Six identically shaped place mats, marked a, b, c, d, e and f, are piled neatly in a stack. how many arrangements are possible if a and b must touch each other?
Round 156, 782 to nearest thousand and the nearest ten thousand.
The answer is 167,000 because if you round to the 6,782 up it is 7,000. If you round 57,782 up it is 60,000. so then just add those 2 together and plug the 100,000 into it.
what hourly rate does the repair shop charge for labor?
The mechanic's hourly rate is $55.
Understanding Labor Costs in a Repair Shop
To determine the hourly rate a repair shop charges for labor, we must analyze the information given and apply simple arithmetic operations. According to the examples provided, an auto mechanic charges a flat fee and an hourly rate for labor. For instance, a mechanic charging a flat fee of $75 per car, plus an hourly rate of $55 can be represented by the linear equation y = 75 + 55x, where 'y' is the total labor charge, and 'x' is the number of hours worked.
Example Calculation
Using the equation above, if the job takes 3.5 hours, the labor charge (y) would be calculated as $75 + ($55 imes 3.5) = $75 + $192.50 = $267.50. Hence, we can infer that the mechanic's hourly rate is $55.
The measure of ∠AKG is 133°.
What is m∠AKD?
Enter your answer in the box.
m∠AKD =
To find m∠AKD, subtract the measure of ∠AKG from 180 degrees.
Explanation:To find the measure of ∠AKD, we need to use the fact that the sum of the measures of angles in a triangle is 180 degrees. Since we know that ∠AKG is 133 degrees, we can subtract this from 180 to find the remaining angle.
180 - 133 = 47 degrees
Therefore, m∠AKD = 47 degrees.
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Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.
If Roni and Allie work together to mow the field, what part of the field would Roni mow?
A. about 0.52 of the field
B. about 0.64 of the field
C. about 0.71 of the field
D. about 0.87 of the field
Answer: C. about 0.71 of the field
Step-by-step explanation:
Since, Roni can mow the field in 30 minutes.
Thus, the work done by Roni in one day = 1/30
And, Allie can mow the field in 75 minutes.
Thus, the work done by Allie in one day = 1/75
⇒ The total work done by Roni and Allie in one day when they worked simultaneously,
= [tex]\frac{1}{30} + \frac{1}{75}[/tex]
= [tex]\frac{5}{150} + \frac{2}{150}[/tex]
= [tex]\frac{7}{150}[/tex]
[tex]\implies \text{The part of work done by Roni} = \frac{\text{the work done by her in one day}}{\text{Total work they done in one day}}[/tex]
[tex]= \frac{1/30}{7/150}[/tex]
[tex]= \frac{5}{7}=0.714285714\approx 0.71[/tex]
⇒ Option C is correct.
Make a table for a function whose graph has a y-intercept of 4 and a slope of 2/3.
A quota is when one country
To the nearest tenth, find the perimeter of ∆ABC with vertices A(2,4), B(-2,1) and C(2,1). Show your work.
Which graph represents the system of inequalities?
Standard form of 5y=35+10x
Answer:
[tex]5y - 10x - 35 = 0[/tex]
Step-by-step explanation:
The standard way to write a linear relationship between the x and y variables is through a homogeneous equation as a combination of the x and y variables with real coefficients. The form is given by the expression:
[tex]ax + by + c = 0[/tex]
The equation [tex]5y = 35 + 10x[/tex] can be written in standard form if terms are transposed, obtaining [tex]5y - 10x - 35 = 0[/tex]
Identify where the given information is sufficient for graphing a linear equation. Check all that apply.
A.one point and the slope of the line
B.one point
C.one of the intercepts and the slope of the line
D.both the intercepts
E.two points
To graph a linear equation, you need at least two pieces of information: the slope and a point, both intercepts, or two points. One point and the slope, or one intercept and the slope, are also sufficient to graph a linear equation.
Explanation:For graphing a linear equation, there are several options that provide sufficient information:
A. One point and the slope of the lineC. One of the intercepts and the slope of the lineD. Both the interceptsE. Two pointsTo graph a linear equation, you need at least two pieces of information, such as the slope and a point or both intercepts. Having two points is also sufficient since it helps determine the slope. Having just one point or one intercept along with the slope is also enough to graph the line.
