Answer:
26 pens
Step-by-step explanation:
Let P and R be the numbers of Pens and Rulers Saj purchases.
The cost of P Pens and R Rulers:
Pens = P(20p)
Rulers = R(60p)
P(20p) + R(60p) = £10
P(0.20) + R(0.60) = 10
R = 8
P(0.20) + (8)*(0.60) = 10
P(0.20) + 4.8= 10
P(0.20) = 5.2
P = (5.2/0.20)
P = 26 pens
CHECK:
8 Rulers = 8*(60p) = 480p
26 Pens = 26*(20p) = 520p
Total = £10
Emily estimated that there were
315 students at a soccer game.
The actual number of students at
the game was 350. What was the
percent error of her estimate?
I thought it was 8%. Please show your work, and maybe tell me why I was right or wrong? Thank you!
The percentage error in the measurement of the number of student at the soccer game. given that 315 student was estimated and 350 student were actually at the game is 10%
What is a percentage error?The percentage error is the measure of the difference between an actual value and a estimate given as a percentage.
The percentage error of her estimate is found from the percentage error formula, as follows;
[tex]\delta = \dfrac{v_A - v_E}{v_E} \times 100\%[/tex]Where:
δv=The percentage error
[tex]v_A[/tex] = The approximate value or estimated value = 315
[tex]v_E[/tex] = The exact or correct value = 350
Therefore; [tex]\delta = \dfrac{|315 - 350|}{350} \times 100\%= 10\%[/tex]
The percentage error of her estimate is 10%
The method and information used in calculating the percentage error determines the value of the error in percentage, however, based on the values of estimated value of 315, and the actual value of 350, the percentage error is 10%
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Points A(-1, 2) and B(5,8) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 2/3 the length of AB
The coordinates of point C on AB such that AC is 2/3 the length of AB is (2,0)
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
To find out how long AC is, we must first find the length of AB.
According to Pythagoras’ theorem,
[tex]a^2 + b^2 = c^2[/tex].
Thus [tex]4^2 + 6^2 = c^2[/tex].
[tex]16 + 36 = c^2[/tex].
The square root of this is;
c = √52.
AB is 7.21 units long.
2/3 of 7.21 is 4.8
The coordinate that fits this is (2,0).
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1/2 n + 3/4 n = 1/2
Solve for n =
Answer:
n=2/5
Step-by-step explanation:
Please look at the image below! :D
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex] [tex]\frac{1}{2}[/tex] means the same as [tex]\frac{2}{4}[/tex]
[tex]\frac{2}{4}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex]
[tex]\frac{5}{4}[/tex] n = [tex]\frac{1}{2}[/tex] multiply each side by [tex]\frac{4}{5}[/tex]
[tex](\frac{4}{5})[/tex][tex]\frac{5}{4}[/tex] n = [tex](\frac{4}{5})[/tex][tex]\frac{1}{2}[/tex]
n = [tex]\frac{4}{10}[/tex] = [tex]\frac{2}{5}[/tex]
write the equation of a line through ( 3, 1), parallel to y = 2/3x + 1.
Answer:
y = 2/3 x - 1
Step-by-step explanation:
Parallel slopes are equal.
y = mx + b
m = 2/3
x = 3 Use the x and y given in the point (3,1)
y = 1
Solve for b the y-intercept
y = mx + b
1 = 2/3(3) + b
1 = 2 + b Subtract 2 from both sides
-1 = b
y= mx +b
y = 2/3x -1
Nick is splitting 4 quarts of ice cream with 9 members of the team. If the ice cream is split evenly, how many cups will each person get? Explain1 quart equals _ pints, which equals _ cups, so 4 quarts equals _ cups. Dividing the ice cream among _ people means each gets _ cup(s)
ANSWER
[tex]\text{1}\frac{7}{9}\text{ cups}[/tex]EXPLANATION
Nick has 4 quarts of ice and he wants to split it with 9 members of the team.
