Answer:812/1000
Step-by-step explanation:
A college student receives an interest-free loan of $9,400 from a relative. The student will repay $200 per month until the loan is paid off.
(a) Express the amount P (in dollars) remaining to be paid in terms of time t (in months). (Give your answer in slope-intercept form.)
(b) After how many months will the student owe $5000?
Answer:
(a) P = - 200 T + 9,400
(b) After 22 months the student will owe $5000.
Step-by-step explanation:
Here, the amount loaned out to the student = $9,400
The installment amount of each month = $200
(a) P : Amount remaining to be paid
T: time in months
Now, the remaining amount = Actual amount - Amount paid in T months
or, P = 9,400 - $200 (T)
⇒ P = - 200 T + 9,400 ( y = mx + C form)
(b) The remaining amount left = $5000
As we know, P = 9,400 - $200 (T)
⇒ 5,000 = 9,400 - 200 T
⇒200 T = 9,400 - 5,000 = 4,400
⇒ T = 4400/200 = 22
or T = 22 Months
Hence, After 22 months the student will owe $5000.
the sum of two numbers is 126 and their difference is 42. what are two numbers
Answer:
84, 42Step-by-step explanation:
[tex]x,\ y-numbers\\\\\text{The system of equations:}\\\\\underline{+\left\{\begin{array}{ccc}x+y=126\\x-y=42\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=168\qquad\text{divide both sides by 2}\\.\qquad x=84\\\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\84+y=126\qquad\text{subtract 84 from both sides}\\y=42[/tex]
Final answer:
The two numbers that have a sum of 126 and a difference of 42 are 84 and 42.
Explanation:
To find the two numbers whose sum is 126 and whose difference is 42, we can set up a system of equations:
x + y = 126 (Sum of the numbers)
x - y = 42 (Difference of the numbers)
By adding these two equations, we can eliminate y and solve for x:
x + y + x - y = 126 + 42
2x = 168
x = 84
Now that we have the value of x, we can find y by substituting x back into either of the equations. For example:
84 + y = 126
y = 126 - 84
y = 42
Therefore, the two numbers are 84 and 42.
What is the length of line segment BC?
2 cm
3 cm
6 cm
8 cm
Answer:
3
Step-by-step explanation:
HELP PLEASE HARDEST QUESTION IN THE WORLD :(
MICKEY AND MINNIE ARE EXPECTING.
THEY ARE A VERY HAPPY COUPLE.
THE DOCTOR SAID THEY ARE HAVING 5 BOYS AND 5 GIRLS.
MICKEY AND MINNIE ARE RATS.
EVERY THREE WEEKS AN ADULT RAT COUPLE CAN HAVE BABIES.
IT TAKES 6 WEEKS FOR A BABY RAT TO BECOME AN ADULT
AND BE OLD ENOUGH TO HAVE A BABY.
ASSUMING MICKEY AND MINNIE WANT TO HAVE AS MANY CHILDREN AS POSSIBLE AND THEIR OFFSPRING WANT TO HAVE AS MANY CHILDREN AS POSSIBLE,
WHAT WILL BE THEIR ENTIRE POPULATION IN ONE YEAR? (52 WEEKS)
(INCLUDING MICKEY AND MINNIE)
(ASSUME EVERY PREGNACY WILL CONSIST OF 5 BOYS AND 5 GIRLS)
Answer: 6, 570
Step by step explanation: If Minnie and Mickey have 5 girls and 5 boys every 3 weeks for 52 weeks this means they will have 17 pregnancies. At the end of one year Minnie and Mickey alone will have produced 170 children. It takes these children 6 weeks to grow up and be ready to reproduce. Every 6 weeks 10 new rats will be able to have children at a rate of 10 per 3 weeks. This means that a single set of 10 offspring will have 100 children every 3 weeks. There will be 8 sets of offspring that can reproduce before the year is over. This means if the sets have 100 children every 3 weeks starting with one set and adding one more set every 6 weeks, at the end of the year the offspring's offspring will total 6,400. 6,400 + 170 will equal 6,570. The total population is 6,570.
8x raise 2 -36 is a linear expression true or false
Answer:
False. [tex]8x^2-36[/tex] is not a Linear expression.
Step-by-step explanation:
Given: [tex]8x^2-36[/tex]
we need to find whether it is a linear expression or not.
By Definition of Linear expression we say,
Linear expression is an algebraic expression where the power of variable(s) is equals to 1
Or we can say that:
Polynomial having power of variable(s) as 1, is known as Linear Expression
In the above expression the power of variable is 2 hence it is not a linear expression.
