Answer:
926.35
Step-by-step explanation:
first find 9.5% x $845.98
=$80.37
then add $845.98 to $80.37
= $926.35
Suppose that $3^a = 2$ and $3^b = 5$. If \[3^x = 150,\]then write an expression for $x$ in terms of $a$ and $b$.
Use logarithms to solve for a.
[tex]3^a = 2 \implies \log_3(3^a) = a\log_3(3) = \log_3(2) \implies a = \log_3(2)[/tex]
Similarly, for b and x.
[tex]3^b = 5 \implies b = \log_3(5)[/tex]
[tex]3^x = 150 \implies x = \log_3(150)[/tex]
Factorize 150:
150 = 2 • 3 • 5²
Then we can expand log₃(150) using the product-to-sum and exponent property,
[tex]\log_3(150) = \log_3(2\times3\times5^2) = \log_3(2) + \log_3(3) + \log_3(5^2)[/tex]
[tex]\implies \log_3(15) = \log_3(2) + 1 + 2 \log_3(5) \iff \boxed{x = 1 + a + 2b}[/tex]
jessica spent 20% of her money for snacks. She spent 25% of the remainder for school supplies. She has P30 left. How much money did Jessica start with?
Which expression is equivalent to (2x^4y)^3?
Answer:
8x^{12}yx^{3}
Step-by-step explanation:
Simplify the expression.
Hopefully this helps you
- Matthew
5 Four children are measuring their height.
Aisha
1.39 metres
Teddy
1.37 metres
Scott
1.4 metres
Kim
1.43 metres
Order the children from tallest to shortest.
Find the length of the arc.
120°
6ft
Answer:
The length of the arc is 8*pi cm. An arc that subtends a central angle of 120 degrees has a length of 120/360 = 1/3 the length of the total circumference of the circle. We know the entire circumference of the circle is 2πr, which in this case is 2π*12 = 24π.
Step-by-step explanation:
sorry I only have the 8
The length of a rectangle is five more than double the width. If the perimeter is 100 inches, find the dimensions.
width?
length?
Write a propotion that can be used to convert 50 meters into kilometers. Then solve
Answer:
0.05km
Step-by-step explanation:
There are 1000 meters in a single kilometer. Using some dimensional analysis, we get set up the following expression:
[tex]\frac{50}{1} \frac{meters}{1}\frac{1}{1000} \frac{kilometers}{meters}[/tex]
The meters will cancel leaving the units of kilometers:
[tex]\frac{50}{1000} km=0.05km[/tex]
Suppose 3 and 8 are the only individual scores that can be made in a certain game. How many integer total scores are impossible to obtain?
Answer: 3
Step-by-step explanation:
3x8 = 24
24x2= 48!
8x12= 96!
Answers must be divisible by both numbers, and achievable by both inputs.
Hope This Helped
Pleas I need help this is so hard
Answer:
Equation:
C = 1.75x + 5 25
A 22-mile ride costs $43.75.
Step-by-step explanation:
Because there is a flat fee of 5.25, only the first two equations could possibly be correct.
Then check with the examples given. If a 7 mile ride costs 17.50, the second equation cannot possibly be right. 7 miles times over $5 per mile will cost more than $35 not even including the flat fee.
Check:
1.75(7) + 5.25 = 17.50
and
12(1.75) + 5.25 = 26.25
So, the correct equation is
C = 1.75x + 5.25
Next use this equation to find the cost of the 22 mile ride.
1.75(22) + 5.25
= 43.75
Enrique estimates that his utilities will cost him $86.00 per month over the courses of the next 3 years. What is his total estimated cost for utilities over the next 3 year period??
Please help thank you !!!
Answer:
$3096
Step-by-step explanation:
There are 12 months in 1 year.
3 × 12 = 36
There are 36 months in 3 years.
$86 × 36 = $3096
Answer:
3096
Step-by-step explanation:
I just completed the quiz.
A candle's height, in inches, is a function of the number of hours it has been burning. After 4 hours the
candle's height is 10 inches, and after 16 hours the candle's height is 7 inches. The candle is burning at
constant rate.
Construct an equation that can be used to determine the candle's height, y, after x hours.
Enter your equation in the space provided. Enter only your equation.
The linear function that gives the candle's height, y, after x hours, is defined by:
y = -0.25x + 11.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, in 12 hours, the height decayed 3 inches, hence the slope is given by:
m = -3/12 = -0.25.
So:
y = -0.25x + b.
After 4 hours, the height was of 10 inches, hence we use this to find b:
10 = -0.25(4) + b
b = 11
Thus the equation is given by:
y = -0.25x + 11.