To solve this, we have to convert quarts to cups. We have that:
1 quart = 2 pints
and
1 pint = 2 cups
This means that:
1 quart = 2 * 2 cups
1 quart = 4 cups
So, 4 quarts will be:
4 quarts = 4 * 4 cups
4 quarts = 16 cups
Therefore, dividing the ice cream among 9 people would mean that we have to divide 16 cups by 9 people.
That is:
[tex]\begin{gathered} \frac{16}{9} \\ =\text{ 1}\frac{7}{9}\text{ cups} \end{gathered}[/tex]The complete statement is:
1 quart equals 2 pints, which equals 4 cups, so 4 quarts equals 16 cups. Dividing the ice cream among 9 people means each gets 1 7/9 cup(s)
what is 1656 divided by 16
Answer:
103.5
Step-by-step explanation:
Answer:
103.5
Step-by-step explanation:
The question is,
→ what is 1656 divided by 16?
Forming as problem,
→ 1656 ÷ 16
Let's solve the problem,
→ 1656 ÷ 16
→ 103.5
Thus, the answer is 103.5.
my tutors keep getting cut off due to connection and i need help!!
Let:
(x1,y1) = (0,4)
(x2,y2) = (4,0)
The slope m is:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1 \\ \end{gathered}[/tex]Using the point slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-4=-1(x-0) \\ y=-x+4 \\ \text{ In standard form:} \\ x+y=4 \end{gathered}[/tex]PLEASE HELP FASR ILL GIVE BRAINLIEST IF CORRECT!!!!
Victor sells candles. The graph shows the number of candles sold and the
income from the sales. It represents a linear function.
Which statement best describes Victor's income from selling these candles?
A. He sells 4 candles per dollar.
B. He sells 7.5 candles per dollar.
C. He gets $4 per candle.
D. He gets $7.50 per candle.
Answer:
D
Step-by-step explanation:
22.5÷3 is 7.5 and 52.5÷3 is 7.5 as well
Money is y axis (x,y) and candles is x axis (x,y)
12. Troy made 5 out of 7 jumps on his dirt bike. What percentage ofjumps did he make?62%57%85%71%
Question: Troy made 5 out of 7 jumps on his dirt bike. What percentage of jumps did he make?
Answer:
Note that, the 7 jumps are 100 percent of the jumps. Therefore, we make a rule of three, that is:
that is equivalent to say the following equation:
percentage of jumps = (5x 100%) ÷ 7 = 500% ÷ 7 = 71.42 = 71,3
that is, approximately 71 %
can you explain each step please for i can write it on a paper along with you
The two groups are given one is those who are studied and other is those who are not studied.
Studied - 88,100,94,79,92,100,95,83,89,99,100,91,89,95,100,93,96,84.
Arrange in order.
79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100
The mean of this group is
[tex]\frac{88+100+94+79+92+100+95+83+89+99+100+91+89+95+100+93+96+84}{18}[/tex][tex]\frac{1667}{18}=92.6[/tex]The mean is 92.6.
The median of this group is
Use the median formula for even
[tex]m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}^{}}{2}[/tex]Substitute the value of n =18
[tex]m=\frac{(\frac{18}{2})^{th}+(\frac{18}{2}+1)^{th}^{}}{2}=\frac{9^{th}+10^{th}^{}}{2}[/tex][tex]m=\frac{93+94}{2}=93.5[/tex]The median is 93.5.
The mode of this group is 100 as it is appears 3 times .
The another group is not studied group.
Not studied - 82,72,45,91,58,83,65,87,90,77,73,89.
Arrange in order-
45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91
The mean is determined as
[tex]\frac{82+72+45+91+58+83+65+87+90+77+73+89}{12}=\frac{912}{12}=76[/tex]The median is determined as
[tex]m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}[/tex]Substitute n=12.
[tex]m=\frac{(\frac{12}{2})^{th}+(\frac{12}{2}+1)^{th}^{}}{2}=\frac{6^{th}+7^{th}}{2}=\frac{77+82}{2}=79.5[/tex]There is no mode.
So, from the all the data given.