What's the greatest common factor of 45,9,63
Answer:
GCF = 9
Step-by-step explanation:
Write an equation of an ellipse with vertices of (-3, 0) and (3, 0), and co-vertices (0, -5) and (0, 5). Graph the ellipse.
This graph is the answer:
The population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 7 years, how long will it take to triple? (round your answer to one decimal place.)
To determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(rt) for t. Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.
Explanation:To solve this problem, we can use the equation P = P0e^(rt), where P is the population at a given time, P0 is the initial population, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time in years.
In this case, the population has doubled in 7 years, so we can write the equation as 2P0 = P0e^(r*7). We need to solve for r.
Dividing both sides of the equation by P0 gives us 2 = e^(7r). Taking the natural logarithm of both sides gives us ln(2) = 7r. Solving for r, we find that r ≈ ln(2)/7.
Now, to determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(r*t) for t. Substituting the value of r we found, we get 3 = e^((ln(2)/7)*t). Taking the natural logarithm of both sides to solve for t, we have ln(3) = (ln(2)/7)*t. Solving for t, we find that t ≈ 7 * ln(3)/ln(2). Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.
It takes approximately 11.1 years for the population to triple.
The population growth can be modeled by the exponential function [tex]P(t)=P_0 \times e^{k t}[/tex], where [tex]P_0[/tex] is the initial population, k is the growth rate, and t is time.
In this case, since the population doubles in 7 years, we have the relationship P(7) = 2 x [tex]P_0[/tex].
[tex]P(7)=P_0 \times e^{7 k}[/tex]
[tex]2 \times P_0=P_0 \times e^{7 k}[/tex]
Divide both sides by [tex]P_0[/tex].
[tex]2=e^{7 k}[/tex]
Take the natural logarithm (ln) of both sides to solve for k:
ln(2) = 7k
[tex]k=\frac{\ln (2)}{7}[/tex]
Now that we have the growth rate k, we can use it to find the time it takes for the population to triple.
[tex]P(t)=P_0 \times e^{k t}[/tex]
For tripling, [tex]P(t)=3 \times P_0[/tex].
[tex]3 \times P_0=P_0 \times e^{k t}[/tex]
[tex]3=e^{k t}[/tex]
Take the natural logarithm again:
ln(3) = kt
[tex]t=\frac{\ln (3)}{k}[/tex]
Substitute the value of k we found earlier:
[tex]t=\frac{\ln (3)}{\frac{\ln (2)}{7}}[/tex]
Using natural logarithm values:
[tex]t \approx \frac{1.0986}{\frac{0.6931}{7}}[/tex]
[tex]t \approx \frac{1.0986}{0.0990}[/tex]
t ≈ 11.09
Sue has 18 sweets. tony has 18 sweets.sue gives tony x sweets. Sue then eats 5 sweets. Tony then eats half of his sweets. Write expressions for the number of sweets sue and tony have now
The expressions for the number of sweet Sue and Tony have are 13 - x and
18 + x / 2 respectively
Sue has 18 sweet.
Tony has 18 sweet.
Sue gives Tony x sweet . Sue sweet will be
18 - xSue then eats 5 sweets then his sweet will be
18 - 5 - x = 13 - xTony collected x sweet from Sue. His sweet will be
18 + xTony ate half of his sweets . His remaining sweet will be
18 + x / 2The expression for Sue sweets is : 13 - x
The expression for Tony sweets is : 18 + x / 2
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Expressions for the number of sweets sue and tony have now :
Sue: 13 - x sweets
Tony: (3/2)x + 18 sweets
Here are the expressions for the number of sweets Sue and Tony have now:
Sue: 18 - x - 5 = 13 - x
Tony: 18 + x - (1/2)x = (3/2)x + 18
Here's a breakdown of the calculations:
Sue's sweets:
Sue starts with 18 sweets.
She gives Tony x sweets.
She then eats 5 of her sweets.
Therefore, Sue now has 18 - x - 5 sweets, which can be simplified to 13 - x.
Tony's sweets:
Tony starts with 18 sweets.