Hence the statement is False, the [tex]8x^2-36[/tex] is not a Linear expression.
The area of a rectangle is 99 ft^2, and the length of the rectangle is 7 more than double the width. Find the dimensions of the rectangle.
Answer:
width =5.5ft
length =18
Step-by-step explanation:
w=x
L=2x+7
area=w*L
99 = x(2x+7)
[tex]99=2x^{2} +7x[/tex]
[tex]2x^{2} +7x-99=0[/tex]
[tex]2x^{2} +18x-11x-99=0[/tex]
2x(x+9)-11(x+9)=0
(2x-11)(x+9)=0
2x-11=0
2x=11
x=11/2
x=5.5
L=2x+7=2*5.5+7=11+7=18
Please help!!
Write an exponential function (in terms of x) to model the following situation.
A population of 110,000 grows 5% per year for 16 years.
How much will the popluation be after 16 years?
Answer:
The population will be 240,116
Step-by-step explanation:
Exponential growth can be represented by the expression:
[tex]P(t) = P_i\,(1+r)^t[/tex]
where:
[tex]P(t)[/tex] is the population at time (t)
[tex]P_i[/tex] is the initial value of the population
"r" is the annual rate of growth (written in decimal form)
and "t" is the time in years.
Therefore in this situation, P(16) is what we want to find [the population after 16 years]
the initial population [tex]P_i[/tex] is 110,000
the rate of growth is 0.05 [decimal form of 5%]
and t is 16 years.
Replacing all these in the given functional form gives:
[tex]P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116[/tex]
An exponential function to model a population of 110,000 that grows at 5% per year for 16 years is P(t) = 110,000 ∙ (1.05)^t. After 16 years, using this exponential function, the population would be approximately 242,884.
Explanation:To model the population growth using an exponential function, we can use the formula P(t) = P0 ∙ (1 + r)t, where P(t) is the population after t years, P0 is the initial population, r is the growth rate, and t is the time in years. In this case, the initial population P0 is 110,000, the growth rate r is 5% (or 0.05), and the time t is 16 years.
The exponential growth function would be:
P(16) = 110,000 ∙ (1 + 0.05)16
To find the projected population after 16 years, we'll calculate:
P(16) = 110,000 ∙ (1.05)16
P(16) = 110,000 ∙ 2.20804
P(16) = 242,884.4
After rounding, the population would be approximately 242,884 after 16 years.
Please help me idk howwwwww
Answer:
OPTION B: y = [tex]$ \frac{1}{2} $[/tex]x - 2
Step-by-step explanation:
To find the equation of the line substitute the value of x and compare the corresponding value of y.
OPTION A:
y = 2x + 4
Substitute x = 0. We get, 2(0) + 4 = 4
When x = 0, y = -2 [tex]$ \ne $[/tex] 4.
OPTION B:
y = [tex]$ \frac{1}{2} $[/tex]x - 2
Substitute x = 0, we get [tex]$ \frac{1}{2} (0) - 2$[/tex]
= -2
When x = 2, [tex]$ \frac{1}{2}(2) - 2 $[/tex] = 1 - 2
=-1
Similarly, When x = 4, [tex]$ \frac{1}{2}(4) - 2 = 2 - 2 $[/tex]
= 0.
Since, all the values are satisfied, OPTION B is the answer.
Substitute OPTION C and OPTION D. They do not satisfy the values either.
How much dollars is 100,000 nickels
Answer:
$5000
Step-by-step explanation:
A nickel is worth 5 cents, or 0.05 dollars.
Multiply the number of nickels by the worth of a nickel in dollars.
100,000 * $0.05
= $5000
Therefore, 100,000 nickels is worth $5000.
Answer:
THE ANSWER IS $5000
Step-by-step explanation:
A NICKLE IS WORTH 5 CENTS, OR $0.05. SO YOU MULTIPLY THE 100,000 BY THE WORTH OF NICKLES IN A DOLLAR. SO YOU DO 100,000 X 0.05= $5000. SO 100,000 NICKLES IS WORTH $5000.
Which of these sets could represent the side lengths of a right triangle?
Group of answer choices
{4, 8, 12}
{6, 8, 10}
{6, 8, 15}
{5, 7, 13}
Answer:
{6, 8, 10} is a set which represents the side length of a right triangle.
