁/b₂ = c₁/c₂
p/12 = 3/p = p-3/p
--------------------------------------
p/12 = 3/p
cross multiply ,
p² = 36
p = √36
p = 6
for the value of p = 6 , the equations will have infinitely many solutions
what is the value of B
Answer:
B = 2
Step-by-step explanation:
using the rule of exponents
• [tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
consider [tex]83^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{83^{2} }[/tex]
⇒ B = 2
Lia finds a second dress that was originally $72.00 and now was marked 15% off. How much did she pay for the second dress?
Answer:
The answer is $61.20
Step-by-step explanation:
First you multiply 72 by .15 (which is 15% converted to a decimal), which gives you 10.8. You then subtract 10.8 from 72.
What is the formula to
u-5=-4(w-1)
Answer: u = -4w + 9
Step-by-step explanation:
u - 5 = -4(w - 1)
u - 5 = -4w + 4
+5 +5
u = -4w + 9
The proper formula to solve the equation u - 5 = -4(w - 1) for w is w = (u + 9) / 4, after rearranging and simplifying the terms of the equation.
The question involves solving a linear equation with variables u and w. Initially, we have the equation u - 5 = -4(w - 1). To solve for w, we need to isolate w on one side of the equation. A statement in the information provided seems to mistakenly give the result of w, which probably arises from a typo or error, stating w = -40 - 5. However, this is incorrect given the initial equation.
Let's start by expanding the right side of the initial equation:
u - 5 = -4w + 4And then rearranging to solve for w:
Add 4w to both sides: u + 4w - 5 = 4Add 5 to both sides: u + 4w = 9Divide by 4: w = (u + 9) / 4From this process, we see that the correct formula to isolate and solve for w is w = (u + 9) / 4.
Simplify completely 12x+36/x^2-4x-21 and find the restrictions on the variable
Answer:
[tex]\dfrac{12}{x-7},[/tex]
[tex]x\neq 7,\ x\neq -3.[/tex]
Step-by-step explanation:
Consider the expression
[tex]\dfrac{12x+36}{x^2-4x-21}.[/tex]
1. The numerator can be factored as
[tex]12x+36=12(x+3).[/tex]
2. The denominator [tex]x^2-4x-21[/tex] has the discriminant
[tex]D=(-4)^2-4\cdot (-21)\cdot 1=16+84=100.[/tex]
Then
[tex]x_{1,2}=\dfrac{-(-4)\pm \sqrt{100}}{2\cdot 1}=\dfrac{4\pm 10}{2}=7,\ -3.[/tex]
Then
[tex]x^2-4x-21=(x-7)(x+3).[/tex]
Note that restrictions on the variable x are [tex]x\neq 7,\ x\neq -3.[/tex]
3. Simplify the fraction:
[tex]\dfrac{12x+36}{x^2-4x-21}=\dfrac{12(x+3)}{(x-7)(x+3)}=\dfrac{12}{x-7}.[/tex]
Gabriela has dinner at a cafe and the cost of her meal is \$45.00$45.00. Because of the service, she wants to leave a 15\%15% tip.
What is her total bill including tip?
Answer: Her total bill including tip is $51.75
Step-by-step explanation:
Hi, first, we have to multiply the cost of the meal by the tip percentage in decimal form (percentage divided by 100).
Mathematically speaking:
45 x (15/100) = 45 x 0.15 = 6.75 tip amount
Finally, add the amount of the tip to the meal's cost.
45 +6.75 = $51.75
Her total bill including tip is $51.75
Feel free to ask for more if needed or if you did not understand something.
Please help me with this and dont get any wrong!!!!!
1. The answer is A.
Based on the line plot, we can see that Sandy drank 12 juice boxes on October 12th. Each X on the plot represents 2 juice boxes, and there are 6 of them, meaning she drank 12. October 2nd has 1 X, meaning she drank 2 that day.
2. The answer is A.
On a graph, the point (1, 3) would mean that 1 is on the x-axis, and 3 is on the y-axis. Therefore, point B is correct because it is 1 space to the right, and 3 spaces up from the origin.
