Answer:
she cannot go on the field trip.
Step-by-step explanation:
Day 1 = 5, done = 3, remaining = 2.
Day 2 = 2 + 5, done = 6, remaining = 1
Day 3 = 1 + 5, done = 2, remaining = 4
Day 4 = 4 + 5, done = 4, remaining = 5
Day 5 = 5 + 5, done = 3, remaining = 2 + 5
Day 6 = 2 + 5 + 5, done = 7, remaining = 5
Day 7 = 5 + 5, done = 1, remaining = 4 + 5
Day 8 = 4 + 5 + 5, done = 3, remaining = 1 + 5 + 5
Day 9 = 1+ 5+ 5+ 5, done = 2, remaining = 4+5+5
Day 10 = 4+5+5+5, done = 10(maximum assignment done assumed), remaining = 4 + 5
At the end of day 10, she had 9 remaining assignments, so she cannot go on the field trip.
(ii) Find p if 3^p =
3 square root 9/3
We must know the following exponent rules to help us solve this question:
[tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex][tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex][tex](a^m)^n=a^{mn}[/tex][tex]a^m=a^n, \therefore m=n[/tex]Solving the Question
[tex]3^p=\dfrac{\sqrt[3]{9}}{3}[/tex]
⇒ Rewrite [tex]\sqrt[3]{9}[/tex] as [tex]9^\frac{1}{3}[/tex]:
[tex]3^p=\dfrac{(3^2)^\frac{1}{3}}{3}[/tex]
⇒ Multiply:
[tex]3^p=\dfrac{3^\frac{2}{3}}{3}[/tex]
⇒ Subtract:
[tex]3^p=3^{\frac{2}{3}-1}[/tex]
[tex]p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}[/tex]
Answer[tex]p=-\dfrac{1}{3}[/tex]
1. Use the slope to find the speed of the object in the graph below.252015-distance (miles)105-150(1.39, 11.6)23time (hour)
Notice that the slope of the line is equal to the speed
[tex]\text{Slope (speed) = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{20\text{ -10}}{4\text{ - 2}}\text{ =}\frac{10}{2}=5\text{miles / hour}[/tex]hence, the speed = 5 miles / hour
Brett earns a base salary of £78 per week plus a commission of 20% of sales. How much did Brett make last week if he managed to sell £85 worth of merchandise?
By taking the 20 percent of £85 and adding that to the base salary, we can see that last week Brett earned £95
How much did Brett make last week?Here we need to work with percentages. We know that Brett wins a commission of 20% of sales.
So, if he sells a total amount of A (A is in dollars). Then what he gets is:
0.2*A
Where 0.2 is the decimal form of 20%.
Here we know that Brett wins £78 as a base, and last week he sell a total of £85, then the amount he gets by the commission is:
0.2* £85 = £17
Adding that to the base he already earns each week, we get:
£78 + £17 = £95
In this way, we conclude that last week Brett earned £95
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The hypotenuse of a right triangle is 29.0 centimeters. the length of one of its legs is 20.0 centimeters. what is the length of the other leg? a. 49.0 centimeters b. 24.5 centimeters c. 21.0 centimeters d. 4.5 centimeters e. 9.0 centimeters
We found the length of the other leg by using Pythagoras’ theorem y is equal to 21.0 centimeters when the length of one of its legs is 20.0 centimeters.
In this question we have to make an equation by using the right triangle's value which is given in the question,
by putting these values in the Pythagoras’ theorem.
As given, the hypotenuse of a right triangle = 29.0 centimeters.
The length of one of its leg = 20.0 centimeters
Now, by using Pythagoras’ theorem we will find the length of the other leg:
hypotenuse^2 = base^2 + perpendicular^2,
We put the value according as given in question:
29^2 = 20^2 + y^2
After finding the square of number of both side:
841 = 400 + y^2
Now we will rearrange this equation:
y^2 = 841 - 400
y = 21 centimeters is the length of the other leg.
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A line has equation y=-½x−3
Find the gradient.
Answer:
gradient is 1/2 = 0.5
Step-by-step explanation:
y= 1/2 x−3
Swap sides so that all variable terms are on the left hand side.
1/2 x−3=y
Add 3 to both sides.
1/2 x=y+3
Multiply both sides by 2.
1/2 x = 1/2 y+3
Dividing by 1/2 undoes the multiplication by 1/2
x= 1/2 y+3
Divide y+3 by 1/2 by multiplying y+3 by the reciprocal of 1/2
.
x=2y+6
Find the equation of the line.
Use exact numbers.
Answer:
y = 4x + - 9
Step-by-step explanation:
(3, 3), (4, 7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 7 - 3 4
m = ------------ = ------------ = ------- = 4
x₂ - x₁ 4 - 3 1
y - y₁ = m(x - x₁)
y - 3 = 4(x - 3)
y - 3 = 4x - 12
+3 +3
----------------------
y = 4x - 9
I hope this helps!
I need help with this math question. Can someone help me? Thanks!
Answer: Eiko
Step-by-step explanation:
Eiko has the shortest time.
Probability involving one die or choosing from n distinct objects
The probability of picking an odd number ball in fraction form is; 6/11
What is the probability of selection?
We are told that a bag contains eleven balls labelled 1 through 11. These numbers are;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. This is a total of 11 numbers.
The even numbers are a total of 5 while the odd numbers are a total of 6.
Now, the probability of selecting an odd number will be;
P(selecting odd number) = Number of possible odd numbers/Number of Total Numbers
Plugging in the relevant numbers gives;
P(selecting odd number) = 6/11
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Select three names for the angle.
∠K , ∠1 and ∠JKL are the three names of the angle 1 indicated by red color in the figure given in the question.
We need to select three names of the angle 1 indicated by red color in the figure given in the question . We are provided with the following options ∠JLK , ∠K , ∠LJK , ∠1 , ∠JKL and ∠J .
∠JLK is not similar to ∠1 . ∠K and ∠1 are same angle. ∠LJK is not similar to ∠1 . ∠JKL and ∠1 are same angle. ∠J and ∠1 are different angles. So, we can finally conclude that the three names of the angle 1 indicated by red color in the figure given in the question are ∠K , ∠1 and ∠JKL .
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how many solutions does the expression |x + 8| + 5 = 2 have??
Answer:
x= -11
It only has one solution.
Step-by-step explanation:
Consider the matrices.
A =
[-1 7 -2 -6 2 -3 -1 10]
B = [- 2 -3 1 2]
C = [-6 -8]
D = [0 0 0 0]
E = [[-8 -2 1 4 3 9 2 -7]
Operation is defined.
What operations are defined for these matrices?
Drag the operation to the boxes to correctly complete the table.
Operation is defined
Operation is not defined.
E-A
A+C
B+D
C-B
help meeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!
Answer:
[tex]\frac{h^6}{h^8}[/tex]
Step-by-step explanation:
1. For now, let's leave the [tex]g^{-6}[/tex] to the side and just worry about the [tex]\frac{h^8}{h^2}[/tex].
2. When you apply the exponent rule you should have learned in class, we know that when you divide two bases with exponents, the exponents subtract. So, you can subtract 8 - 2, and then the greater digit's place in the fraction stays. So, since [tex]h^8\\[/tex] is the greater number (and it's in the numerator), you put the [tex]h^6[/tex] in the numerator as well.
The point ( 3, -7 )is on a line with the slope . 2/3 Find another point on the line.
Answer: (6, -5)
Step-by-step explanation:
The slope 2/3 means that there is a positive change of 2 in the y-value ( + 2) and a positive change in the x-value of 3 (+ 3) for every new point. To find another point on the line, we can add 2 to the y-value and 3 to the x-value.
➜ Slope is written as y over x
➜ Coordinate points are written as (x, y)
(3, -7)
(3 + 3, -7 + 2)
(6, -5)
We can also find a point on the line by graphing. See attached.
A rental car company charges $40 per day to rent a car and $0.08 for every mile driven. Justin wants to rent a car, knowing that:
He plans to drive 125 miles.
He has at most $170 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Justin can afford to rent while staying within his budget.
Answer:
He will only afford to rent the car for 4 days, he will spend 160 dolars to just have the car for 4 days. Since he plan to drive 125 miles, the cost for the miles will be 10 dolars. So if we add 160 (4 days with the car) plus 10 (for the miles) it would give 170.
Step-by-step explanation:
If g(x) and f(x) are inverse functions, which graph represents g(x)?
--6-5 1-3-2-1 1 2 3 4 5 6
Mark this and return
7 7 7 7 4
Save and Exit
Next
Submit
Answer:
A) 2nd graph
Explanation:
The 1st graph shows a radical expression, where:
to find the inverse, replace f(x) with y, switch the x and the y, then solve for y. The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)
GCF(a, b)• LCM (a, b) = 77
What are the possible values of a and b?
The variables a and b have a possible value of 7 and 11
How to determine the possible values of a and b?The given parameters are
GCF(a, b)• LCM (a, b) = 77
As a general rule, the product of two numbers equals the product of the greatest common factor and the least common multiple of the numbers
This implies that
a * b = GCF(a, b)• LCM (a, b)
So, we have
a * b = 77
Express 77 as 7 * 11
a * b = 7 * 11
By comparison, we have
a = 7 and b = 11
Hence, the possible values are a = 7 and b = 11
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Write an equation that represents the line.
Use exact numbers.
Answer:
y = (3/2)x + 3
Step-by-step explanation:
Point 1: (0, 3) Point: (2, 6)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 6 - 3 3
m = ------------ = ------------ = --------
x₂ - x₁ 2 - 0 2
y - y₁ = m(x - x₁)
y - 3 = (3/2)(x - 0)
y - 3 = (3/2)x
+3 +3
------------------------
y = (3/2)x + 3
I hope this helps!
please please please help me I’m going to die
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{x}{13}~~ = ~~\cfrac{11}{x}\implies x^2=(13)(11)\implies x^2=143\implies x=\sqrt{143}[/tex]
ndustry standards suggest that 10% of new vehicles require warranty service within the first year. jones nissan in sumter, south carolina, sold 12 nissans yesterday. (round your mean answer to 1 decimal place and the other answers to 4 decimal places.)
The probability that none of these vehicles requires warranty service is 0.2824
The probability exactly one of these vehicles requires warranty service is
0.3766
The probability that exactly two of these vehicles require warranty service is 0.2301
The mean of this probability distribution is 1.2
Given, n=12, and the probability is 0.1, we use the binomial distribution formula to solve the probabilities:
[tex]P(X=0)=C^{n}_{x} } P^{x} Q^{n-x}[/tex]
The probability that none of these vehicles requires warranty service
[tex]P(X=0)=C^{12}_{0} } (0.1)^{0} (0.9)^{(12-0)}[/tex]
=0.2824
The probability exactly one of these vehicles requires warranty service
[tex]P(X=1)=C^{12}_{1} } (0.1)^{1} (0.9)^{(12-1)}[/tex]
=0.3766
The probability that exactly two of these vehicles require warranty service.
[tex]P(X=2)=C^{12}_{2} } (0.1)^{2} (0.9)^{(12-2)}[/tex]
=0.2301
Compute the mean of this probability distribution
Mean = n*P, where n = 12, P=0.1
=12*0.1
=1.2
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Draw a graph that
a. Has no x-intercepts
b. Has one y-intercept of (0,-2)
c. Is continuous
d. Is not a function
Answer:the answer is b
Step-by-step explanation:
The lateral surface area of a cylinder is given by the formula S = 2pirh . Solve the equation for r.
What fraction is equal to 50% from 1 over 6
Rewrite 50% as 1/2
We need a fraction that is equal to 1/2 of 1/6.
-> That fraction equals to 1/2 x 1/6 = 1/12 (or 1/6 : 2)
Answer:
1/12
Step-by-step explanation:
1/6*100/50=1/12.
2) Mr. Jonas took out a loan of $12,400. The interest rate is 3% per year, and the
interest is not compounded. How much amount will Mr. Jonas have to repay
after 4 years?
The amount which Mr. Jonas will have to repay after 4 years is $13,888 when the interest rate is 3% per year on a loan of $12,400.
According to the question,
We have the following details:
The amount of the loan or the principal amount = $12,400
Interest rate = 3% per year
Time = 4 years
Now, it is given that the interest is not a compound interest. So, the total interest can be found using the formula of simple interest.
Simple Interest (S.I.) = (Principal*rate*time)/100
S.I. = (12400*3*4)/100
S.I. = (12400*12)/100
S.I. = 148800/100
S.I. = $1,488
Now, the total amount Mr. Jonas have to repay will be the sum of the loan he has taken out and the simple interest after 4 years.
Total amount = Principal + S.I.
Total amount = 12400+1488
Total amount = $13,888
Hence, the total amount of loan Mr. Jonas has to repay is $13,888.
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1. A train travels at 80 miles per hour. What equation that compares the time (t) with the distance (d)?
d = 80t
t = 80d
t = d + 80
d = t + 80
the answer is T becouse T is the time which is what you get when distance is divided by 80 mph
Find the value of (-10)⁰
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1 except for 0. If the base is o, the answer is undefined. It is will dividing by 0. That is also undefined.
Answer:
-10degree
Step-by-step explanation:
because the 0 is the degree
Find the value of x
(A) x= 135
(B) x= 25
(C) x= 35
(D) x= 90
THE SUM OF THE INNER ANGLES IS 180°
[tex](x - 7) + (2x - 8) + 90 = 180 \\ x - 7 + 2x - 8 + 90 = 180 \\ x + 2x = 180 + 7 + 8 - 90 \\ 3x = 105 \\ \frac{3x}{3} = \frac{105}{3} \\ x = 35[/tex]
THEREFORE x=35°OPTION C IS THE RIGHT ANSWER.
Solve the following system of equations
5x-2y=4
8x+5y=-10
[tex]5x - 2y = 4 \\ 5x = 4 + 2y \\ \frac{5x}{5} = \frac{4 + 2y}{5} \\ x = \frac{4 + 2y}{5} ......(3)equation[/tex]
NOTE I AM SOLVING BY SUBSTITUTION
[tex]8( \frac{4 + 2y}{5} ) + 5y = - 10 \\ \frac{32 + 16y}{5 } + 5 y = - 10 \\ \frac{32 + 16y}{5} (5) + 5y(5) = - 10(5) \\ 32 + 16y + 25y = - 50 \\ 41y = - 50 - 32 \\ \\ \\ \\ 41y = - 82 \\ \frac{ - 41y}{41} = \frac{ - 82}{41} \\ y = - 2[/tex]
[tex]x = \frac{4 + 2( - 2)}{5} \\ x = \frac{4 - 4}{5} \\ x = \frac{0}{5} \\ x = 0[/tex]
ATTACHED IS THE SOLUTION
Answer: (0,-2)
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{5x-2y=4\ \ \ \ \ (1)} \atop {8x+5y=-10\ \ (2)}} \right.[/tex]
Multiply equation (1) by 5, and equation (2) by 2:
[tex]\displaystyle\\\left \{ {{25x-10y=20\ \ \ \ (3)} \atop {16x+10y=-20\ \ (4)}} \right.[/tex]
Add equations (3) and (4):
[tex]41x=0[/tex]
Divide both parts of the equation by 41:
[tex]x=0[/tex]
Let's substitute the value of x into equation (2):
[tex]8(0)+5y=-10\\0+5y=-10\\5y=-10[/tex]
Divide both parts of the equation by 5:
[tex]y=-2[/tex]
Thus, (0,-2)
Find the value of x show your steps
71.1g of sugar is needed to make 9 cakes. How much sugar is needed for 4 cakes?
Base on the given ratio of quantity of sugar to number of cakes, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar
How much sugar is needed for cakes?Ratio refers to a number representing a comparison between two named things or quantities. The ratio of sugar and cake is the comparison between the quantity of sugar used to make cake.
If 71.1g of sugar is needed to make 9 cakesQuantity of sugar needed to make 4 cakes = xFind the ratio of quantity of sugar to number of cakes
Quantity of sugar : Number of cakes
71.1 g : 9 cakes = x : 4 cakes
71.1 / 9 = x / 4
cross product71.1 × 4 = 9 × x
284.4 = 9x
divide both sides by 9x = 284.4 / 9
x = 31.6g of sugar
In conclusion, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar
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it took 2/3 minute to fill a barrel 1/4 full of water. find the unit fate in barrels per minute
Answer:
3/8 barrels / minute.
Step-by-step explanation:
Rate = fraction of barrel filled / time
= 1/4 / 2/3
= 1/4 * 3/2
= 3/8.