In three months, he will owe his father $2500 less $1200, or $1300.
One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
Tom's payment for 7 months is 400 * 7 = $2800.
He borrowed $5300 ($2500 plus $2800).
His monthly payment for three months is 400*3.
In three months, he will owe his father $2500 less $1200, or $1300.
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The Smith and Jones manufacturing company keeps a third of its cash in the bank, which pays 0.5% interest, and the other two-thirds in long-term investments that give 3.5% interest. If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank?
If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank is; $937,500.
How to solve Algebra Word Problems?This is about the concept of compound interest which is defined as the interest on savings that is calculated on both the initial principal and the accumulated interest from previous periods.
From the question, let us make x to represent the amount of cash.
Now, we are told that one portion of it pays 0.5%and as such this will be 0.005x.
Now, the other portion pays 3.5% and as such this is 0.035x.
Combining both knowing that the total the company earned in the last year was $37,500 and we have;
0.005x + 0.035x = 37500
0.040x = 37500
Solve for x to get;
x = (37500)/(0.04)
x = 937500
Therefore, the company started with $937,500.
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Given the domain (-5,-1,3,5) find the first number in the range of the function f(x)=-2x -3 .
The first number in the range of the function is 7
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?The function is given as
f(x) = -2x - 3
Also, we have the domain to be
(-5,-1,3,5)
The first value in this domain is
x = -5
So, we have
f(-5) = -2 x -5 - 3
Evaluate
f(-5) = 7
This represents the first number in the range
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team A and team B play in a competition
team A has twelve more points than team B
team A has five times as many points as team B
how many points does each team have
Answer:
A = 15
B = 3
Step-by-step explanation:
Since Team A has 12 more points than team B, then,
A - 12 = B
A = B + 12 ( equation 1 )
team A has 5 times as many points as team B, so,
5B = A. ( equation 2 )
Substitute equation 1 into equation 2
A = B + 12
5B = B + 12
5B - B = 12
4B = 12
B = 3
we'll substitute the answer into equation 2
5B = A
5(3) = A
A = 15
I hope this helps :D
have a nice day dear...
Rewrite with Common Denominator
-⅗ + -7/10
By multiplying 2 on both the numerator and denominator of [tex]\frac{-3}{5}[/tex] .
The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as
[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]
What is a fraction?A fraction is written with a numerator and a denominator where the numerator is less than the denominator.
Example: 1/3 is a fraction
We have,
[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex]
We have different denominators and we need to make the denominator the same.
We will multiply 2 on both the numerator and denominator of [tex]\frac{-3}{5}[/tex].
= [tex]\frac{2 \times -3}{2 \times 5}[/tex]
= [tex]\frac{-6}{10}[/tex]
We see that,
The denominator in [tex]\frac{-6}{10}[/tex] and [tex]\frac{-7}{10}[/tex] is the same.
i.e 10.
Now,
[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] can be written as [tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]
Thus,
By multiplying 2 on both the numerator and denominator of [tex]\frac{-3}{5}[/tex] .
The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as
[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]
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Mathematics Diagnostic Assessment
Maria wants to add to her CD collection. If a CD costs $8, which expression shows the cost of d CDs?
OA. 8 + d
OB. 8-d
OC. 8-d
OD. 8x d
Which of the following whole numbers are perfect squares? (Please select ALL correct answers for full credit).
Answer: 9, 144, 225, 10,000
Step-by-step explanation:
9=3x3
144=12x12
225=15x15
10,000=100x100
help
D’Neese said that 1/10^5 is equivalent to 10^5 . Which statement is true about what D’Neese said?
D’Neese is correct because a^-n =1/a^n
D’Neese is correct because a^-n = 1//a^-n
D’Neese is incorrect because a^-n = -1/a^n
D’Neese is incorrect because a^-n = a/-n
The statement that is true about what D’Neese said is (d) D’Neese is incorrect because a^-n = a/-n
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the true statement about the equation statement ?The equation statement is given as
1/10^5 is equivalent to 10^5
The above statement can be rewritten in another way
So, we have the following equation
1/10^5 = 10^5
As a general rule of indices, we have the following exponent rule
So, we have the following equation
1/a^n = a^-n
This means that the equation statement is false
This is so because
1/10^5 is not equivalent to 10^5, instead 1/10^5 is equivalent to 10^-5
Hence, the true option about the statement is (d)
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Charis invested 140$ . She earned a simple interest of 3%per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
The amount of interest would be $8.4 Charis received at the end of two years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Principal (P) = $140
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 2 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 140 × 0.03 × 2
⇒ Simple interest = $8.4
Therefore, the amount of interest would be $8.4 Charis received at the end of two years.
