The answer to the given word problem is as follows. From the calculations: Johanna purchased
4 pens, 8 notebooks, and 5 highlighters.What is a word problem?A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation.
The calculations is given as follows:
Step 1 - First, let's define the variables to represent the unknowns.
Let p = number of pens
Let n = number of notebooks
Let h = number of highlighters
p + n + h = 17 ......................... 1 (purchased 17 items)
.5p + 4n + 1.5h = 41.5 ...................2 (total cost $41.50)
n = h+3 ................................3 (3 more notebooks than highlighters)
Step 2...............Solve for P in equation 1
P = 17 - n - h..................4
Recall that in equation 3,
n = h + 2
If we make n the subject of the expression, we have:
n = h+ 3
Substituting that into equation 4, we have
p = 17 - (h+3) - h
p = 17 -2h - 3 ..................5
Going back to equation 2, let's substitute n with h+3 and replace p with 17 -2h - 3
.5(17 -2h - 3) + 4 (h+3) + 1.5h = 41.5
To remove all decimals, we can multiply all with 10 to get:
5(170-20h -30) + 40(10h +30) + 15h = 415
Expand all brackets and we have:
850 - 100h - 150 + 400h + 1200 + 15h = 415
Collect like terms
-100h + 400h + 15h = 415-850+150-1200
315h = -1485
h = -1485/315
h = -4.71
Since a physical item cannot be negative, we utilize the absolute value which is:
h = 4.71
h [tex]\approx[/tex] 5 highlighter
Recall that
n = h + 3
Hence
n = 5 +3 = 8 notebooks
Recall that
p + n + h = 17
Hence we have
p + 8 + 5 = 17
p = 17 -8 - 5
p = 17 - 13
P = 4 pens.
Hence Johanna purchased
4 pens, 8 notebooks and 5 highlighters.
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What is the circumference of a circle with a radius of 14 feet using pie?
Answer:
Circumference 87.92 ft
Step-by-step explanation:
You have a radius of 14 so u multiply by 2 to get the diameter, then u mulptiply by pie (3.14) thats how u get the circumference.
14×2=28
28×3.14=87.92
Question 4 (10 points)
Answer:
1024
Step-by-step explanation:
4^5
= 4*4*4*4*4
= 16*4*4*4
= 64*4*4
= 256*4
= 1024
20 pointsssss
HELPPPPPPPPP
The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
What is meant by partition segment?A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.
Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.
Where P exists at the origin and line segment is a horizontal one.
The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).
The segment exists not a horizontal or vertical line:
The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].
Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).
where neither P nor Q exists at the origin.
Use the end points of the segment PQ to estimate the components of the directed segment.
[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle[/tex]
= (6,-4)
The components of the segment PX where X exists a point on the segment 1 / 3 of the way from P to Q are
[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle=(2,-1.25)$$[/tex]
To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.
Therefore, the coordinates of the point X exists (1+2,6-1.25) = (3, 4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
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the object on the scale drawing is 4 inches long. How many feet long is it in real life?
Answer:
half of a foot
Step-by-step explanation:
How many miles does the car travel in 1.5 hours
Answer:
97 miles
Step-by-step explanation:
pls mark brainlest
Answer:
97 miles
Step-by-step explanation:
65 mph * 1.5 hours = 97 miles
Work out the circumference of this circle. Take n to be 3.142 and write down all the digits given by your calculator. 10 cm
The circumference of the circle will be given by 62.84 cm.
A circle is a closed figure having a fixed point known as center of the circle and the distance from the center to any point on the boundary of circle is known as the radius of the circle. Circumference is the total length of the boundary of the circle. The circumference of the circle is given by the formula
C = 2πr where r is the radius of the circle and the value of π is given as 3.142.
Now, according to question r = 10cm
C = 2×3.142×10
C = 20×3.142
=> C = 62.84 cm
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In triangle OPQ, m/O = (2x - 5)°, m/P = (3x − 8)°, and m/Q = (10x - 17)°. What is the value of x?
The value of x is 14 °
What is angle sum property of triangle?The sum of the interior angles in a triangle is supplementary. In other words, the sum of the measure of the interior angles of a triangle equals 180°. So, the formula of the triangle sum theorem can be written as, for a triangle ABC, we have ∠A + ∠B + ∠C = 180°.
In ΔOPQ,
∠O = (2x- 5)°
∠P = (3x-8)°
∠Q= (10x- 17)°
Thus by angle sum property of triangle we know:
∠O+ ∠P + ∠Q = 180
thus 2x - 5 + 3x - 8 + 10x - 17 = 180
15x - 30 = 180
= 15 x = 180 + 30
= 15 x = 210
= x= 210 / 15
= x = 14 .
Thus ∠O = (2x- 5)° = 2X 14 - 5 = 23 °
∠P = (3x-8)° = 3× 14 - 8 = 44°
∠Q= (10x- 17)° = 10 × 14 - 17 = 123°
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The area of the Mojave desert is 25000 square miles.
A scale drawing of the Mojave desert has an area of 10 square inches.
What is the scale of the map
The scale of the map given the area of the desert and the area of the scale drawing is 1 square inch represents 2,500 square miles.
What is the scale?A scale drawing is either a larger or smaller image of another image or object. A scale drawing is enlarged or reduced using a scale. A map is a smaller scale drawing of an area. The scale is used to keep the proportion of the dimensions between the scale drawing and the original place similar.
In order to determine the scale of the drawing, divide the original square area by the square area of the scale drawing.
Scale of the drawing = original dimensions / dimensions of the scale drawing
25,000 square miles / 10 square inches = 2,500 square miles
The scale is 1 square inch represents 2,500 square miles. or 1 : 2,500.
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in the usa, the cost of a phone is $1200. in the uk a phone is £920. using the exchange rate £1 = $1.36, work out the difference in cost of the phones in the usa and the uk
The difference between of the cost of the phones in the USA and the UK is $51. 2
What is exchange rate?Exchange rate can be defined as the price of the unit of foreign currency in terms of the home currency.
It is also known as the rate at which a currency is exchanged to another currency
From the information given, we have that;
The cost of a phone in the USA is $1200The cost of a phone in the UK is £920We also have that;
The exchange rate is expressed as;
£1 = $1.36
Now, let's convert the cost from dollars to euros, we have;
If £1 = $1.36
Then, £920 = $x
cross multiply, we have;
x = 920 × 1. 36
x = $1251. 36
Now, let's find the difference between the cost in the USA and UK, we have;
= $1251. 36 - $1200
= $51. 2
Hence, the difference is $51. 2
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Final exam scores in a mathematics course are normally distributed with a mean of 71 and a standard deviation of 12. Fill in the missing information
Percentile: 99.87
Z-score: ?
Exam score: ?
Answer:
See below
Step-by-step explanation:
99.87-71 = 28.81 this is 28.81/12 = z-score = +2.4
corresponding to .9918 ( from z-score table) = a score of 99.18%
PRACTICE Describe the domain and range of each function using inequality or set-builder notation.
In the picture there are 4 graphs.
1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).
2nd graph we get domain as [-4,4] and range as [3,-1].
3rd graph we get domain as [-4,1] and range as [1,-4].
4th graph we get domain as (-∞,4] and range as (-∞,-2].
Given that,
In the picture there are 4 graphs.
We have to find the domain and range of the each function using inequality or set-builder notation.
A function's domain is the set of values that we are allowed to enter into our function.
This set consists of the values of the x-axis for a function like f. (x).
The range of values that can be used as input for a function is called this. The values in this set hence, once we input an x value, the function returns. The y values are those.
1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).
2nd graph we get domain as [-4,4] and range as [3,-1].
3rd graph we get domain as [-4,1] and range as [1,-4].
4th graph we get domain as (-∞,4] and range as (-∞,-2].
