Using the Work time problem solving technic, Betty and Bullwinkle to mow the entire lawn in 30 minutes if they are working together.
As we know that if A is complete the work of z in x days and B is complete the same work (z) in y days then both of can do complete work together then Equation of both A and B are completing work (z) together in
( 1/x + 1/y = 1/z ) days
Since Betty can mow a lawn is 120 minutes, then
Betty's mowing rate is 1/120th of a lanw per minute.
Since Bullwinkle can mow a lawn is 40 minutes, then Bullwinkle mowing rate is 1/40th of a lawn per minute.
Suppose working together they can a lawn in x minutes.
both together they can mow a lawn is x minutes, then their combined mowing rate is 1/x th of a lawn per minute.
To get the equation,
the sum of their mowing rates must equal their combined mowing rate,
1/40 + 1/120 = 1/x
Solve that by multiplying through by LCD of 40 and 120 is 120 then 4x = 120 => x = 30
Hence, when both are working together they complete the work together in 30 minutes .
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Select all the values (d, n) that could be solutions to the equation.
(118,209)
(172,101)
(233,21)
(0.50,435)
(0,445)
Diego is collecting dimes and nickels in a jar. He has collected $22.25 so far. The relationship between the numbers of dimes and nickels, and the amount of money
in dollars is represented by the equation 0.10d+0.05n = 22.25.
The values (d,n) that will be the solution of the equation are
A. (0,445)
D.(118,209)
E.(172,101)
The equation that we have in this problem is:
0.10d+0.05n=22.25
here
d is the number of dimes
n is the number of nickels
Diego collected a total of $22.25 and put it in the jar.
Simply substitute each pair (d,n) into the left term of the equation and see if the answer is 22.25 to determine which values can be the equation's solutions.
Now,
A. (0,445)
0.10d+0.05n=22.25
0.10(0)+0.05(445)=22.25
22.25=22.25
Yes, The point satisfy the condition.
B. (0.50,435)
0.10d+0.05n=22.25
0.10(0.50)+0.05(435)=22.25
21.08≠22.25
No, The point does not satisfy the condition.
C. (233,21)
0.10d+0.05n=22.25
0.10(233)+0.05(21)=22.25
24.35≠22.25
No, The point does not satisfy the condition.
D.(118,209)
0.10d+0.05n=22.25
0.10(118)+0.05(209)=22.25
22.25=22.25
Yes, The point satisfy the condition.
E.(172,101)
0.10d+0.05n=22.25
0.10(172)+0.05(101)=22.25
22.25=22.25
Yes, The point satisfy the condition.
Therefore, The values (d,n) that will be the solution of the equation are
A. (0,445)
D.(118,209)
E.(172,101)
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1. What number is 1.23 x 10^6 without scientific notation?
The number 1.23 x 10⁶ without scientific notation is 12,30,000.
Scientific Notations:Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper.
We use positive exponents for base 10 when expressing any huge integers in scientific notation. For example:
500000 = 5 x 10⁵, where 5 is the positive exponent.
We use negative exponents for base 10 when expressing any small integers in scientific notation. For example:
0.00005 = 2 x 10⁻⁵, where -5 is the negative exponent.
Here we have
The number 1.23 x 10⁶
We need to write the given number without scientific notation
In the given number the exponent of 10 = 6 and positive
Then we need to move the decimal place 7 places to the right or multiply the given decimal number with 1000000
Therefore,
1.23 x 10⁶ = 1.23 × 1000000 = 12,30,000.
Hence,
The number 1.23 x 10⁶ without scientific notation is 12,30,000.
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I really need help on this question to so here’s a
A total of 123 fifth grade students are going to Fort Verde State historic Park. Each bus host 38 students all of the bus harmful except one. How many students will be in the bus that is not full.
Whoever is going to be answering this question, please give me a valid answer and show your work
Answer: 9 students will be on a bus that is not full
Step-by-step explanation:
123/38 = 3.23684210526 = 3 bus that is full.