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x^5/x^2 can be simplified to what
Answer:
x^3
Step-by-step explanation:
Because they are the same base in a division question, you subtract the exponents.
5-2=3.
Answer = x^3
Hope this helps!
Btw, if this is right, please give me brainliest, thanks!
Answer:
x^3
Cancel the common factor of x^5 and x^2.
Hope you have a wonderful day :)
It takes 200 coins to get a bag upgrade in Pokémon Go. The creators decided to throw a sale on bag upgrades. For one day only anybody can upgrade their bag for 125 coins. Find the percent of change
price change: 125 - 200 = -75 coins
percent of change = price change/original price *100 = -75/200*100 = -37.5%
that is, a discount of 37.5%
Factor x^2 -2x -2. Show all steps
Answer:
x = 1 ± √3
Step-by-step explanation:
Factorizing using quadratic formula:x² - 2x - 2
Co-efficient of x² = a = 1
Co-efficient of x = b = -2
Constant = c = -2
D = b² - 4ac
= (-2)² - 4 *1*(-2)
= 4 + 8
= 12
[tex]\sf x = \dfrac{-b \ \± \sqrt{D}}{2a}[/tex]
[tex]\sf = \dfrac{2 \ \± \sqrt{12}}{2*1}\\\\\\=\dfrac{2 \± \sqrt{2*2*3}}{2}\\\\\\= \dfrac{2 \±2\sqrt{3}}{2}\\\\\\= \dfrac{2}{2} \± \dfrac{2\sqrt{3}}{2}\\\\\\= 1 \± \sqrt{3}[/tex]
[tex]\sf x = 1 + \sqrt{3} ; \ ; or \ x = 1 - \sqrt{3}[/tex]
help i need help with this question
HELP PLS IM MARKING BRAINLEIST
The formula for the volume of a sphere is 4/3πr³. The formula for r is d/2. We know d, so we can substitute this for r.
4/3(3.14)(32/2)^3
4/3(3.14)(16)^3
4/3(3.14)4096
4.19(4096
17612.24 cm^3
[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ the\ diameter\ to\ radius\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Finding\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]
Which relation represents a function?
The relation that represents a function is the mapping in: B.
How to Determine if a Relation is a Function?A relation is defined as a function if each of the x-value (domain element of input) in the relation corresponds to exactly one y-value (range element of output).
The relation in option A is not a function because it has two different y-values, 7 and 5 that corresponds to an x-value, 6. The relations in option C and D do not represent a function also.
The mapping in option B shows a relation where each x-value (domain element) is related or corresponds to only one y-value (range element). Therefore, it is a function.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
74°
(8x-19)°
45°
Answer:
x = 10
Step-by-step explanation:
The internal angles of a triangle sum 180°
74° + 45°+ (8x-19)° = 180°
119 + 8x - 19 = 180
119 - 19 + 8x = 180
100 + 8x = 180
8x = 180 - 100
8x = 80
x = 80/8
x = 10
Check:
74 + 45 + (8x-19) = 180
1100 + 8*10 = 180
100 + 80 = 180
ken makes trail mix. the ratio of nuts to raisins is 3 to 5 . find the amount of nuts used in a trail mix that had ten cups of raisins
answer: 3 to 5 = 6 to 10 = 9 to 15
so the answer would be 6 raisins
Answer:
3x+4x=10x=10/7=1.42
Step-by-step explanation:
3x+4x=10x
7x=10x
10/7=
1.42
What’s x??
Solve for X
5x-9=3x+3
Answer:
x = 6
Step-by-step explanation:
5x - 9 = 3x + 3 ( subtract 3x from both sides )
2x - 9 = 3 ( add 9 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6
A cylindrical hollow metal pipe is 16 cm long.
It has an external diameter of 10 cm and an internal diameter of 8 cm.
The density of the metal from which the pipe is made is 8 grams per cm3
What is the mass of the pipe in grams?