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i need help with this, thanks
Answer:
151, 29, 151
Step-by-step explanation:
[tex]m\angle 2=29^{\circ}[/tex] (vertical angles)
[tex]m\angle 1=m\angle 3=151^{\circ}[/tex] (linear pair)
Answer:
[tex]m \angle 1= \boxed{159}\;^{\circ}\\\\m \angle 2= \boxed{21}\;^{\circ}\\\\m \angle 4= \boxed{21}\;^{\circ}[/tex]
Step-by-step explanation:
Angles on a straight line sum to 180°.
⇒ m∠3 + m∠4 = 180°
⇒ 159° + m∠4 = 180°
⇒ m∠4 = 21°
Vertical Angle Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Applying the Vertical Angle Theorem:
m∠1 = m∠3 = 159°m∠2 = m∠4 = 21°Keiko's penny bank is 1/6
full. After she adds 320 pennies, 1/2 it is full. How many pennies can Keiko's bank hold?
Answer: 960
Step-by-step explanation:
Let the number of pennies Keiko's bank hold be x
Now, According to the question,
[tex]\frac{1}{6} \times x+320=\frac{1}{2} \times x[/tex]
⇒ [tex]\frac{1}{6} \times x+320=\frac{x}{2}[/tex]
⇒ [tex]\frac{(x+1960)}{6}=\frac{x}{2}[/tex]
⇒ 2(x + 1920) = 6x
⇒ 2x + 3840 = 6x
⇒ 6x - 2x = 3840
⇒ 4x = 3840
⇒ [tex]x = \frac{3840}{4}[/tex]
⇒ x = 960
Hence, the total number of pennies Keiko's bank hold = 960.
Vincent made a 2000 deposit into an account on august1 that yields 2% interest compounded annually. How much money will be in that account at the end of 5 years
The money in the account at the end of 5 years is 2208.16
Compound interestThe formula for calculating the compound interest is expressed according to the formula:
Compound interest = P(1+r)^t
Given the following parameters
Principal = 2000
rate = 2 % = 0.02
time = 5 years
Substitute
A = 2000(1+0.02)^5
A = 2000(1.02)^5
A = 2208.16
Hence the amount of money that will be in that account at the end of 5 years is 2208.16
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In Exercises 5 and 6, use the translation (x,y) → (x + 1, y - 3) to find the image
of the given point.
5. Q(5,9)
6. M(-3,-8)
After using translation the image of the given points will be at Q( 6 , 6 ) and M( -2 , -11 ).
What is translation ?
The linear movement of a point relative to its initial position is known as translation. The horizontal position is labeled first and the vertical position is labeled second when describing a point's coordinates with respect to the origin of an x-y coordinate plane.
The translation is given to be (x,y) → (x + 1, y - 3)
The tow points are Q(5,9), M(-3,-8)
using translation we get,
Q( 5 , 9 ) → (5 + 1, 9 - 3) = Q( 6 , 6 )
M( -3 , -8 ) → (-3+ 1, -8- 3) = M( -2 , -11 )
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Given that 2 x 108 = 20 × 107
Work out (2 x 108) + (4 × 107)
Give your answer in standard form.
The solution of the given expression will be ( 2.4 x 10⁸ ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 2 x 10⁸ = 20 × 10⁷. The sum of the two exponential numbers will be calculated as:-
Sum = 2 x 10⁸ + ( 4 x 10⁷ )
Sum = 20 x 10⁷ + ( 4 x 10⁷ )
Sum = ( 20 + 4 ) x 10⁷
Sum = 24 x 10⁷
Sum = 2.4 x 10⁸
Therefore, the solution of the given expression will be ( 24 x 10⁷ ).