3. The answer is C.
If the coordinate we're looking for is (4, 0) then on a graph you would move 4 spaces to the right, and 0 spaces up or down. Therefore, point B is the correct choice.
if you have a net spendable income of $1,450 per month, what is the maximum amount of money you should spend on food each month
Answer:
The maximum amount of money that should be spent on housing each month is $522.
The maximum amount of money that should be spent on transportation each month is $290.
The maximum amount of money that should be spent on food each month is $246.50.
The maximum amount of money that should be spent on entertainment each month is $116.
Answer:
$522
Step-by-step explanation:
The maximum amount of money that should be spent on housing each month is $522.
The maximum amount of money that should be spent on transportation each month is $290.
The maximum amount of money that should be spent on food each month is $246.50.
The maximum amount of money that should be spent on entertainment each month is $116.
Anu bought an air cooler as shown below. Its water tank is in the shape of a cuboid and can take 40 litres of water. Its dimensions are 50cmx 20cm. What will be the length of the water tank?
Answer:
40 cm
Step-by-step explanation:
Using the conversion
1 litre = 1000 cm³, then
40 litres = 40 × 1000 = 40000 cm³
The volume ( V) of a cuboid is
V = lbh ( divide both sides by bh )
l = [tex]\frac{V}{bh}[/tex] = [tex]\frac{40000}{50(20)}[/tex] = [tex]\frac{40000}{1000}[/tex] = 40 cm
Length of water tank is 40 cm
Given that;
Capacity of tank = 40 liters
Dimensions of tank = 50cm × 20cm
Find:
Length of water tank
Computation:
Capacity of tank = 40 liters
Capacity of tank = 40 × 1000
Capacity of tank = 40,000 cm³
Length of water tank = 40,000 / [50cm × 20cm]
Length of water tank = 40,000 / 1,000
Length of water tank = 40 cm
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Step by step problem solving for 3.99 + 39.9 decimal problem
Answer:
You are going to line up the decimal points to each other and add a zero to the end of the shortest decimal.
3.99+39.9=43.89
Step-by-step explanation:
You are going to take the 3.99 and add that to the 39.9 like normal but you are first going to line up the decimals.
"The area of a triangle is given by the formula A = 1/2bh. Solve this equation for the height, h, in terms of the base, b, and area, A." Help!!!!
Answer:
2A/b =h
Step-by-step explanation:
A = 1/2bh
Multiply each side by 2
2*A = 2*1/2bh
2A = bh
Divide each side by b
2A/b = bh/b
2A/b =h
In 1990 sales at ABC electronics totaled 4.9 million dollars 1996 total sales amounted to 12.1 million. Assuming the growth in sales is a linear relation, what total sales can the company expect in 2001
Answer:
18.1 million
Step-by-step explanation:
12.1 - 4.9 = 7.2 million increase in 6 years
7.2 / 6 = increase of 1.2 million a year
1.2 x 5 years = 6 million
12.1 million + 6 million = sales of 18.1 million in 2001
Based on linear growth from 1990 to 1996, ABC Electronics can expect total sales of approximately $18.1 million in 2001.
To predict sales for ABC Electronics in 2001 based on a linear growth pattern from 1990 to 1996, we first calculate the annual increase in sales over that period. In 1990, sales were $4.9 million and in 1996, sales were $12.1 million. This is an increase of $12.1 million - $4.9 million = $7.2 million over 6 years, which gives us an annual increase of $7.2 million / 6 years = $1.2 million per year.
Since we're assuming linear growth, we can extend this annual increase to predict sales for subsequent years. From 1996 to 2001 is 5 years, so we calculate the expected sales for 2001 by adding 5 times the annual increase to the 1996 sales figures: $12.1 million + (5 × $1.2 million) = $12.1 million + $6.0 million = $18.1 million.
Therefore, we can expect ABC Electronics to have total sales of approximately $18.1 million in the year 2001 if the linear growth trend continues.
Find the distance using the modulus of the difference between z1 = -8 + 3i and z2 = 7 - 4i. Show all work for full credit.