Answer:
3617.28 grams
Step-by-step explanation:
Find the volume of the metal as following:
[tex]V_{metal}=V_{external}-V_{internal}[/tex][tex]V_{external} = \pi d_{external}^2h/4=\pi *10^2*16/4=1256[/tex] cm³[tex]V_{internal} = \pi d_{internal}^2h/4=\pi *8^2*16/4=803.84[/tex] cm³[tex]V_{metal}=1256-803.84 = 452.16[/tex] cm³Find the mass:
[tex]mass = volume*density[/tex][tex]mass = 452.16*8=3617.28[/tex] gramsAnswer:
3619.1 grams (nearest tenth)
Step-by-step explanation:
Volume of a cylinder
[tex]V=\pi r^2 h[/tex]
where:
r is the radius.h is the height.The radius of a circle is half its diameter.
Find the volumes of the external and internal cylinders by substituting the given values into the formula for volume of a cylinder:
[tex]\implies \textsf{Volume of the external cylinder}&=\pi \cdot 5^2 \cdot 16=400 \pi \; \sf cm^3[/tex]
[tex]\implies \textsf{Volume of the internal cylinder}&=\pi \cdot 4^2 \cdot 16=256 \pi \; \sf cm^3[/tex]
Find the volume of the cylindrical hollow metal pipe by subtracting the volume of the internal cylinder from the volume of the external cylinder:
[tex]\begin{aligned}\implies \textsf{Volume of the metal pipe}&=\sf Volume_{external}-Volume_{internal}\\&=400 \pi - 256 \pi\\& = 144 \pi \sf \; cm^3\end{aligned}[/tex]
Density formula
[tex]\rho=\dfrac{m}{V}[/tex]
where:
ρ = densitym = massV = volumeGiven:
ρ = 8 g/cm³V = 144π cm³Substitute the given values of density and the found volume into the density formula and solve for m:
[tex]\begin{aligned}\implies \rho&=\dfrac{m}{V}\\8&=\dfrac{m}{144 \pi}\\m&=8 \cdot 144\pi\\m&=1152 \pi \\m&=3619.11473...\\m&=3619.1\; \sf g \;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the mass of the pipe is 3619.1 grams (nearest tenth).
Note: I have used the exact value of π (not a rounded value).
Please help!
Choose the mathematical sentence that most accurately expresses the
information in the problem, and would be most helpful in solving it.
After taking 4 pieces of fruit out of a bag, 12 pieces of fruit remained. How
many pieces of fruit were in the bag to start?
A. 12 + f = 4
B. 12 ÷ f = 4
C. 4+ f = 12
D. 12 - 4 = f
E. F ÷ 4 = 4
F. F - 4 = 12
Answer:
Option F
F - 4 = 12Step-by-step explanation:
According to given information
1) You had F fruits and took 4 pieces out of a bag, it is:
F - 42) Then you have 12 pieces of fruit remained:
F - 4 = 12This equation matches the answer choice F.
True or False
1. 28<0
2. 126<0
3. 688<0
Answer:
1. False, 2. False, 3. False
Step-by-step explanation:
help help help help help
Answer:
1 4/10
Step-by-step explanation:
3 1/2 turns into 3 5/10 minus 4 9/10 blah blah blah anyways yeah
guys please help ive been trying to figure it out for like an hour. i need to khow whats the value of x khowing that the perimeter is 51 cm
Answer:
x=4
Step-by-step explanation:
first, you have to add all of the sides up:
x+2x+x+3x+7+5x-4=12x+7-4=12x+3
12x+3=51. now, we can subtract 3 from both sides, so that we can isolate x.
-3 -3
12x=48
x=4
Set both given equations equal to zero, then combine them into one standard form equation. Simplify if possible.
7x + 3 = 5 and y - 1 = 6
Equation 1 -
Equation 2 -
Combined Equation -
Answers:
a. 7x - 2 = 0
b. 7x - y = 1
c. 7x + 8 = 0
d. y - 7 = 0
e. 7x - y = -5
f. y + 7 = 0
The standard equation is 7x + y = 9
layoff Ax + By = C is the usual form for two-variable direct equations. A standard form direct equation is, for case, 2x + 3y = 5. When an equation is given in this format, chancing both intercepts is rather simple( x and y). When trying to break systems involving two direct equations, this form is also relatively helpful.
Given
7x + 3 = 5 and y - 1 = 6
Add the bottoms from the two given equations to produce a single standard-form equation.
By shifting the constant fromR.H.S. toL.H.S., the equations are reset to zero.
7x + 3 - 5 = 0
7x - 2 = 0----( 1)
y - 1 = 6
y - 1 - 6 = 0
y - 7 = 0-----( 2)
Equation 1 and equation 2 must be combined.