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Can someone explain how to do this to me!! Please thanks
Answer:
MP = 19
Step-by-step explanation:
MP = MN + NO + OP
we require to find OP and MN before we can evaluate MP
NO + OP = NP , that is
8 + OP = 15 ( subtract 8 from both sides )
OP = 7
and
MN + NO = M0 , that is
MN + 8 = 12 ( subtract 8 from both sides )
MN = 4
Then
MP = MN + NO + OP = 4 + 8 + 7 = 19
i need help on this, thanks
Answer:
9
Step-by-step explanation:
Vertical angles are congruent, so:
[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]
A(-3, 13), B(4, -15) Find the slope
PLEASE PLEASE PLEASE HELP DUE IN AN HOUR I WILL GIVE BRAINLIEST IF YOU ANSWER SHOW WORK HELPPPP ME THANK YOUU
The mean of the number of hours spent watching television is 15.75
The mean absolute deviation of the number of hours spent watching television is 6.625.
What is the mean and mean absolute deviation?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(10 + 11 + 22 + 7 + 17 + 17 + 20 + 31 + 0 + 12 + 19 + 23) / 12 = 189/12 = 15.75
Mean absolute deviation is the average of the sum of the absolute difference between the numbers and the mean.
MAD = 1/n ∑ l x - m(x) l
(|10 - 15.75) + |11 - 15.75| + |22 - 15.75| + |7 - 15.75| + |17 - 15.75|+ |17 - 15.75| + |20 - 15.75| + |31 - 15.75| + |0 - 15.75| + |12 - 15.75| + |19 - 15.75| + |23 - 15.75|
= (5.75 + 6.75 + 6.25 + 8.75 + 1.25 + 1.25 + 4.25 + 15.25 + 15.75 + 3.75 + 3.25 + 7.25) / 12 = 6.625
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what is 6 times 10 equal
Answer:
60
Step-by-step explanation:
10 + 10 + 10 + 10 + 10 + 10 = 60
Answer:
60
Step-by-step explanation:
Everytime you are multiplying by 10, you add a 0 to the number that you are multiplying by. In this case, the 6 turns into 60. This is a trick for the multiples of 10. Hope this helps!
Please help, I honestly have no clue what I’m doing.
Given the table below, determine the following
Y = -4x+15
(Picture below)
Answer:
y=-1
y=43
x=14
Step-by-step explanation:
So, you have the equation: [tex]y=-4x+15[/tex], and if we know one value we can easily solve for the other using some algebraic manipulation.
Find y when x=4.
For this we know one value, "x", and the other "y" value is unknown. This is actually not to hard if you notice that the equation we're given expresses the value of "y" in terms of "x".
So let's plug in the x-value: [tex]y=-4(4)+15\implies y=-16+15=-1[/tex]
So we get: y=-1, which turns out to be the solution!
Find y when x=-7
This is a similar process, so let's just get straight into it and plug x as -7
[tex]y=-4(-7)+15\\y=28+15\\y=43[/tex]
This is our solution, y=43
Find x when y = -41
So this case is a bit different since we're given the y-value and not the x-value, and as I mentioned the equation represents the value of y in terms of x.
We still do a similar process, except we'll use some more algebraic manipulation, but let's start by plugging in the known value:
[tex]-41=-4x+15[/tex]
Let's move the constant, 15, to the other side by subtracting by 15 to cancel both sides.
[tex]-56 = -4x[/tex]
Now we want to get the x alone, and the only "operation" being done on the x, is that it's being multiplied by the coefficient of -4. To cancel this out we want to divide both sides by -4 to maintain equality & cancel out the coefficient of -4 to one, which is just 1 * x which can be expressed as x as it's implied the coefficient is 1
[tex]14=x[/tex]
Now we have our solution!
lenge You buy 3.16 pounds of oranges, 1.15 pounds of peaches, and 2.24 pounds of apples.
Using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds
The cost of the oranges = 3.16 pounds
The cost of the peaches = 1.15 pounds
The cost of the apples = 2.24 pounds
Then the total bill = The cost of the oranges + The cost of the peaches + The cost of the apples
Here we have to use the addition
Substitute the values in the equation
Then the total bill = 3.16 + 1.15 + 2.24
= 6.55 pounds
Hence, using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds
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What’s x-5=1
Please please please help
round 38.4561 to 2 dp
Answer: 38.46
Step-by-step explanation:
↓
38.456 It means round by 0.05, so when you round you look at the place value after the specified digit.
Bob purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Bob paid.