The mean of the group that studied is over 15 percent points higher than the mean of the group that did not studied.
[tex]92.61-76=16.61[/tex]The median of the group that did not studied is less than 80.
In general , those students that studied scored much higher than those students that did not study.
The correct options are a , c and e.
our football team has members, of which only are strong enough to play offensive lineman, while all other positions can be played by anyone. in how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver?
By using Permutation, the total number of ways in which we can choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver is 1512.
Permutation is defined as the arrangement of items in a specific or a particular order.
Since there are 3 choices for the position of offensive lineman, and for the next position there are 9 choices, similarly 8 choices for the next position and 7 choices remain for the last position.
So we get, 3x9x8x7 =1512, by the concept of Permutation.
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The value of 4 + n when n = 17
Answer:
21Step-by-step explanation:
The value of 4 + n when n = 17
4 + n =
replace n with 174 + 17 = 21
If f(x)=x²-x³ + x² and g(x) = -x², where x # 0, what is (f/g)(x)?
The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0 and the definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)".
What is function?A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x². Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
Here,
f(x)=2x²-x³
g(x)=-x²
f(x)/g(x)=(2x²-x³)/-x²
=x²(2-x)/-x²
f(x)/g(x)=x-2
The definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)". The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0.
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Lines a and b are parallel. Line c is perpendicular to line a. Must it also be perpendicular to line b? Explain your thinking.
Line c is also perpendicular to line a.
Suppose that c and b are perpendicular. This implies that:
option 1) b and a are the same line or,
option 2) b is parallel to a
Since we know that a and b are different lines, hence, the option 2 is the correct.
This question has two parts. First, answer Part A. Then, answer Part B.
part B :
The length of the incline of the ramp will be [h] = 12.0415 ft. The estimated length of the incline would be - 12ft
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -
h² = p² + b²
Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.
[A]
From the data given, we can consider the ramp construction as right angled triangle. We can write -
base [b] = 12 ft
height [p] = 1 ft
Using the Pythagoras theorem -
h² = (12 x 12) + (1 x 1)
h² = 144 + 1
h = √145
h = 12.0415
[B]
For estimating the length of the incline, we will round it off to the exact value. The rounding of length for zero digits after decimal will give the desired result as 12 ft
Therefore, the exact length of the incline of the ramp will be [h] = 12.0415 ft. The estimated length of the incline would be - 12ft
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[ This answer is the answer of part B of the question whose part A is attached with the answer.]
An artist is going to cut four similar righttriangles from a rectangular piece of paperlike the one shown to the right. What is thedistance from B and D to the diagonal AC?Write an equation and solve, showing ALLthe work.
First let's find the length of AC using the Pythagorean theorem in the right triangle with legs of 5 and 12:
[tex]\begin{gathered} AC^2=5^2+12^2 \\ AC^2=25+144 \\ AC^2=169 \\ AC=13 \end{gathered}[/tex]So the diagonal of the rectangle is 13 units. Now, since the area of a triangle is calculated as the product of a base and the corresponding height, we can use the legs as base and height or we can use the segment AC and the corresponding height, and the result is the same, so we have:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ A=\frac{5\cdot12}{2} \\ A=\frac{13\cdot h}{2} \\ \\ \frac{5\cdot12}{2}=\frac{13\cdot h}{2} \\ 60=13h \\ h=\frac{60}{13} \end{gathered}[/tex]So the distance from B or D to the diagonal AC is 60/13 units.
Simplify. I^61
(I is invisible number)
PLEASE HELP
After simplifying i^61 we get the answer is i
Define Complex number
Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labelled i sometimes known as the imaginary unit, and satisfying the equation i² = 1.
We have the given expression : i ^ 61
Rewrite it,
i ^ 61 as (i^4)^15 * i
we know, i² = -1
so, i ^ 4 = i² * i² = -1 * -1 = 1
so, put i ^ 4 value,
⇒1^15 * i
power 1 to the 15 is 1,
⇒1 * i
⇒ i
Hence, the answer is ' i '
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solve the following problems by writing a proportion. a) what is 70% of 4b) 5 is what percent of 20?