38 x 3 = 114, 123 - 114 = 9
So, 9 students will be on a bus that is not full while the other 3 bus will be full of students.
Answer:
there will be nine students in the bus that is not full.
Step-by-step explanation:
if each bus holds 38 in your first bus you have 38 and then there are 85 students left so in the second bus there are also 38 and you should have 47 students left that need to go in a bus so then again in bus 3 there are also 38 which means in the fourth/last bus there are only 9 students left
A, B & C lie on a straight line. G, B & F lie on a different straight line. D, E & F lie on a straight line parallel to AC. DEB = 104°. GBA = 24°. Work out EBF.
The measure of angle EBF is 80° .
In the question ,
it is given that ,
point A, B and C lie on a straight line .
and G , B and F lie on a different straight line .
angle GBA = 24° so ,
GBA + GBC = 180° ...because linear pair
So , GBC = 180 - 24 = 156°
angle CBF = 24° ......because vertically opposite angles are equal .
from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,
156° = ABE + EBF .....(1)
Since the line AC and DF are parallel and BE is the transversal
So , angle DEB + angle ABE = 180°
104° + ABE = 180°
ABE = 180-104
ABE = 76°
Substituting ABE = 76° in the equation (1) ,
we get ,
156 = 76+ EBF
EBF = 156 - 76
EBF = 80°
Therefore , The measure of angle EBF is 80° .
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Julie made 7 out every 10 baskets she attempted during a basketball game. If she attempted to make 30 baskets, how many did she make?
Answer: 21
Step-by-step explanation:
If she makes 7 out of 10 shots she makes 70% of her shots (7/10 x 100 = 70%)
So if she makes 30 shots, 21 will go in the basket
(30)(0.70) = 21
in government data, a household consists of all occupants of a dwelling unit. choose an american household at random and count the number of people it contains. here is the assignment of probabilities for the outcome. the probability of finding 3 people in a household is the same as the probability of finding 4 people.
The probability that the household contains 3 people must be 0.16
The probability of finding 3 people in a household is the same as the probability of finding 4 people.
The probability = Number of favorable outcomes / Total number of outcomes
The probability is the occurrence of the random event. The value of the probability varies from 0 to 1
Therefore if we add all the probability together, the result will be one
Also The probability of finding 3 people in a household is the same as the probability of finding 4 people.
Consider the probability of finding 3 people = Probability of finding 4 people = x
Then the equation will be
0.25 + 0.32 + x + x + 0.07 + 0.03 + 0.01 = 1
Add the terms
0.68 + 2x = 1
2x = 1 - 0.68
2x = 0.32
x = 0.32 / 2
x = 0.16
Hence, the probability that the household contains 3 people must be 0.16
The complete question is:
In government data, a household consists of all occupants of a dwelling unit. choose an American household at random and count the number of people it contains. here is the assignment of probabilities for the outcome. the probability of finding 3 people in a household is the same as the probability of finding 4 people. what is the probability of finding 3 people in the household ?
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Statement Let V be any vector space and let x, y, z be in V. Prove that if x + z = y + z, then x = y. Proof Suppose for full generality that V is any vector space and x, y, z are any vectors in V. Suppose x+z= y + z. Show that x = y. Since z is in V, there exists a vector —z in V such that z+(-2) = 0 because implies Thus, x +z = y + z (x + 2) + (-2) = (y + 2) + (-2) and thus x+(2+(-2)) = y + (z + (-2)) because X+0 = y + 0 because and thus X = y by properties of the zero vector. Therefore, x +z = y + z implies x = y, and V has the cancellation property
By the zero vector property x=y.