More can be learned about linear functions at https://brainly.com/question/24808124
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A sweater is marked 30% off the original price. The original price was $37.50. What is the sale price of the sweater before sales tax?
(I will give brainliest if you show your work)!!
Answer:
$26.25
Step-by-step explanation:
To find the discounted price, subtract the discount amount from the original price. The amount of the discount is the product of the discount rate and the original price.
__
discounted price = original price - (original price) × (discount rate)
You can calculate it this way, or you can factor out the original price:
discounted price = (origina price) × (1 - discount rate)
= $37.50 × (1 -0.30) = $37.50 × 0.70 = $26.25
The sale price of the sweater is $26.25.
__
Additional comment
The amount of the discount is ...
$37.50 × 0.30 = $11.25
which makes the discounted price be ...
$37.50 -11.25 = $26.25
If 43,560 square feet equals one acre, how many acres are in one square mile?
Answer: 640
Step-by-step explanation:
How many acres are there in 1 square mile? There are 640 acres in 1 square mile. To convert from square miles to acres, multiply your figure by 640 (or divide by 0.0015625) .
Answer:
640 acres²
Divide the area value by 68
[tex]43,560 / 68 = 640[/tex]
or
[tex]1~mile^2 * 640 = 640[/tex]
you multiply the area value by 640 for each square mile, since there is only one square mile, the answer is 640
Rapunzal travels 27 miles per hour. How long does it take her to travel 3 miles. Nearest tenth
Answer:
6.4 minutes or 384 seconds
Which two values of x are roots of the polynomial below?
x^2 + 5x + 7
A. x = 5
B. x = -5-√-3 /2
C. x = -5+√-3 /2
D. x = 1/2
E. x = 5+√17 /2
F. x = 5-√17 /2
Answer:
B. and C.
Step-by-step explanation:
1. Set the polynomial equal to zero:
x² + 5x + 7 = 0
2. Plug the given values of a, b, and c into the quadratic formula:
[tex]x=\frac{-5+-\sqrt{5^{2}-4(1)(7) } }{2(1)}[/tex]
3. Solve the square root:
[tex]x=\frac{-5+-\sqrt{25-4(1)(7)} }{2(1)}[/tex]
[tex]x=\frac{-5+-\sqrt{25-28} }{2(1)}[/tex]
[tex]x=\frac{-5+-\sqrt{-3} }{2(1)}[/tex]
4. Simplify the rest:
[tex]x=\frac{-5+-\sqrt{-3} }{2}[/tex]
5. Separate the solutions:
[tex]x=\frac{-5+\sqrt{-3} }{2} , x=\frac{-5-\sqrt{-3} }{2}[/tex]
Thus, options B and C are the answers.
hope this helps!
please answer correctly don't answer a link thanks. FUNDAMENTAL PRINCIPLE OF COUNTING.
The answer is [tex] {2}^{5} [/tex] or 32.
The best way to represent this is with a binary tree. Each split represents a choice, and each line represents a possible outcome. Choice #1 at the top of the tree has 2 possible outcomes. The second level repeats that process with 2 possible choices and 4 possible outcomes, this repeats for all 5 levels giving us 32 possible outcomes at the bottom.
2)There will be eight outcomes.
Sample space : {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
Find the length of the third side . If necessary , round to the nearest tenth .
Answer:
umm 9?
Step-by-step explanation:
Amari pays $7,440 in taxes on his income of $46,500. What percentage of his income is going toward taxes???
Thank you so much!
Answer:
16 percent
Step-by-step explanation: 16 percent of 46500 is 7440
Find the area of the shaded shape. Write the area in square units
Answer:
Area = 224 square yards
Step-by-step explanation:
Width = 3.5 squares
Length = 4 squares
Multiply to yards (x4)
Width = 14 square yards
Length = 16 square yards
Area = Width*Length
Area = 14 * 16
Area = 224 square yards
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
17.51
Step-by-step explanation:
this is a right triangle, so sohcahtoa applies
we want x
relative to the angle, x is opposite of it and 25 is adjacent to it (the hypotenuse is the other side)
the formula that combines opposite and adjacent is tan
tanθ = opposite/adjacent
tan(35°) = x/25
multiply both sides by 25 to isolate x
tan(35°) * 25 = x
x ≈ 17.51
The grades on a language midterm at Loyola are roughly symmetric with u = 69 and standard deviation = 4.0. Vanessa Scored 65 on the exam.
Answer:
the question can be understand but the question is not telling what to find
it is comfugen to answe're the question
Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS! im not getting myself a virus
Answer:
r = 50 degrees.
Step-by-step explanation:
r = 50 degrees ( vertical angles are congruent).
