Answer:
375
Step-by-step explanation:
Lily paid $750 each month for 36 months to pay off her car loan.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the amount that Lily paid each month, we can divide the total cost of the car by the number of monthly payments:
So,
Amount paid each month
= Total cost / Number of payments
In this case,
The total cost is $13,500 and the number of payments is 36:
Amount paid each month = $13,500 / 36
We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor of 13,500 and 36, which is 18:
Amount paid each month = $750
Therefore,
Lily paid $750 each month for 36 months to pay off her car loan.
Learn more about expressions here:
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At Shimla, the temperature was -14°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Shimla on Tuesday?
Answer:
-14-2= -16
I hope it helps :)
If a = pi +3j - 7k, b = pi - pj +4k and the angle between a and is acute then the possible values for p are given by
Answer:
The family of possible values for [tex]p[/tex] are:
[tex](-\infty, -4) \,\cup \,(7, +\infty)[/tex]
Step-by-step explanation:
By Linear Algebra, we can calculate the angle by definition of dot product:
[tex]\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|}[/tex] (1)
Where:
[tex]\theta[/tex] - Angle between vectors, in sexagesimal degrees.
[tex]\|\vec a\|, \|\vec b \|[/tex] - Norms of vectors [tex]\vec {a}[/tex] and [tex]\vec{b}[/tex]
If [tex]\theta[/tex] is acute, then the cosine function is bounded between 0 a 1 and if we know that [tex]\vec {a} = (p, 3, -7)[/tex] and [tex]\vec {b} = (p, -p, 4)[/tex], then the possible values for [tex]p[/tex] are:
Minimum ([tex]\cos \theta = 0[/tex])
[tex]\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0[/tex]
Maximum ([tex]\cos \theta = 1[/tex])
[tex]\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1[/tex]
With the help of a graphing tool we get the family of possible values for [tex]p[/tex] are:
[tex](-\infty, -4) \,\cup \,(7, +\infty)[/tex]
The dot product between the two vectors is the product of the magnitude between them times cosine angle.
The possible values for [tex]p[/tex] is (7,-4), when the angle is acute between [tex]a[/tex] and [tex]b[/tex].
To find the value of [tex]p[/tex] we need to perform the dot product of two equation.
How do you multiply vector in dot product?The dot product between the two vectors is the product of the magnitude between them times cosine angle
Given information-
The vector equation given in the problem is,
[tex]a = p\hat i +3\hat j - 7\hat k[/tex]
[tex]b = p\hat i - p\hat j +4\hat k[/tex]
For acute angle, the dot product of [tex]a,b[/tex] less than equal to zero.
Thus,
[tex]a .b<0[/tex]
Put the values,
[tex](p\hat i +3\hat j - 7\hat k)(p\hat i - p\hat j +4\hat k)<0[/tex]
In the dot product the multiplication of different unit vector is zero. Thus,
[tex]p^2-3p-28<0[/tex]
Factorize above equation using the split the middle term method as,
[tex]p^2-7p+4p-28<0\\(p-7)(p+4)<0[/tex]
As the factor of the above equation is 7 and -4.
Thus the possible values for [tex]p[/tex] is (7,-4), when the angle is acute between [tex]a[/tex] and [tex]b[/tex].
Learn more about the dot product here;
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Can you please help and I will mark brainliest if its correct
Step-by-step explanation:
diamonds and hearts are red cards
spades and clubs are black cards
15+11=26
26/52 is the probability of selecting a black card, 50%
Andres went out to a restaurant for dinner. His total bill before tax and tip was $27.30. He was charged an additional 9% tax and he also paid a 15% tip on the original bill.
Answer:
$25.66
Step-by-step explanation:
Given data
Total Bill before tax and tip= $27.30
Tax= 9%
Tip= 15%
Let us find the tax
=9/100*27.30
=0.09*27.30
=$2.457
Let us find the tip
=15/100*27.30
=0.15*27.30
=$4.095
Therefore his bill after tax and tip is
=27.30+2.457-4.095
=$25.66
Need some assistance please
Answer:I hope this could help !ut the answer is 4
Step-by-step explanation:
2 of them left so there are 4 left
If A and B are (-2,-2) and (2,-4). Find the coordinates P such that AP=3/7 AB and P lies on the line segment ab
Answer:
The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].