7x - 2 + y - 7 = 0
7x + y - 9 = 0
layoff Ax + By = C is the equation's conventional form.
A, B, and C are integers and x and y are variables in this type of equation.
Accordingly, the common equation is
7x + y - 9 = 0
7x + y = 9
therefore the standard equation is 7x + y = 9
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Lloyd is making a bouquets of flowers. He has 25c roses and 15v snapdragons.he divides flowers equally to make as many bouquets as possible . He uses all the flowers .what number snapdragons are in beach bouquet.
Answer:
A. 3
Step-by-step explanation:
45 + 15 + 25 = 85
There are 85 flowers.
There are 25 roses, 45 tulips, an 15 roses.
What are all 3 of these divisible by?
5!
That means that there will be 5 bouquets.
Let's divide each number by 5 to find out how many of each type of flower is in each bouquet.
25/5 = 5
5 roses in each bouquet
45/5 = 9
9 tulips in each bouquet
15/5 = 3
3 snapdragons in each bouquet
5 + 9 + 3 = 17
There are a total of 17 flowers in each bouquet.
Out of those 17 flowers, 3 are snapdragons.
A. 3
A stadium has 52,000 seats. Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium
takes in $1,307,200 from each sold-out event. How many seats does each section hold?
Section A holds seats.
The number of seats in Section A is 26000 ,The number of seats in Section B is 14800 and, The number of seats in Section C is 11200.
What is a equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Let the number of seats in Section A is "a".
Let the number of seats in Section B is "b".
and, Let the number of seats in Section C is "c".
Now using the statement "stadium has 52,000 seats"
we can make equation: a + b + c = 52000
Now using the statement "Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C" and "stadium takes in$1,307,200 from each sold out event".
we can make equation: 28a + 24b + 20c = $1,307,200
Now using the statement "he number of seats in Section A equals the total number of seats in Sections b and C"
we can make equation: a = b + c
Solving these three equations. We get,
a = 26000 , b = 14800 and c = 11200
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Solve and graph the solutions of the inequality - |x - 2| + 9 > 6.
i solved it
you graph it :)
The enrollment for a school in 2010 was 1245 students. in 2020, the enrollment was 715 students. find and interpret the rate of change in enrollment from 2010 to 2020
The rate of change in enrollment from 2010 to 2020 is -53 students per year.
Interpretation:
A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.
Here, we have,
To find the rate of change in enrollment from 2010 to 2020, we can use the formula for calculating the rate of change:
Rate of change = (Change in enrollment) / (Time interval)
Where:
Change in enrollment = Enrollment in 2020 - Enrollment in 2010
Time interval = Year in 2020 - Year in 2010
Let's calculate the rate of change:
Change in enrollment = 715 - 1245 = -530
Time interval = 2020 - 2010 = 10 years
Rate of change = (-530) / 10 = -53
The rate of change in enrollment from 2010 to 2020 is -53 students per year.
Interpretation:
A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.
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can someone help with my homework? Thank you !
Answer:
1000-0=1/2(2000-0)
y= 1/2x
-1x + 2y = 0
i need this answer cause I have no clue what I'm supposed to do
The missing co-ordinate r = 8
(6,9) and (r,-1) are two points on a line whose slope is given as -5.
Slope of a line is the change of y co-ordinates divided by the change in x co-ordinates between two points on a line.
Take (x₁, y₁) = (6,9) and (x₂, y₂) = (r, -1).
The slope of a line is given by,
Slope, m = (y₂-y₁)/ (x₂-x₁)
⇒ -5 = (-1-9)/(r-6)
⇒ -5 = -10/(r-6)
⇒ 1 = 2/(r-6)
⇒ r-6 = 2
⇒ r = 2+6
⇒ r = 8
So the points are (6,9) and (8,-1).
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Carlson Middle School has a total of 500 students in sixth, seventh, and eighth grades. The table below shows the number of students in each grade.
Grade Number of Students
Sixth 203
Seventh 126
Eighth 171
The principal randomly selects 25 students to receive a free school lunch today. What is the most likely number of sixth graders in the group of 25 selected by the principal?
There is also a picture down below
Answer: Around 10 sixth graders would get free lunch.
Step-by-step explanation: first, divide 500/25 to find the percentage of students receiving free lunches. You should get 0.05, or 5%. Then, multiply the number of sixth graders (203) by 5%. Your answer is 10.15, rounded down to 10. (Because it is impossible to have 0.15 of a student)