Step-by-step explanation:
In a right triangle:
[tex](Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}[/tex]
Now, in the given triplets:
(a) {4, 8, 12}
Here, [tex](4)^{2} + (8)^{2} = 16 + 64 = 80\\\implies H = \sqrt{80} = 8.94[/tex]
So, third side of the triangle 8.94 ≠ 12
Hence, {4, 8, 12} is NOT a triplet.
(b) {6, 8, 10}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10
Hence, {6, 8, 10} is a triplet.
(c) {6, 8, 15}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10 ≠ 15
Hence, {6, 8, 15} is NOT a triplet.
(d) {5, 7, 13}
Here, [tex](5)^{2} + (7)^{2} = 25 + 49 = 74\\\implies H = \sqrt{74} = 8.60[/tex]
So, third side of the triangle 8.60 ≠ 13
Hence, {5, 7, 13} is NOT a triplet.
what is the median,lower quartile,maximum,upper quartile,and the minimum of 34, 37, 39, 32, 48, 45, 53, 62, 58, 61, 60, 41
Answer:
Median = 46.5
Minimum = 32
Maximum = 62
Lower quartile = 38
Upper quartile = 59
Step-by-step explanation:
Before we can proceed to solving any of these, it is best you arrange your data first from least to greatest
32 34 37 39 41 45 48 53 58 60 61 62
First we have the median. The Median is the middle value. In this case we an even number of data, which is 12 data points. The middle value of the data would be found in between the 6th and 7th data point:
45 and 48
To get the middle value, you need to solve for the value that is in the middle of 45 and 48 by getting the sum of both numbers and dividing it by two.
45 + 48 = 93
93 ÷ 2 = 46.5
The minimum and maximum value is merely the least and greatest number.
Here we have:
Minimum = 32
Maximum = 62
To get the lower and upper quartiles, just remember that quartiles divide the data into 4 equal parts. All you need to do is find the value that is in between each quarters of the data:
Q1 (Lower) Q2(Median) Q3(Upper)
32 34 37 | 39 41 45 | 48 53 58 | 60 61 62
Like the median, we will find the value that comes in between each quarter.
Q1
37 + 39 = 76
76 ÷ 2 = 38
Lower quartile = 38
Q3:
58 + 60 = 118
118 ÷ 2 = 59
Upper quartile = 59
Answer:
the person on top has it right ^^^^^^^^^^ did the work and it right thx :))
The ratio of incomes of two persons is 9:7. The difference in their weekly incomes is $200. What are their weekly incomes?
What’s the answer
Answer:
The weekly savings of first person = $900
The weekly savings of second person = $700.
Step-by-step explanation:
Let us assume the income of first person = $ m
Now, as the difference in the income is $200.
⇒ And the income of first person - income of first person = $200
⇒ Income of second person = m - $200
So, according to the question:
Ratio of Income of First person : Second Person's Income = 9: 7
or, m : ( m - 200) = 9: 7
[tex]\implies \frac{m}{m - 200 } = \frac{9}{7}[/tex]
[tex]7 \times m = (m - 200) \times 9\\\implies 7 m = 9m - 1800\\\implies 7m - 9m = -1800\\\implies -2m = -1800\\m = \frac{1800}{2} = 900[/tex]
or,m = $900
Hence, the weekly savings of first person = $900
and the weekly savings of second person = m - 200 = $900 - 200 = $700.
Final answer:
To find the weekly incomes of two persons with a ratio of 9:7 and a difference of $200, represent their incomes as 9x and 7x. Solving for x, we get $100, so their incomes are $900 and $700 respectively.
Explanation:
The question asks us to solve for the weekly incomes of two persons given that the ratio of their incomes is 9:7 and the difference between their incomes is $200.
Let's represent the incomes of the two persons as 9x and 7x respectively, where x is a common multiplier. According to the information provided,
9x - 7x = $200
Solving for x:
(9x - 7x) = 2x
2x = $200
x = $200 / 2
x = $100
Now calculating each person's income:
Person A: 9x = 9 * $100 = $900
Person B: 7x = 7 * $100 = $700
Therefore, the weekly incomes of the two persons are $900 and $700 respectively.
[20 pts] evaluate the logarithm log(6)1/36, show work pls!