Step-by-step explanation:
Point P:
The coordinates of point P are (x,y).
AP=3/7 AB
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
We apply this both for coordinate x and coordinate y.
Coordinate x:
[tex]x - (-2) = \frac{3}{7}(2 - (-2))[/tex]
[tex]x + 2 = \frac{12}{7}[/tex]
[tex]x = \frac{12}{7} - 2 = \frac{12}{7} - \frac{14}{7} = -\frac{2}{7}[/tex]
Coordinate y:
[tex]y - (-2) = \frac{3}{7}(-4 - (-2))[/tex]
[tex]y + 2 = -\frac{6}{7}[/tex]
[tex]y = -\frac{6}{7} - 2 = -\frac{6}{7} - \frac{14}{7} = -\frac{20}{7}[/tex]
The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].
Copy and complete the statement using < or >
-7 or -8
Answer: -7
Step-by-step explanation:
Well since where going below degrees the answer would be -7 because it is closer to 1
The answer to this maths question
Given:
Toilet rolls com in packs of 4 and 9.
4-pack is priced at £2.04.
9-pack is priced at £4.68.
To find:
The pack that has better value by calculating the price per roll.
Solution:
We have, the 4-pack is priced at £2.04.
So, the price per roll for this pack is:
[tex]\dfrac{2.04}{4}=0.51[/tex]
In the pack of 4 rolls the price per roll is £0.51.
It is given that, the 9-pack is priced at £4.68.
So, the price per roll for this pack is:
[tex]\dfrac{4.68}{9}=0.52[/tex]
In the pack of 9 rolls the price per roll is £0.52.
Since the price per roll in the pack of 4 rolls is less that the price per roll in the pack of 9 rolls because 0.51 < 0.52, therefore the pack of 4 rolls has better value.
If Andrea traveled 300 miles in 5 hours at what rate was she driving?
Answer:
60
Step-by-step explanation:
[tex]\frac{300}{5}[/tex]
60
Hence, 60 is the answer
Answer:
60 mph
Step-by-step explanation:
For this problem, we are looking at the rate, miles per hour. We know that Andrea traveled 300 miles in 5 hours, but how many miles did she travel in one hour? Let's do the math:
[tex]300[/tex]÷[tex]5=60[/tex] miles.
So, in one hours, Andrea travels 60 miles. We get the rate, 60mph.
Andrea was driving at 60 mph.
I hope this helps! Please let me know if you have any questions :)
Two similar triangles have a scale factor of 2 : 3. For numbers 7a – 7d, determine whether each statement about the triangles is true or false.
7a. The ratio of their perimeters is 2 : 3. True or False
7b. The ratio of their areas is 4 : 6. True or False
7c. Their perimeters could be 14 cm and 21 cm. True or False
7d. Two corresponding sides could be 6 in and 7 in. True or False
Answer:
Step-by-step explanation:
Two similar triangles have a scale factor of 2 : 3.
7a. The ratio of their perimeters is 2 : 3.
As the sides are 2 : 3, the perimeters which are sums of all sides will also be 2 : 3
True
7b. The ratio of their areas is 4 : 6. True or False
As the sides are 2 : 3, the areas which are the products of two sides will be in the ratio of 2*2 : 3*3 = 4 : 9
False
7c. Their perimeters could be 14 cm and 21 cm. True or False
As the perimeter ratio for 14cm and 21 cm is 14 : 21 = 2 : 3 which complies with 7a. So they could be the perimeters.
True
7d. Two corresponding sides could be 6 in and 7 in. True or False
As the corresponding sides of 6in and 7in, the ratio is 6 : 7 and is different from 2 : 3. So they cannot be corresponding sides.
False
Answer:
Step-by-step explanation:
7a. perimeter=3 sides added so the ratio is the same
The ratio of their perimeters is 2 : 3.
True
7b. area= sidexside so the ratio is 2x2:3x3 = 4:9
The ratio of their areas is 4 : 6.
False
7c. 14:21 =2:3
Their perimeters could be 14 cm and 21 cm.
True
7d. 6:7 <> 2:3
Two corresponding sides could be 6 in and 7 in.
False
Which is the graph of f(x) = 4[1/2]x ?
Step-by-step explanation:
answer is in picture see
hope it helpful
What is the cube root of 216xy18?