We have in a) that
[tex]\begin{gathered} 70\cdot\text{ }\frac{4}{100}\text{ = }\frac{\text{70 }\cdot\text{ 4}}{100} \\ =\text{ 2.8} \end{gathered}[/tex]So the answer for a) is 2.8
Now in b) we have that
[tex]5\cdot\text{ }\frac{100}{20}\text{ = 25}[/tex]So the answer for b) is 25%.
Hello I'm trying to figure out this math problem can anyone help me
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Earnings:
January = $2350
February = january + $500
March = twice as much (february)
Step 02:
March's earnings:
February = $2350 + $500 = $2850
March = 2 * $2850 = $5700
The answer is:
She earned $5700 in March
Please help me
I have a math HW that needs to be solved asap but I have lots of things on my hands right now. Thank you
For first, ∠J=55°, ∠L=55°, ∠K=70°. For second, ∠T=34°, ∠S=34°, ∠R=112°,
For third, AB=5, BC=10, AC=10. For fourth, XY=29, XZ=48, YZ=29
What is isosceles triangle?An isosceles triangle definition states it as a polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180°.
For 1,
in ΔKJL,
KJ=KL
So,
∠J=∠L
∠J=180-125
∠J=55°
∠L=55°
∠K=180-(55+55)
∠K=70°
For 2,
in ΔRST,
RS=RT
So,
∠T=∠S=3x-2
3x-2+3x-2+9x+4=180°
15x=180°
x=12
∠T=3x-2=34°
∠S=3x-2=34°
∠R=9x+4=112°
For 3,
in ΔABC,
AC=BC
So,
3x+4=10
3x=6
x=2
AB=x+3=5
BC=10
AC=3x+4=10
For 4,
in ΔXYZ,
XY=YZ
So,
4x+1=29
4x=28
x=7
XY=4x+1=29
XZ=7x-1=48
YZ=29
For first, ∠J=55°, ∠L=55°, ∠K=70°.
For second, ∠T=34°, ∠S=34°, ∠R=112°,
For third, AB=5, BC=10, AC=10.
For fourth, XY=29, XZ=48, YZ=29
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what is 5x squared if x is 10
Answer: 2500
Step-by-step explanation: 5x10 = 50. 50x50 = 2500
Answer:
2500
Step-by-step explanation:
Directions are with the pic below. Please help with question #1.
Solution:
Let each cubic block be represented with x
Let each spherical block be represented with y
Let each cylindrical block be represented with z
For A,
3x + y = 2y + z
For B,
3x = 5y
For c,
We want to find 3x + 3y
From
3x + y = 2y + z
3x +y -2y =z
3x-y = z-----------------------(m)
From B,
3x = 5y
Substitute 3x = 5y into (m) above
3x-y = z
5y-y = z
4y = z----------------------------------(b)
From C,
3x + 3y = 5y + 3y = 8y
3x + 3y = 2(4y)
3x + 3y = 2z
Recall, z = cylindrical block
The two blocks that will balance C is cylindrical block
Kylie has ten chocolate squares.
His friend Allison takes three of them.
What fraction of chocolate did Kylie give his friend?
3/10ths if im not wrong
15yards to 18 yard increase or decrease
Answer:
Increase
Step-by-step explanation:
You start at 15 yards then proceed to MOVE UP(Increase) 3 more yards getting you to 18.
Answer:
increase
Step-by-step explanation:
because your going 3 more yards on a number line you would travel right
A Large bag contains 7/12 pound of nails. How many 1/4 pound bags can be filled with this amount of nails?
The number of 1/4 pound bags that can be filled with this amount of nails is 2 1/3 bags.
How to calculate the fraction?The large bag contains 7/12 pound of nails.