Answer:
[tex]\large\boxed{\log_6\dfrac{1}{36}=-2}[/tex]
Step-by-step explanation:
[tex]\text{We know:}\\\\\log_ab=c\iff a^c=b\\\\\log_6\dfrac{1}{36}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_636^{-1}=\log_6(6^2)^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\log_66^{(2)(-1)}=\log_66^{-2}\qquad\text{use}\log_ab^n=n\log_ab\\\\=-2\log_66\qquad\text{use}\ \log_aa=1\\\\=-2(1)=-2[/tex]
[tex]\log_6\dfrac{1}{36}=-2\ \text{because}\ 6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}[/tex]
The solution of logarithmic function is, - 2
We have to given that,
Logarithmic function is,
⇒ log ₆ (1/36)
Now, We can apply the logarithmic rule to solve as,
⇒ log ₆ (1/36)
⇒ log ₆ (36)⁻¹
⇒ log ₆ (6)⁻²
⇒ - 2 log ₆ (6)
⇒ - 2 × 1
⇒ - 2
Therefore, The solution of logarithmic function is, - 2
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17 more than twice Gail’s age
Answer:
34
Step-by-step explanation:
i just know t hat this is th answer
I NEED HELLPPPP!!!!!!
Find (3 × 104) − (5 × 102).
A) 2.905 × 102
B) 2.905 × 104
C) 2.95 × 102
D) 2.95 × 104
Answer:
-198
Step-by-step explanation:
you will deal with the ones in the bracket first
that is [3×104]=312
[5×102]=510
312-510=-198
according to me there is no answer in your option my answer is negative198
If 4x=18, what is the value of 4(X-2)?
Answer:16
Step-by-step explanation:
If 4x=18 then 4x-2=16
Tj had 20 baseballs pitched to him he hit the ball 17 times what percentage of balls pitched did Tj hit?
Tj hit 85% of the balls pitched to him.
Step-by-step explanation:
Baseballs pitched to Tj = 20
Baseballs hit by Tj = 17
Percentage = [tex]\frac{baseballs\ hit\ by\ Tj}{baseballs\ pitched\ to\ Tj}*100\\[/tex]
Percentage= [tex]\frac{17}{20}*100[/tex]
Percentage=[tex]\frac{1700}{20} = 85\%\\[/tex]
Tj hit 85% of the balls pitched to him.
Keywords: percentage, division
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Plz Help Me!
cross multiplying write the proportion:
2/310,5/c
m/3,32/4
Answer:
Step-by-step explanation:
2/310=5/c
simplify 2/310 into 1/155
1/155=5/c
cross product
155*5=1*c
775=c
c=775
---------------------------------
m/3=32/4
simplify 32/4 into 8,
m/3=8,
m=8*3=24
m=24
2 + 1.25f = 10 - 2.75f
Answer:
f=2
Step-by-step explanation:
1.25f+2.75f= 10-2
You must take positive two to the other side to get negative 2. Also, you should take the negative 2.75f to the other side to get positive 2.75f.
4f= 8
f= 2
Answer:
f=2
Step-by-step explanation:
Triangle ABC has side lengths: V6, V2, and 2/2 units.
The measures of the angles of the triangle are
If the base of the triangle has a length of 16 then the measure of the base angle is
Answer:
90°, 60°, and 30°
60°.
Step-by-step explanation:
The triangle ABC has side lengths √6, √2, and 2√2 units.
It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.
Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is [tex]\theta[/tex], then
[tex]\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} } = \frac{1}{2}[/tex]
Hence, [tex]\theta[/tex] = 60°
Therefore, the three angles of the triangle are 90°, 60°, and 30°.
Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.
And in that case the base angle will remain 60°. (Answer)
Brenda considers geometric figures and concepts that are related to lines. Which terms are considered undefined?
Check all that apply.
line
line segment
distance along a line
O parallel lines
perpendicular lines
point
Answer:
A, C, F
Step-by-step explanation:
Answer:
1,3&6
Step-by-step explanation:
line
distance along a line
point
LOTS OF POINTS
The lengths of the sides of a triangle are in the extended ratio 8 : 9 : 10. The perimeter of the triangle is 81 cm. What are the lengths of the sides?
The lengths of the sides are 24cm, 27cm and 30cm.
Step-by-step explanation:
The ratio of lengths is 8:9:10
Perimeter = 81 cm
Let x be the length of side.
Therefore,
The length of sides is 8x, 9x and 10x.
Perimeter is the sum of 3 sides, therefore,
[tex]8x+9x+10x=81\\27x=81[/tex]
Dividing both sides by 27;
[tex]\frac{27x}{27}=\frac{81}{27}\\x=3[/tex]
Therefore, the lengths of sides are [tex]8(3), 9(3)\ and\ 10(3)[/tex]
The lengths of the sides are 24cm, 27cm and 30cm.