Answer:
Cost Function is:
c = 4n
Or, using n as a function variable, we write:
c(n) = 4n
Step-by-step explanation:
c represents total cost
n represents notebook
4 represents cost per notebook
Line AB is a straight
line.
9
1. m∠AOB = ____
Statement
1. ________
Reason
2. m∠AOE+m∠EOF+m∠FOB=m∠____ 2. ________
3. x + ____ +20° = ____ 3. Substitution
4. x = ____ 4. Algebra
The two column proof of the given angles are;
Statement 1; m∠AOB = 180°
Reason 1; Sum of angles on a straight line sums up to 180°
Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB
Reason 2; Opposite angles
Statement 3; x + 3x + x + 12 = 152
Statement 3; Substitution
Statement 4; x = 28°
Reason 4; Algebra
How to solve two column proof?From the attached image, we can complete the two column proof as follows;
Statement 1; m∠AOB = 180°
Reason 1; Sum of angles on a straight line sums up to 180°
Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB
Reason 2; Opposite angles
Statement 3; x + 3x + x + 12 = 152
Statement 3; Substitution
From statement 3, we can use algebra to find x as;
x + 3x + x + 12 = 152
5x + 12 = 152
5x = 152 - 12
5x = 140
x = 28°
Thus;
Statement 4; x = 28°
Reason 4; Algebra
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asap help please brainly okay
Answer:
2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
given
[tex]\sqrt{5}[/tex] × [tex]\sqrt{8}[/tex]
= [tex]\sqrt{5(8)}[/tex]
= [tex]\sqrt{40}[/tex]
= [tex]\sqrt{4(10)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex]
= 2[tex]\sqrt{10}[/tex]
Conditional Statement: If the object has a remote, then it is a television.
Part A: Write the converse to the conditional statement.
Part B: Write a biconditional statement from the conditional statement.
Part C: Validate the biconditional statement from Part B. Use details to support your answer.
For given conditional statement 'If the object has a remote, then it is a television.'
Part A: converse to the conditional statement
'If it is a television, then the object has a remote.'
Part B: a biconditional statement
'The object has a remote if and only if it is a television.'
Part C: validation of biconditional statement
The biconditional statement is true because the conditional statement and the converse are true.
In this question, we have been given a conditional statement: 'If the object has a remote, then it is a television.'
Part A:
We need to write the converse to the conditional statement.
The converse of given conditional statement would be:
'If it is a television, then the object has a remote.'
Part B:
We need to write a biconditional statement from the conditional statement.
A biconditional statement of the given conditional statement would be:
'The object has a remote if and only if it is a television.'
Part C:
We need to validate the above biconditional statement.
The biconditional statement is true because the conditional statement and the converse are true.
Therefore, for given conditional statement 'If the object has a remote, then it is a television.'
Part A: converse to the conditional statement
'If it is a television, then the object has a remote.'
Part B: a biconditional statement
'The object has a remote if and only if it is a television.'
Part C: validation of biconditional statement
The biconditional statement is true because the conditional statement and the converse are true.
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**Please Help Im Trying To Make My Parent Proud Of Me i'll try to brainlistt!!** Angelina added 0.45 to 0.333 and made the conclusion that the sum of two rational numbers is rational. Is Angelina correct? Explain.
a
No, she is incorrect because 0.45 and 0.333 are irrational numbers.
b
Yes, she is correct because 0.45 and 0.333 are integers.
c
Yes, she is correct because 0.45 and 0.333 are rational numbers.
d
No, she is incorrect because the decimal numbers must be the same.
Answer:
c. Yes, she is correct because 0.45 and 0.333 are rational numbers. The sum of two rational numbers is a rational number.