We also want to fill them into 1/4 pounds of bags. The number of bags needed will be calculated through division. This will be:
= Amount in large bags / Smaller bags
= 7/12 ÷ 1/4
= 7/12 × 4/1
= 28/12
= 2 1/3
Therefore, 2 1/3 1/4 bags are required
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Question 2 of 6
A truck rental company charges $50 plus $10 per hour. Identify a function that represents the total
charge for renting a truck for a certain number of hours. What is the value of the function for an input
of 4, and what does it represent?
Of(h) 50h + 10
=
$210, which is the total charge in dollars for renting 4 trucks
Of(h) = 50 - 10h
$40, which is the total charge in dollars for renting a truck for 4 hours
f(h) = 50h - 10
$190, which is the total charge in dollars for renting 4 trucks
Of(h) = 50+ 10h;
$90, which is the total charge in dollars for renting a truck for 4 hours. PLEASE HELP
What is 2c - 5 = 15? Step by step please!!!
Answer:
c=10
Step-by-step explanation:
2c-5= 15
+5 +5
2c=20
/2 /2
c=10
Hello!
The solution to the problem 2c - 5 = 15 is
c = 10
Step-by-step explanation:
The first step is to add 5 to both sides of the equation.
2c - 5 = 15
2c - 5 + 5 = 15 + 5
The second step is to simplify by adding the numbers.
2c - 5 + 5 = 15 + 5
2c = 20
The third step is to divide both sides of the equation by the same factor.
2c = 20
2c ÷ 2 = 20 ÷ 2
The fourth step is to simply by canceling out the numbers which are present in both the denominator and numerator, then divide.
2c ÷ 2 = 20 ÷ 2
c = 10
Hope this helped!
17. A container is partially filled with 12 liters of whole milk containing 4% butterfat. How
much 1% milk must be added to get a mixture that is 2% butterfat? Construct a table,
then solve.
Step-by-step explanation:
a table ? why? what kind ?
it is relatively simple to solve :
x liters of 1% had to be mixed with 12 liters of 4% to get 12+x liters of 2%
x×0.01 + 12×0.04 = (12+x)×0.02 = 12×0.02 + x×0.02
12×0.02 = x×0.01
x = 12×0.02/0.01 = 12×2 = 24 liters
so, 24 liters of 1% had to be added to the 12 liters of 4% to get a 2% mixture (12 + 24 = 36 liters).
13 FUNDRAISER The Cougar Pep Squad wants to sell T-shirts in the bookstore for
the spring dance. The cost in dollars to order T-shirts in their school colors is
represented by the equation C = 2t + 3.
a. Make a table of values that represents this relationship.
b. Rewrite the equation in function notation.
c. Graph the function.
d. Describe the relationship between the number of T-shirts and the cost.
Answer:
See attached worksheet.
Step-by-step explanation:
See attached worksheet for the table and graph.
I assume that "functation notation: simply means using x and y:
y = 2x + 3
The relationship between the number of T-shirts and cost is defined by y = 2t + 3, where:
y is the total cost,
x is the number of t-shirts,
the 2 is the cost for 1 t-shirt ($/t-shirt), and
3 is a one=time charge of $3 for each order.
The graph (attached) shows a straight line with a y-intercept of 3, the initial order fee. It is linear since the cost of a t-shirt remains the same egardless of order size.
in a certain school district in a large metropolitan area, the sat scores over that past five years are normally distributed with a mean of 1468. furthermore, p 20 p20 is 1216. what is the p 98 p98 score for this population?
Using the normal distribution, the 98th percentile of the distribution of scores is of 2084.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean of the scores is given as follows:
[tex]\mu = 1468´[/tex]
The 20th percentile is of 1216, meaning that when X = 1216, Z = -0.84, hence the standard deviation is calculated as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{1216 - 1468}{\sigma}[/tex]
[tex]0.84\sigma = 252[/tex]
[tex]\sigma = \frac{252}{0.84}[/tex]
[tex]\sigma = 300[/tex]
The 98th percentile is X when Z = 2.054, hence it is calculated as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
2.054 = (X - 1468)/300
X - 1468 = 300 x 2.054
X = 2084.
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