Suppose for full generality that V is any vector space and x,y,z is any vector in V. Suppose, x+z = y+z. Show that x=y. Since z is in v, there exists a vector z in v, such that
= z + (-z) = 0, because x+y=y+z
Thus x+z=y+z
= (x+z)+(-z) = (y+z)+(-z) and thus
= x+(z+(-z)) = y + (z+(-z)) because addition is associative in vector
= x+0 = y+0 because additive inverse exists in a vector
= and thus x=y by the properties of zero vector
Also according to the question, it is now proved that x+z=y+z implies x=y and v has the cancellation property.
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Local stores have donated 30 packets of flower seeds and 105 packets
of vegetable seeds. Carter wants to know what portion of the seeds are
flower seeds. Write a fraction to represent the ratio of flower seeds to the
total amount of seeds. Then, write the fraction as a decimal number.
The ratio of flower seeds to the total amount of seeds is 2/7 = 0.2857.
What is meant by GCF?The greatest common divisor of two or more numbers that are not all equal to zero is the largest positive integer that divides each of the integers. This term is used in mathematics. The symbol represents the two integers x and y's greatest common factor. The GCF of two or more numbers is the greatest number among all the common factors of the given numbers.
Given that,
The local stores have donated 30 packets of flower seeds and 105 packets of vegetable seeds.
30/105
We have to find the GCF of 30 and 105=15
30/15=2
105/15=7
So, the answer is 2/7
The ratio of flower seeds to the total amount of seeds is 2/7.
By converting fractions as a decimal number we get,
2/7=0.2857
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1. 6:N=2:5
2. 5:3=N:6
3. N:20=5:10
4. 1:4=2:N
please help me find the zero of y=-5x+5
Answer:
1
Step-by-step explanation:
To find the zero of an equation you set the equation equal to 0
That means you do this:
-5x+5=0
Then you solve for x
-5x=-5
x = -5/-5
x= 1
Of 350 solitaire games that Jay played, he won 154 times. What percent of the games did Jay win?
Please help
The percentage of games which Jay won is 44 percent.
What is Percentage?This is referred to as a number or ratio expressed as a fraction of 100 and is usually denoted as %.
Percentage is calculated by : parts/whole × 100.
In this scenario we can deduce that the part is 154 while the whole is 350. Therefore: 154/350 × 100 = 44 percent.
Hence the most appropriate choice is 44 percent.
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1. Giuseppe is 74 inches tall, and Raymond is 6 feet 1 inch tall. Who is
taller? Explain.
Answer: Giuseppe is taller.
Step-by-step explanation:
Giuseppe is 74 inches tall, and we know that 12 inches is one foot, so 74/12 is ~6.1677777... versus 6.1.
Another way you can check this is by converting feet to inches. So 6 feet 1 inch would be (6 x 12) + 1 which is ~73.
Create an equivalent expression for (1.3 3/1.2 4)-6
1.2²4/1.3 18
1.2²/ 1.3 3
1.3 18/ 1.2 24
1.3 3 / 1.2²
The equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18]). So option(1) is correct.
Equivalent expressions are expressions that work the same way despite their appearance. When we plug in the same value(s) for the variable, two algebraic expressions have the same value (s).
Equivalent means that different terms and expressions with similar values are considered equal in mathematical form.
The given expression is
[(1.3^3)/(1.2^4)]^-6
Apply the indices power law to the above expression.
[(1.2^4)/(1.3^3)]^6
The exponents are then expanded using the power law of indices.
(1.2^[4x6])/(1.3^[3x6])
(1.2^[24])/(1.3^[18])
Hence, the equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18])
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is a stockbroker. earns 12% commission each week. Last week, sold 7200$ worth of stocks. How much did make last week in commission? If averages that same amount each week, how much did make in commission in 2011?
The amount earned as commission in 2011 is $44928
How to determine the amount earned as commission?From the question, we have the following parameters that can be used in our computation:
Commission percentage = 12%
Average sales per week = $7200
The amount earned as commission in the 2011 is then calculated as
Amount = Commission percentage x Average sales per week x Number of weeks
Substitute the known values in the above equation
So, we have
Amount = 12% x 7200 x 52
Evaluate
Amount = 44928
Hence, the commission amount is $44928
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Which i the inequality in factored form that repreent the region greater than or equal to the quadratic function with zero –3. 5 and 11. 5 and include the point (8. 5, –54) on the boundary?
y greater-than-or-equal-to three-halve (x minu 3. 5)(x 11. 5)
y greater-than-or-equal-to negative three-halve (x 3. 5)(x minu 11. 5)
y greater-than-or-equal-to negative three-halve (x minu 3. 5)(x 11. 5)
y greater-than-or-equal-to three-halve (x 3. 5) (x minu 11. 5)
The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).
What is the expression of the quadratic inequality?
Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic function by solving this system of linear equations:
(x₁, y₁) = (- 3.5, 0)
12.25 · a - 3.5 · b + c = 0 (1)
(x₂, y₂) = (11.5, 0)
132.25 · a + 11.5 · b + c = 0 (2)
(x₃, y₃) = (8.5, - 54)
72.25 · a + 8.5 · b + c = - 54 (3)
The solution of the system is a = 3.6, b = - 54, c = 144.9.
Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:
y ≥ 3.6 · (x² - 15 · x + 40.25)
y ≥ 3.6 · (x - 11.5) · (x + 3.5)
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Write an equation of the line passing through the point $A\left(-6,\ 5\right)$ that is parallel to the line $y\ =\ \frac{1}{2\ }x-7$
.
The equation of the line through the point (-6,5) and parallel to the line is y=[tex]\frac{1}{2}[/tex]x-7 is y=[tex]\frac{1}{2}[/tex]x+8.
What is equation of line ?
Any location with an x and y axis can have a line equation constructed using the slope of the line. To build a line with a certain point, one uses the equation for a straight line. Any two points can be used to find the slope. Slope is the part of a straight line that is steep.
Here the given equation is y=[tex]\frac{1}{2}[/tex]x-7
We know that equation of line is y=mx+c , where m = slope.
Then slope of given line is m= 1/2 . Now the line is parallel to given line so slope of the equation is also equal.
=> slope m=1/2.
Now the given point [tex](x_1,y_1)=(-6,5)[/tex] .
Using equation of the line is ,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-5 = 1/2(x+6)
=> 2y-10=x+6
=>2y=x+16
=>y=[tex]\frac{1}{2}[/tex]x+8
Hence the equation of the line is y=[tex]\frac{1}{2}[/tex]x+8.
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The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam
Passed exam Did not pass exam Row Totals
Completed exam review
55%
10%
65%
Did not complete exam review
20%
15%
35%
Column Totals
75%
25%
100%
Part A: What is the percentage of students who completed the exam review, given that they passed the exam? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who completed the exam review, given that they failed the exam? Round to the nearest percentage (2 points)
Part C: Is there an association between completing the exam review and passing the exam? Justify your answer. (2 points)
From the given relative frequency table , answer of the following questions are as follow:
a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.
b. Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.
c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.
As given in the question,
From the given relative frequency table , answer of the following questions are as follow:
Total percentage of students completing the exam review = 65%
a. Completed the exam review with the condition that they have passed the exam = 55%
b. Completed the exam review with the condition that they have failed the exam = 10%
c. Yes, there is association between the two completing the exam review and passing the exam is only 55% and those who have completing the exam review but failed are 10%.
Therefore, from the given relative frequency table , answer of the following questions are as follow:
a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.
b. Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.
c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.
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For what values of x and y are the triangles congruent by HL?
Answer:
Step-by-step explanation:
4x maybe
Marc has $256 to spend on coins for his collection. He buys the first coin for $8.
If he pays twice as much for each coin as he paid for the previous coin, how many coins can he buy in all?
OA. 7
OB. 6
O C. 5
OD. 4
Answer:
Option C: 5
Step-by-step explanation:
1st coin = $8
2nd coin = $16
3rd coin = $32
4th coin = $64
5th coin = $128
Total spent = $248
Help me with this problem 16 point s
The difference is 4[tex]x^{2}[/tex] - 14x - 4
Given,
In the question:
To find the difference:
The difference of [tex]2x^2-9x+8[/tex] subtract from [tex]6x^2 -5x-12[/tex] .
Now, According to the question:
Based on the given condition:
Formulate:
[tex]6x^2 -5x-12[/tex] - [tex]2x^2-9x+8[/tex]
Simplify and expand:
[tex]6x^2 -5x-12[/tex] - [tex]2x^2-9x+8[/tex]
Reorder and gather like terms:
[tex](6x^2-2x^2)[/tex] + (-5x - 9x) + (-12 + 8)
Collect coefficient of like terms
(6 - 2)[tex]x^{2}[/tex] + (-5 -9)x + (-12 + 8)
Calculate the sum or difference:
4[tex]x^{2}[/tex] - 14x - 4
Hence, The difference is 4[tex]x^{2}[/tex] - 14x - 4 .
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Write a function for the tranformations described below:
"The cubic function shifts 7 units right and 5 units up."
The function for the transformation "The cubic function shifts 7 units right and 5 units up. is written as f(x) = (x - 7)^3 + 5.
How to write the function for the given transformationLet the cubic function be = f(x) = x^3
The transformation required include shifts 7 units right and 5 units up
shifting 7 units to the right is achieved by subtracting 7 units from x in the function hence f(x) = (x - 7)^3
moving 5 units up is achieved by adding 5 units to the function hence
f(x) = (x - 7)^3 + 5
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Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answer:
153.9 units squared
Step-by-step explanation:
A = pi*r^2
A = pi* 7^2
A = pi* 49
A = 153.9
If the sale of jacket is 160 what is the original price before the 80 percent
How do i write the equation
Answer:
[tex]y=-\frac{1}{5}x[/tex]
Step-by-step explanation:
Start by finding the slope of the line. Slope is defined as the RISE over the RUN. Find two points on the line with clear coordinate pairs. The line clearly passes through the origin, and the point (5,-1). To get from one point to the other, I have to go DOWN 1 unit. This is the RISE. The rise is -1 because I am going down. I also have to go RIGHT 5 units. This is the RUN. Slope is rise divided by run. Since a positive number divided by a negative number is a negative number, I move the negative sign outside the fraction: [tex]-\frac{1}{5}[/tex]. This is the slope!
The line crosses the y-axis at 0, so the y-intercept is 0.
Point-slope form is a way to write linear equations. It looks like this:
[tex]y=mx+b[/tex]
The letter m represents the slope, and the letter b represents the y-intercept. Let's plug in the values we found for those respectively:
[tex]y=-\frac{1}{5}x+0[/tex]
This simplifies to the equation below! This is the equation of the line!
[tex]y=-\frac{1}{5}x[/tex]
a bag contains 10 red marbles, 5 white marbles, and 6 blue marbles. you draw 5 marbles out at random, without replacement. what is the probability that exactly two marbles are red?
The probability that exactly two marbles are red, is 0.365.
In the given question we have to find the probability that exactly two marbles are red.
A bag contains 10 red marbles, 5 white marbles, and 6 blue marbles.
Total marbles is
10+5+6=21
We draw 5 marbles out at random, without replacement.
Marbles taken out =5
Total possibility of taking 5 marbles out of 21 marbles is [tex]^{21}C_{5}[/tex].
Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
So [tex]^{21}C_{5}=\frac{21!}{5!(21-5)!}[/tex]
[tex]^{21}C_{5}=\frac{21!}{5!16!}[/tex]
[tex]^{21}C_{5}=\frac{21\times20\times19\times18\times17\times16!}{5\times4\times3\times2\times1\times16!}[/tex]
Simplifying
[tex]^{21}C_{5}[/tex] =7×19×9×17
[tex]^{21}C_{5}[/tex] = 20,349
Probability of exactly two marbles are red is
Possible out comes of exactly two red marbles equal to 2 red and other color marble 3.