O 4xy
O 6xy
O 72xBy15
O 213x®y 15
Please help thanks! Brainliest
[tex]5[/tex] ✅
Step-by-step explanation:
[tex]14 + {6}^{2} \div ( - 4) \\ \\ \: = 14 + \frac{6 \times 6}{ - 4} \\ \\ \: = 14 - \frac{36}{4} \: \\ \\ = 14 - 9 \\\\ \: = 5[/tex]
Note:-
[tex]\sf\purple{BODMAS\: rule.}[/tex]
B = Brackets
O = Orders
D = Division
M = Multiplication
A = Addition
S = Subtraction
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Answer:
12.5
Step-by-step explanation:
14+6²÷(-4)
=14+6×6÷(-4)
=14+36÷(-4)
=50÷-4
=12.5
Use SOH CAH TOA to identify the Tangent Z.
SOH = Sine Opposite Hypotenus
CAH = Cosine Adjacent Hypotenus
TOA = Tangent Opposite Adjacent
Based on the key I wrote above, TOA is what you will use. Starting from angle Z look at the opposite side and adjacent side. (Opposite = 21 and Adjacent = 20) Make sure you're not looking at the hypotenus which is the side that is always across from the 90° angle.
Going by opposite over adjacent, that would be 21/20
The answer is the first choice 21/20
write an equivalent logarithmic equation for e^x=24
Answer:
x=ln 24
Step-by-step explanation:
e^x=24
If we take the ln of both sides
ln e ^x= ln 24
x=ln 24
the expanded form of 6,398 is
Answer:
The expanded form of 6,398 is 6000 + 300 + 90 + 8
a 25% tip was payed on a 30$ meal what is the amount of the tip
Answer:
$7.50
Step-by-step explanation:
30 x 0.25= 7.50
help me pls ill give brainliest and no links pls:)!<3
As both the angles are linear, their sum is equal to 180°
i.e m<EFG+m<GFH = 180
=>( 2n+17 )+(4n+37) = 180
=> 6n + 54 = 180
=> 6n = 180-54
=>6n =126
=> n= 21
m<EFG = 2(21)+17 = 59°
m<GFH =4(21)+37 =121°
Given: ∠EFG and ∠GFH are a linear pair
We know that: Sum of the angles which make a linear pair should be equal to 180°
⇒ ∠EFG + ∠GFH = 180°
Given :
∠EFG = 2n + 17
∠GFH = 4n + 37
⇒ 2n + 17 + 4n + 37 = 180°
⇒ 6n + 54 = 180°
⇒ 6n = 180 - 54
⇒ 6n = 126
⇒ n = 21°
Substituting the value of n in ∠EFG and ∠GFH, We get:
⇒ ∠EFG = 2(21) + 17 = (42 + 17) = 59°
⇒ ∠GFH = 4(21) + 37 = (84 + 37) = 121°
Set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three. Set Y is made up of the possible ways five students can be formed into groups of three if student A must be in all possible groups. Which statements about the situation are true? Select three options.
I NEED THIS RIGHT AWAY
Set X has 10 possible groupings.
X Y
Set Y = {ABC, ABD, ABE, ACD, ACE, ADE}
If person E must be in each group, then there can be only one group.
There are three ways to form a group if persons A and C must be in it.
The answer is
A. Set X has 10 possible groupings.
C. Set Y = {ABC, ABD, ABE, ACD, ACE, ADE}
E. There are three ways to form a group if persons A and C must be in it.
Good luck :)
Answer:
It’s A,C,E
Step-by-step explanation:
i did the quiz friends
ur wlcm :)
hope i helped /made life easier
[tex] {10}^x = 5[/tex]
What is x?
×= 5/log 10 ^10
x= In 5
x=log 10^5
x=1/2
Answer:
below
Step-by-step explanation:
10ˣ = 5
applying log to both sides
xlog 10 = log5
x = 0•699
3) The triangles shown are congruent using ASA, but they arb not marked completely. Mark the corresponding parts in this drawing that must be congruent in order to apply the ASA. Then write the congruence statement in the spaces provided. (2 pts) CAB FDE ____=____
Answer:
angle A = Angle E
ΔCAB ≅ΔFED
Step-by-step explanation:
ASA means Angle side Angle Where the side is between the two angles
We have an angle C= F and a side AC = EF
We need angle A = Angle E
ΔCAB ≅ΔFED
SUPER URGENT: Find secθ.