Sheila is 1.7 m tall her son is 109 cm tall how many meters taller is Sheila than her son
Answer:
61 cm or 0.61 m
Step-by-step explanation:
1. One meter is 100 cm, so you multiply 1.7 meters by 100 to get 170 cm.
2. Now that they are in the same units, to get their difference in height, you subtract Sheila's height from her son's (170 - 109) and get 61 cm.
3. Convert it back to meters by dividing by 100 and you get their difference in height in meters, 0.61 m.
Answer:
0.61
Step-by-step explanation:
One cenimeter is equivalent to 0.01 meter.
109cm • 0.01 = 1.09m
1.7m - 1.09m = 0.61m
Sheila is 0.61m taller than her son
solve the given equation state the number and type of roots x^2+x-12=0
Answer:
Step-by-step explanation:
x 1= 3 x 2=−4
Find an equation for the graph
Answer:
y=6^x+0.612 - 4
Step-by-step explanation:
x = -4 ---> horizontal asymptote
m = 6 ---> use points (0, -1) and (1, 5)
Parent function of the graph: [tex]y=b^x[/tex]
Our equation: [tex]y=6^x[/tex]
Add alterations:
Reflections = N/AVertical & horizontal shifts = down 4Vertical & horizontal stretches = left approx 0.612Final equation: y=6^x+0.612 - 4
what did the sewer workers boss say to him when he went on vacation?
Answer:
Have a great tret
Step-by-step explanation:
I dont know what
is it
Regan operates an orange juice stand. On Monday she used 1/3 of a bag of oranges. On
Tuesday she used 2/5 as many oranges as on Monday. How many bags of oranges did Reg
use on Tuesday?
Write your answer as a fraction or as a whole or mixed number.
Please help meee
Answer:
0.825 bags of oranges
Step-by-step explanation:
1/3 is 0.33 and 2/5 is 0.4 so 0.33/0.4 is 0.825
Mary spends 2 2/3 hours on math homework everyday. She also spends 3 1/3 hours on art homework. How much time does Mary spend in total working on math and art homework?
It has to be like an actual fraction. All I know is that 24 is the whole number. Use that to solve the problem.
Answer:
6 hours
Step-by-step explanation:
2 2/3 +3 1/3= 5+1=6
Answer:
2 2/3+ 3 1/3 = 6. Multiply 6 by 4 weeks. 24 as your whole number.
Step-by-step explanation:
hope this helps
Set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-
Jordan elimination.
Sylvia invested a total of $27,000. She invested part of the money in a certificate of deposit (CD) that earns 3% simple
interest per year. She invested in a stock that returns the equivalent of 7% simple interest, and she invested in a bond fund
that returns 2%. She invested three times as much in the stock as she did in the CD, and earned a total of $1140 at the
end of 1 yr. How much principal did she put in each investment?
She invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.
DistributionsGiven that Sylvia invested a total of $27,000, and she invested part of the money in a certificate of deposit (CD) that earns 3% simple interest per year, she invested in a stock that returns the equivalent of 7% simple interest, and she invested in a bond fund that returns 2%, and she invested three times as much in the stock as she did in the CD, and earned a total of $1140 at the end of 1 yr, to determine how much principal did she put in each investment, the following calculation must be made:
9000 x 0.07 + 3000 x 0.03 + 15000 x 0.02 = 630 + 90 + 300 = 10209900 x 0.07 + 3300 x 0.03 + 13800 x 0.02 = 693 + 99 + 276 = 106812,000 x 0.07 + 4,000 x 0.03 + 11,000 x 0.02 = 840 + 120 + 220 = 1,18011400 x 0.07 + 3800 x 0.03 + 11800 x 0.02 = 798 + 114 + 236 = 114810800 x 0.07 + 3600 x 0.03 + 12600 x 0.02 = 756 + 108 + 252 = 111611160 x 0.07 + 3720 x 0.03 + 12120 x 0.02 = 781.2 + 111.6 + 242.4 = 1135.211190 x 0.07 + 3730 x 0.03 + 12080 x 0.02 = 783.3 + 111.9 + 241.6 = 1136.811250 x 0.07 + 3750 x 0.03 + 12000 x 0.02 = 787.5 + 112.5 + 240 = 1140Therefore, she invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.
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The sum of the two numbers is 40. One number is 3 times the other number. Find the 2 numbers
Answer:
10 and 30
Step-by-step explanation:
The sum of 10 and 30 is 40.
30 is three times ten (10 x 3 = 30).
hope this helps!
The answer is 10 and 30
10 times 3 is 30, meaning 10 will be the number times 3 they wanted. 10 + 30 is 40, therefore the answer is 10 and 30