Answer:
[tex]\sqrt{274}[/tex]
Step-by-step explanation:
Given [tex]z_1=-8+3i,\ z_2=7-4i.[/tex]
1. Find the difference [tex]z_1-z_2:[/tex]
[tex]z=z_1-z_2=-8+3i-(7-4i)=-8+3i-7+4i=(-8-7)+(3i+4i)=-15+7i.[/tex]
This complex number has real part [tex]Rez=-15[/tex] and imaginary part [tex]Imz=7.[/tex]
2. The modulus of complex number z is
[tex]|z|=\sqrt{Re^2z+Im^2z}=\sqrt{(-15)^2+7^2}=\sqrt{225+49}=\sqrt{274}.[/tex]
The distance between [tex]z_1\ \text{and}\ z_2[/tex] is:
16.5529 units
Step-by-step explanation:We know that the difference between two complex numbers:
[tex]z_1=a_1+ib_1\ \text{and}\ z_2=a_2+ib_2[/tex] is given by:
[tex]|z_1-z_2|=|(a_1+ib_1)-(a_2+ib_2)|\\\\i.e.\\\\|z_1-z_2|=|(a_1-a_2)+i(b_1-b_2)|\\\\|z_1-z_2|=\sqrt{(a_1-a_2)^2+(b_1-b_2)^2}[/tex]
Here we have:
[tex]z_1=-8+3i\ \text{and}\ z_2=7-4i[/tex]
i.e.
[tex]a_1=-8\ ,\ b_1=3,\ a_2=7\ \text{and}\ b_2=-4[/tex]
i.e. we have:
[tex]|z_1-z_2|=\sqrt{(-8-7)^2+(3-(-4))^2}\\\\|z_1-z_2|=\sqrt{15^2+7^2}\\\\|z_1-z_2|=\sqrt{225+49}\\\\|z_1-z_2|=\sqrt{274}\\\\|z_1-z_2|=16.5529[/tex]
find f(x).g(x) if f(x) = 3x+11 and g(x)= -2x+7
Answer:
f(x)·g(x) = -6x² -x +77
Step-by-step explanation:
Given:
f(x) = 3x + 11
g(x) = -2x+7
f(x) * g(x) = (3x+11)*(-2x+7)
= -6x²+21x-22x+77
= -6x² -x +77
Which set of ordered pairs represents a function?
Answer:
The second one that starts with 3
Step-by-step explanation:
To know if it's a function , check all the domains and make sure there are no repeating ones, if there is a repeating domain , it's not a function
what is the solution to the system of equations y=x+3, y=3x+1
Substitution method
y = x + 3 (*)
y = 3x + 1 (**)
Substitute (*) to (**):
3x + 1 = x + 3 subtract 1 from both sides
3x = x + 2 subtract x from both sides
2x = 2 divide both sides by 2
x = 1Put the value of x to (*):
y = 1 + 3
y = 4Answer: x = 1 and y = 4 → (1, 4).Russell has a collection of 1,200 pennies. Of these pennies, 25% are dated before 1980, 35% are dated from 1980 to 2000, and the rest are dated after 2000. How many pennies in Russell’s collection are dated after 2000
Answer:
The total pennies in Russell's collection dated after 2000 is 800
Step-by-step explanation:
Given
Total Pennies: 1,200
Pennies before 1980: 25%
Pennies between 1980 and 2000: 35%
Required
Number of pennies in Russell’s collection are dated after 2000
Let P1 represent pennies dated before 1980
Let P2 represent pennies dated between 1980 and 2000
Let P3 represent pennies dated after 2000
To calculate the number of pennies dated after 2,000. you have to understand that his total collection of pennies is 100%
This means that
P1 + P2 + P3 = 100%
Where P1 = 25% and P2 = 35%.
So, we're solving for P3
By substituting, P1 = 25% and P2 = 35%, we have
25% + 35% + P3 = 100%
60% + P3 = 100%
Make P3 the subject of formula
P3 = 100% - 60%
P3 = 40%
The quantity of pennies dated after 2,000 is then calculated by P3 * Total.
i.e. 40% * 2000
= 0.4 * 2000
= 800
Hence, the total pennies in Russell's collection dated after 2000 is 800
Write an exponential function to model the following situation
A population of 140,000 grows 4% per year for 16 years .
How much will the population be after 16 years?
Answer:
[tex]y = 140000(1.04)^{x}[/tex]; 262 000
Step-by-step explanation:
The general formula for an exponential function is
[tex]y = a(b)^{x}[/tex]
a = 140 000; b = 1.04; x = 16
[tex]y = 140000(1.04)^{x}[/tex]
y = 140 000(1.04)¹⁶
y = 140 000 × 1.873
y = 262 000
The graph below shows the population growth over time.
Final answer:
An exponential function to model the population growth is P(t) = P_0 * e^{rt}, where the initial population P_0 is 140,000, the rate of growth r is 0.04, and the time t is 16 years. The population after 16 years is calculated by P(16) = 140,000 * e^{0.64}.
Explanation:
To model the population growth, we can use the formula for exponential growth which is P(t) = P_0 e^{rt}, where:
P(t) is the future population after time t,
P_0 is the initial population size,
e is the base of natural logarithms (approximately equal to 2.71828),
r is the rate of growth (expressed as a decimal), and
t is the time in years.
In the given situation, the initial population P_0 is 140,000, the growth rate r is 4% per year which is 0.04 when expressed as a decimal, and the time period t is 16 years. Plugging these values into the formula:
P(16) = 140,000 * e^{0.04 * 16}
To calculate the future population after 16 years, solve the equation:
P(16) = 140,000 * e^{0.64}
Using a calculator to compute e^{0.64}, and then multiplying by 140,000, we obtain the future population.
In Phoenix, Arizona, the average n umber of sunny days is 211 per year. About what percent of the year is Phoenix sunny?
Answer:
21100%
Step-by-step explanation:
Move the decimal point two places to the right.
Provide the first six terms of the following sequence: t1=81 tn=13tn-1n ≥ 2
Answer: 81, 27, 9, 3, 1, 1/3
There are six terms listed. The first five are whole numbers and the sixth term is a fraction.
==============================================
Explanation:
The equation t1 = 81 means that the first term "t" is 81. The second term is t2 = 27 because we multiply 1/3 by 81, or divide 81 over 3, and we end up with 81/3 = 27 as the second term.
We know to multiply by 1/3 because of the equation tn = (1/3)*t_(n-1) where the "n-1" portion is smaller than 't'. We can write it like this[tex]t_n = \frac{1}{3}*t_{n-1}[/tex]
To get the next term, we multiply by 1/3 again: 27*(1/3) = 27/3 = 9 giving us the third term
And repeat until we have six terms
9*(1/3) = 9/3 = 3 is the fourth term
3*(1/3) = 3/3 = 1 is the fifth term
1*(1/3) = 1/3 is the sixth term
So that is how I got the first six terms to be 81, 27, 9, 3, 1, 1/3
A dozen eggs cost 3.84. At this rate how much wood 50 eggs cost
Answer:
$16
Step-by-step explanation:
A dozen is equal to 12 eggs. In order to find the amount for 50 eggs, we need to find the unit rate. In this problem, we can assume that each of the eggs cost the same amount. Therefore, we can divide 3.84 by 12 to get the amount of one egg.
3.84/12= 0.32
Now that we have found the unit rate, we simply have to multiply it by 50 to get the cost. To explain why we do this, I will set it up as a proportion.
3.84/1 = ?/50
In order to get the equivalent amount you must multiply by 50.
0.32 x 50= 16
Therefore, the answer is $16
The cost of 50 eggs is $16.
Given that, a dozen eggs cost $3.84.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, the cost of one egg = 3.84/12
= $0.32
Now, the cost of 50 eggs
= 50 × 0.32
= 16
Therefore, the cost of 50 eggs is $16.
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a Panda eats about 20 kg of bamboo per day. About how many pounds of bamboo will the panda eat in 6 weeks?
Answer:
840 kg of bamboo in 6 weeks
Step-by-step explanation:
if a panda eats 20 kg of bamboo per day he eats 140 kg of bamboo every week. multiply the amount he eats per week (140) by the amount of weeks (6) and you get 840 kg of bamboo
Answer:
1,848
Step-by-step explanation:
The panda eats 20kg of bamboo per day, and 1 L = 2.2 Ib, so multiplying 20 x 2.2 = 44, and there is 42 days in 6 weeks, so you multiply 44 x 22 = 1,848. I hope this is the correct answer, you're welcome!