Answer:
B
Step-by-step explanation:
√((-20)²+21²)=√(400+441)=√841=29
cos θ=-20/29
sec θ=-29/20
Will mark brainliest!
Which of the following is the result of using the remainder theorem to fin F(-2) for the polynomial function F(x)=-2x^3+x^2+4x-3?
A. -23
B. 9
C. -11
D. 3
Answer:
B
Step-by-step explanation:
To find f(- 2) substitute x = - 2 into f(x)
f(- 2) = - 2(- 2)³ + (- 2)² + 4(- 2) - 3
= - 2(- 8) + 4 - 8 - 3
= 16 + 4 - 8 - 3
= 9 → B
Please help asap thanks
Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?
x2 + y2 + 4x + 6y – 51 = 0
x² + y² – 4x – 6y – 51 = 0
x2 + y2 + 4x + 6y – 3 = 0
x2 + y2 – 4x – 6y – 3 = 0
The equation for the given circle is:
[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
How to get the equation of the circle?
Remember that for a circle whose center is (a, b) and has a radius r, the equation is:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
In this case, the center is (-2, -3) and the diameter is 8 units, so the radius is r = 4.
Then the equation is:
[tex](x + 2)^2 + (y + 3)^2 = 4^2[/tex]
Expanding the squares we get:
[tex](x^2 + 2*2*x + 4) + (y^2 + 2*3*y + 3^2) = 16\\\\x^2 + y^2 + 4x + 6y + 4 + 9 - 16 = 0\\\\x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
So the correct option is the third one.
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Bab need someone who can do quick mafs please!
Answer:
18.9 km²
Step-by-step explanation:
Formula for area of a triangle: [tex]\frac{1}{2}bh[/tex]
0.5(7 × 5.4) = 18.9 km²
Answer:
A = 1/2 bh
1/2 x 7 x 5.4
= 18.9km2
According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A.M. and 7:00 A.M. Assuming the arrival times of workers are independent, which of the following is closest to the standard deviation of W?
A. 0.24
B. 4.11
C. 4.24
D. 16.79
E. 16.92
Answer: B. 4.11
Step-by-step explanation:
Using Binomial distribution ( as the arrival times of workers are independent).
Formula for standard deviation: [tex]\sqrt{{p(1-p)}{n}}[/tex], where p= population proportion, n= sample size.
As per given ,
p= 0.06, n=300
Required standard deviation= [tex]\sqrt{0.06\left(1-0.06\right)300}[/tex]
[tex]=\sqrt{(0.06)(0.94)(300)}\\\\=\sqrt{16.92}\approx4.11[/tex]
Hence, the correct option is B.
PLEASE HELP QUICKLY - ATTACHED BELOW MATHS
Answer:
113.081 mm²
Step-by-step explanation:
A semicircle is the half part of a circle. And we know that the semicircle have 24 mm of diameter, and the radius is 24/2 = 12 mm. The small circle is inside the semicircle, so its diameter is equal to the radius of the semicircle, and its radius is 12/2 = 6mm
Now, consider π = 3.141, the area of the small circle is:
π•6² = 3.141 • 36 = 113.076 mm²
The area of the semicircle is (π•12²)/2 = (3.141•144)/2 = 226.151 mm²
Now, you just subtract the areas:
226.151 - 113.076 = 113.081 mm²
Help me I don't know any
Answer:
25%
Step-by-step explanation:
(a)
We need to express in percent 8 as a percent of 32.
We have,
Numerator = 8
Denominator = 32
Percent,
[tex]P=\dfrac{8}{32}\times 100\\\\=25\%[/tex]
Hence, the required percentage is 25%.
Lisa invested $2500 in a bank account. The account has an annual interest rate of 3.5%. How much money will be in the account after 15 years? Use the formula A(t) = P*e^rt to solve the problem. (round to the nearest hundredth)
Answer:
A = $ 4188.38
Step-by-step explanation:
A= $2500
r = 3.5% = 0.035
t = 15years
n = 1
[tex]A = P(1 + r)^t[/tex]
[tex]= 2500 ( 1 + 0.035)^{15}\\\\= 2500 (1.67535)\\\\= \$ 4188.38[/tex]