Total red marbles are 10. So [tex]^{10}C_{2}[/tex]
The remaining marble except red marble is 11. So [tex]^{11}C_{3}[/tex]
[tex]=^{10}C_{2}\times^{11}C_{3}[/tex]
Simplifying
[tex]=\frac{10!}{2!(10-2)!}\times\frac{11!}{3!(11-3)!}[/tex]
[tex]=\frac{10!}{2!8!}\times\frac{11!}{3!8!}[/tex]
[tex]=\frac{10\times9\times8!}{2\times1\times8!}\times\frac{11\times10\times9\times8!}{3\times2\times1\times8!}[/tex]
=5×9×11×5×3
=7,425
So the probability that exactly two marbles are red
P(R)=7,425/20,349
P(R)=0.365
Hence, the probability that exactly two marbles are red, is 0.365.
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−4 1/5x=1.44
Enter your answer as a mixed number in simplest form in the box.
x =
The value of x in the given equation is x = -12/35
Determining the value of x in an equationFrom the question, we are to solve the given linear equation.
The given linear equation is
-4 1/5x = 1.44
To solve the given equation, we will determine the value of x in the equation.
First, we will convert 4 1/5 to an improper fraction
-4 1/5 = -21/5
Also,
We will convert 1.44 to a fraction
1.44 = 144/100 = 36/25
Now,
-21/5(x) = 36/25
-21(x) × 25 = 36 × 5
x = (36 × 5) / (-21 × 25)
x = -180/525
x = -12/35
Hence, the value of x is x = -12/35
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(b) Let m be the number of minutes it takes for the two
towers to contain the same number of gallons. Set
up and solve an equation for m.
Answer:
y = mx + b
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What are the solutions to the following system?
StartLayout Enlarged left-brace 1st row negative 2 x squared + y = negative 5 2nd row y = negative 3 x squared + 5 EndLayout
The given system of equations has solutions (-2, -1) and (-2, -1) respectively.
Solving system of equationsCalculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations.
Finding the value of the variable that makes the condition of all the given equations true is how we solve an equation system.
Given the system of equation below:
-2x² + y = -5
y = -3x² +5
Substitute equation 2 into 1 to have:
-2x² + (-3x+5) = -5
-2x²-3x² +5 = -5
-2x²-3x² +10=0
-5x² = -10
x² = 10/5
x² = 2
x = ±√2
If x = -√2
y = -3x² +5
y = -3(2) + 5
y = -1
If x = √2
y = -3x² +5
y = -3(2) + 5
y = -1
Hence the solutions to the given system of equations are (-√2, -1) and (√2, -1).
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Find the value of 8y +3 given that -11y-9=2. Simplify your answer as much as possible.
Answer:
-5
Step-by-step explanation:
We need to find the value of y to find the value of 8y + 3. So,
-11y - 9 = 2
Add 9 on both sides
-11y = 11
Divide 11 by -11
y = -1
Step 2:
8 x -1 + 3
-8 + 3
-5
So the value of 8y + 3 is -5
Daniel has saved $2,000 in a savings account that earns 0. 5% interest annually. What will most likely happen to the purchasing power of his savings over time?.
Daniel's purchasing power will decrease because the interest rate is lower than the historical rate of inflation.
Purchasing power can be portrayed as the quantity of labor and products that a unit of cash or an amount of cash can buy. The connection between financing cost and inflation rate influences the buying force of a saving record.
At the point when the loan cost is higher than the inflation rate, purchasing power increments. Yet, when the interest rate is lower than the expansion rate, buying power falls. For example, In the United States for the 12 months ending April 2022, the annual inflation rate was 8.3%. Since the 0.5% annual interest rate being earned by Daniel is lower than the 8.3% annual inflation rate, the most likely thing to happen to the purchasing power of his savings over time is to fall.
To learn more about money, inflation,
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