Sue gives him x sweets.
He then eats half of his sweets.
Since Tony eats half of his sweets, he is left with (1/2) of his sweets. Therefore, Tony now has 18 + x - (1/2)x sweets, which can be simplified to (3/2)x + 18.
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Which equation is equivalent to
X/ +11 = 15
Jen bought 5 cds for 57.50. What was the unit price
Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of the amount of toms money to the amount of robs money was 4:7. Rob lost the latest competition, and now the ratio of the amount of robs money is 8:3. If rob had $280 before the last competition, how much rob have now that he lost the bet?
before the bet Rob had 7 out of 11 ( 4+7)
280/7 = 40
after bet Rob had 3
3*40 = 120
he has $120
assume f(x)=4x+8 and g(x)=5. what is the value of (golf)(-1)
idk what is it, show work plz?
let f(x)=4x-7 and g(x)-5+9x. what are f+g and f-g? what are their domains?
In 2003, the population of an african country was about 12 million people, which is 3 million more than 2 times the population in 1950. enter and solve an equation to find the approximate population p (in millions) in 1950. an equation is . the approximate population in 1950 was million people.
Answer:
3 million
Step-by-step explanation:
275 mm = _____ cm
954 g = _____ kg
1mm = 0.1cm
275 * 0.1 = 27.5 cm
1 g = 0.001 kg
954 x 0.001 = 0.954 kg
Sawyer’s mom paid $1.50 for a 3/4 pound box of cereal. How much is that per pound?
A.$1.50
B.$1.75
C.$2.00
D.$2.50
Which conversion factors can be used to multiply to 4 km/min to get meters per hour?
Select each correct answer.
A. 1 h60min
B. 1000 m1 km
C. 1 km1000 m
D. 60min1 h
Answer: the answer is B and D
how i know i took a test and it said thes are the anwer
hope this helps you out you a lot
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A line passes through the point (–2, 7) and has a slope of –5. What is the value of a if the point (a, 2) is also on the line?
A.–7
B.–1
C.1
D.7
Answer:
The correct option is B.
Step-by-step explanation:
The slope of a line is constant.
If a line passes through two points then the slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the line passes through (-2,7) and (a,2).
Using the above formula the slope of the line is
[tex]m=\frac{2-7}{a-(-2)}[/tex]
[tex]m=\frac{-5}{a+2}[/tex]
It is given that the slope of the line is -5. Substitute m=-5 in the above equation.
[tex]-5=\frac{-5}{a+2}[/tex]
On cross multiplication we get
[tex]-5(a+2)=-5[/tex]
Divide both sides by -5.
[tex]a+2=1[/tex]
Subtract 2 from both the sides.
[tex]a=1-2[/tex]
[tex]a=-1[/tex]
The value of a is -1. Therefore the correct option is B.
Answer:
The answer is B.
Step-by-step explanation:
24% of 1321 is how much? round the answer to the nearest hundredth
Prove that composition of injective functions is injective. prove that composition of surjective functions is surjective.
It is found that the composition of injective functions is injective.
What is an injective function?An injective function is not a surjective function. This means that we want a function that has a unique output for each input, that doesn't cover the natural numbers.
Proof 1: Proving the composition of injective functions is injective.
f(x) is injective
f(a) = f(b)
a = b
Thus g(x) is injective
g(a) = g(b)
a = b
To prove; f(g(x)) is injective
f(g(a)) = f(g(b))
f(a) = f(b)
Since, g(x) is injective
a = b
Therefore, if f(g(a)) = f(g(b)), then a = b
That proving g(f(x)) is injective is going to follow a similar path of steps.
Proof 2: Proving the composition of surjective functions is surjective.
f(x) is surjective
The range of the function of x is the set of all real numbers
g(x) is surjective
The range of the function of x is the set of all real numbers
f(g(x)) is also surjective. The range of f(x) is the set of all real numbers. where g(x) represents all reals as well means that we touch all of the inputs needed to generate all the outputs for f(x).
Proving g(f(x)) to be surjective follows a similar path.
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How to find the other endpoint with the given endpoint and midpoint?
what is the solution of x^2+x-6≤0?