Keywords: triangles, perimeter
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The lengths of the sides of the triangle are 24 cm, 27 cm, and 30 cm.
Explanation:To find the lengths of the sides of the triangle, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter. Let's assume the common ratio between the sides is 'x'. So, the lengths of the sides can be written as 8x, 9x, and 10x. According to the problem, the perimeter of the triangle is 81 cm.
Therefore, 8x + 9x + 10x = 81.
Combining like terms, we get 27x = 81.
Dividing both sides by 27, we find that x = 3.
Substituting this value back into the lengths of the sides, we find that the lengths are 8x = 8(3) = 24 cm, 9x = 9(3) = 27 cm, and 10x = 10(3) = 30 cm.
frome 12 to 16 in a month what is the percent of increase for that month round if needed
Answer:
33.33%
Step-by-step explanation:
The value of a variable change from 12 units to 16 units in a month.
We have to calculate the percentage increase for that month.
Therefore, the increase of value from 12 to 16 means by (16 - 12) = 4 units
So, the percentage increase for the month is [tex]\frac{4}{12} \times 100 = 33.33[/tex]%. (Rounded to the two decimal). (Answer)
what is the radical form?
Answer:
B
Step-by-step explanation:
Using the rules of exponents
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex]t^{-\frac{2}{7} }[/tex]
= [tex]\frac{1}{t^{\frac{2}{7} } }[/tex]
= [tex]\frac{1}{\sqrt[7]{t^{2} } }[/tex]
Ashby ate a lot for thanksgiving dinner.he decided to go on a long run. He ran 6 miles in 57 minutes.how long did it take him to run one mile?
Answer: 9.5
Step-by-step explanation: 57 divided by 6 is 9.5
Solve this please and list your steps
Answer:
√125 + 5 or 16.180
Step-by-step explanation:
√5 · 5 · 5 + √5 · 5
√25 · 5 + √25
√125 + 5 or 16.18
Ben starts commision as a real estate agent last month his total sales for all the houses he sold $950,000.If ben earns a 3% rate of commision what was his gross income kast month
Ben's gross income was $28,500.
Step-by-step explanation:
Sales for the month = $950000
Commission rate = 3%
Amount of commission = 3% of sales for the month
Amount of commission = [tex]\frac{3}{100}*950000[/tex]
Amount of commission = [tex]\frac{2850000}{100}[/tex]
Amount of commission = $28500
Ben's gross income was $28,500.
Keywords: percentage, division
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The surface area of this rectangular prism is __ square centimeters.
Answer:
216 sq. cm.
Step-by-step explanation:
If we fold the paper of the given dimensions then we will get a rectangular prism with dimension 10 cm by 6 cm by 3 cm.
Now, a rectangular prism has the total surface area given by
A = 2(LW + WH + HL)
where, L = length = 10 cm.
W = width = 6 cm. and
H = height = 3 cm.
Therefore, total surface area = A = 2(10 × 6 + 6 × 3 + 3 × 10) = 216 sq. cm. (Answer)
Answer:
216 sq. cm.
Step-by-step explanation:
Nancy Gardener is making dresses for her granddaughters. For each dress she will
need between three and four yards of fabric. The fabric she is using costs $4.34
per yard after sales tax is added. If she has four granddaughters, about how much
should she expect to spend at the fabric store?
A- $72 to $96
B- more than $96
C- $48 to $72
D- $24 to $48
Answer:
the answer is c
Step-by-step explanation:
The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y.
y = StartFraction 3 x 10 Superscript 8 Baseline Over x EndFraction
What are the wavelengths for X-rays with frequency 3 × 1018?
1 × 10–10 m
3 × 10–10 m
3 × 1026 m
9 × 1026 m
Answer: The wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]
Step-by-step explanation:
To calculate the wavelength of light, we use the equation:
[tex]\lambda=\frac{c}{\nu}[/tex]
where,
[tex]\lambda[/tex] = wavelength of the light
c = speed of light = [tex]3\times 10^8m/s[/tex]
[tex]\nu[/tex] = frequency of light = [tex]3\times 10^{18}s^{-1}[/tex]
Putting the values in above equation, we get:
[tex]\lambda=\frac{3\times 10^8m/s}{3\times 10^{19}s^{-1}}=1\times 10^{-10}m[/tex]
Hence, the wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]
Answer:
1 x 10 ^-10 m
Step-by-step explanation: