Answer:
A) $1470
B) 5,88%
Step-by-step explanation:
B) Diana will end up with 100% -16% = 84% of the interest she earns, so her effective interest rate is ...
... 7% × 84% = 5.88%
A) Diana's investment earns ...
... 0.0588 × $25000 = $1470
After paying a 16% tax on the interest, Diana will earn $1,470 in interest. This represents 5.88% of her original $25,000 investment.
Diana invests $25,000 in a bank at 7% interest, which she will receive at the end of the year. However, she must pay taxes at a rate of 16% on the interest earned.
First, we calculate the total interest Diana would earn without taxes:
Total Interest = Principal imes Interest Rate
Total Interest = $25,000 imes 0.07 = $1,750.
Next, we calculate the tax on the interest:
Tax on Interest = Interest Earned imes Tax Rate
Tax on Interest = $1,750 imes 0.16 = $280.
Now, we subtract the tax from the total interest to find the interest after taxes:
Interest After Taxes = Total Interest - Tax on Interest
Interest After Taxes = $1,750 - $280 = $1,470.
We find the percentage of the original investment that the interest after taxes represents:
Percent of Investment = (Interest After Taxes / Principal) imes 100
Percent of Investment = ($1,470 / $25,000) imes 100 = 5.88%.
Solve the equation for the variable. Show each step of your solution process.
Answer:
x = 12
Step-by-step explanation:
√(x + 4) - 3 = 1 Add 3 to each side
√(x + 4) = 4 Square each side
x + 4 = 16 Subtract 4 from each side
x = 12
=====
Check:
√(12 + 4) – 3 = 1
√16 – 3 = 1
4 – 3 = 1
1 = 1
Answer:
Step-by-step explanation:
We have equation
[tex]\sqrt{x+4} -3=1[/tex]
to solve for x we first add 3 to both side
[tex]\sqrt{x+4}-3+3=1+3\\\sqrt{x+4} =4[/tex]
now we need to remove square root from left side, so we square both sides
[tex]x+4=4^{2}[/tex]
[tex]x+4=16[/tex]
now we subtract 4 from both sides
[tex]x+4-4=16-4\\x=12[/tex]
Determine the slope of the line that is perpendicular to the line y = -7x - 12.
Select one:
A. 17
B. −3
C. −7
D. −12
A. 1/7
Step-by-step explanation:The slope of the given line is the coefficient of x, -7. The slope of a perpendicular line will be the opposite reciprocal of that:
... -1/(-7) = 1/7 . . . . . seems to match selection A
_____
Comment on the answer choices
We assume this question suffers from a problem seen often on Brainly where questions and/or answers are copied and pasted without any follow-up editing to make sure the copy is faithful. Often, math symbols are special characters that get filtered out in the process.
The fraction bar commonly comes up missing. Here, that makes 1/7 look like 17, which makes the correct answer look like "none of the above."
Geo usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day. If he starts drinking 64 ounces, what is the percent increase? Round to the nearest percent.
78%
Step-by-step explanation:The percentage change is calculated from ...
... percent change = ((new amount) -(old amount))/(old amount) × 100%
... = (64 -36)/36 × 100%
... = 28/36 × 100%
... ≈ 0.78 × 100%
... ≈ 78%
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Try this option. Answer: 72+18π
Step-by-step explanation:
Formula is:
Area= 2*Area_of_two_squares + 1/2 *Area_of_the_circle, where
Area_of_1_square=6*6=36 cm²;
Area_of_the_circle=π*6²=36π cm²;
finally, according to the formula above Area=2*36+0.5*36π=72+18π
Answer:
Step-by-step explanation:
72+18pi
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than a certain number of inches.
Sketch and label the sides of this rectangle. Use an algebraic expression to represent the length of the long sides.
Let x be the certain number of inches mentioned in the problem. So, three less than this quantity is [tex] x-3 [/tex]
This means that you have to sketch a rectangle labelling the short side with 2, and the long sides with [tex] x-3 [/tex]
Can someone pls help me. Find the illegal values of c in the multiplication statement.
Answer:
c ∈ {-7, -3, 2, 5}
Step-by-step explanation:
"Illegal" values are those values that make the expression undefined—that is, they make the denominator zero.
The denominator of the product factors as (c+7)(c-2)(c-5)(c+3), so the values of c that will make this product zero are ones that make the factors zero:
... c = -7, +2, +5, -3
_____
Comment on factoring
Each of the quadratics is factored by finding two factors of the constant whose sum is the coefficient of the linear term. You want ...
... factors of -14 = -1·14 = -2·7 . . . . that add to give +5. They are -2 and 7, so the quadratic factors as (c-2)(c+7)
... factors of -15 = 1·(-15) = 3·(-5) . . . . that add to give -2. They are 3 and -5, so the quadratic factors as (c+3)(c-5).
At the book store, a bag of chips sells for $2.30 each and candy sells for 1.23 each. You have $23 to spend. Write an equation to describe this situation. What does the y represent? What does the x represent?
Answer:
2.3x + 1.23y = 23
Step-by-step explanation:
The bag of chips is x because it is getting multiplied by 2.3.
The candy is y because it is getting multiplied by 1.23.
The reason they equal 23 is to figure out the maximum amount of each snack you can get without going over the money limit.
Drinking 7 fluid ounces of milk provides 236.25 milligrams of calcium. How many fluid ounce of milk are required tho prove 67.5 milligrams of calcium. Round to the nearest tenth
A.1.7 fluid ounces
B.2.0 fluid ounces
C.2.5 fluid ounces
D.2.3 fluid ounces
Answer:
Option B is correct.
2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the given statement: Drinking 7 fluid ounces of milk provides 236.25 milligrams of calcium.
Let x be the fluid ounce of milk.
then, by using proportion method we have;
[tex]\frac{7}{236.25} = \frac{x}{67.5}[/tex] ......[1]
Cross multiply states that an equation of fractions when each side consists of a fraction with a single denominator by multiplying the numerator of each side by the denominator of the other side and then, equating the two products obtained.
Apply cross multiply in [1];
[tex]7 \times 67.5 = 236.25 \times x[/tex]
Simplify:
[tex]472.5 = 236.25x[/tex]
Divide 236.25 we get;
[tex]x = \frac{472.5}{236.25}[/tex]
Simplify:
x = 2.0
therefore, 2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium
There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced by half every 4 hours. What will be the population in 24 hours
1,094 bacteria
Step-by-step explanation:There are 6 periods of 4 hours in 24 hours, so the population will be multiplied by 1/2 6 times. That is, it will be multiplied by (1/2)^6 = 1/64.
The population then will be ...
... 70,000/64 ≈ 1094
Factor completely −5x2 + 10x − 15. −5(x2 − 2x + 3) −1(x2 − 10x + 15) −5x(x2 − 2x + 3) −5(x2 − 2x − 3)
Answer:
-5(x² -2x +3)
Step-by-step explanation:
5 is a factor common to all of the coefficients. It is convenient to have the x² coefficient be positive in the factored form, so the result of factoring out -5 is ...
... -5((-5x²/-5) +(10x/-5) +(-15/-5)) = -5(x² -2x +3)
Answer:
-5(x² -2x +3) your welcome
Step-by-step explanation:
Cameron is going to the carnival. The price of admission to the carnival is $6.50, and each ride costs an additional 0.75 cents. If Cameron can spend at most $20.00 at the carnival, which inequality represents all the possible values of r rides Cameron can go on? A) 0.75 + 6.50r ≤ 20.00 B) 0.75 + 6.50r ≥ 20.00 C) 6.50 + 0.75r ≤ 20.00 D) 6.50 + 0.75r ≥ 20.00
r = the number of rides
0.75r + 6.50 ≤ 20.00
[They charge $0.75 per ride (r) plus an admission fee of $6.50, and he can spend at most (maximum) $20. This means that he can spend $20 or less]
Your answer is C
Answer:
Option C is the correct answer.
Step-by-step explanation:
The price of admission to the carnival is $6.50.
Cost per ride = 0.75
Money Cameron having = 20 $
Let the number of rides be r, he cannot spend more than 20 $
That is
6.50 + 0.75 r ≤ 20.00
Option C is the correct answer.
2. At Fly-Right Airlines, passengers are informed that checked bags must weigh 40 lb or less, or they will have to pay a fee for an oversized bag. (a) Write an inequality that represents the weight of a checked bag that will not result in a fee. Let w represent the weight of the bag. (b) Are there any solutions to the inequality that do not make sense for this situation? Explain.
Answer:
see below
Step-by-step explanation:
a) w <= 40 lbs
b) Do you have any bag that weigh 0 lbs or negative lbs?
We need to rewrite the inequality so that these are not there
0<= w <= 40 lbs
Help plzzzzz I don’t know this
Answer:
$6
Step-by-step explanation:
The graph shows you that 4 pounds of apples (and no cranberries) can be purchased for $24. Thus each pound costs ...
... $24/(4 pounds) = $6/pound
Donovan eats 2 granola bars and drinks 1 glass of orange juice for breakfast every day. The price of a granola bar is B dollars and the price of a glass of orange juice is J dollars. The expression 7(2B+J) describes how much Donovan spends on breakfast in one week. What does 2B represent in the expression?
Answer:
# of granola bars and it's cost.
Step-by-step explanation:
It is asking for the meaning of 2B. Note that inside the question, it states that:
"The price of a granola bar is B dollars".
It also states that:
"Donovan eats 2 granola bars".
This means that to solve for the total spent on granola bars, you multiply the price (B) with the amount gotten (2 in this case).
~
Answer:
2B
Step-by-step explanation:
Means the amount Donovan spends on granola bars each day. Since he has 2 granola bars and the price is B dollars.
HELP MEEEEEEEEEEE PLEASE!
Answer:
55,900 cm²
Step-by-step explanation:
The area of a triangle is half the product of its base and height.
... A = (1/2)·b·h
... = (1/2)(430 cm)(260 cm)
... = 55,900 cm²
Joshua solved this problem. He says the answer is 489 yards. Joshua had 359 yards of his fishing line in the water. Then he reeled in 113 yards of his line from the water. How much of Joshua’s fishing line was still in the water? Solve the problem. Is Joshua’s answer reasonable?
The correct answer to the subtraction problem is 246 yards of Joshua's fishing line remaining in the water after reeling in 113 yards out of 359 yards. Joshua's initial answer of 489 yards is incorrect.
The student is asking for verification of Joshua’s solution to a subtraction problem that involves determining how much fishing line remains in the water after some has been reeled in. Joshua initially had 359 yards of line in the water and reeled in 113 yards. To find the remaining length of the line in the water, we subtract the length of the line reeled in from the initial length.
Step-by-Step Explanation
Start with the initial length of the fishing line in the water: 359 yards.
Subtract the length of the line that was reeled in: 113 yards.
Perform the subtraction: 359 yards - 113 yards = 246 yards.
So, the length of the fishing line that remained in the water was 246 yards.
Joshua’s answer of 489 yards is not reasonable because it does not reflect the correct subtraction (359 - 113 = 246). The correct answer is 246 yards still in the water.
i need help plz plz plz help me. ASAP. and plz type your reasoning.
C = 2.00r +20
Step-by-step explanation:The coefficient is the multiplier of r, the cost of each ride. If it has gone down by $0.50, then its new value is ...
... 2.50 -0.50 = 2.00
The constant in the equation is the initial cost of the wristband. It is the value of C when r=0. If it has gone up by $5, its new value is ...
... 15 + 5 = 20
D 0,-2(x, y)(3, 5). The point (x, y) is: (1, 3) (-3/2, -5/2) (-6, -10)
Answer:
(-3/2, -5/2)
Step-by-step explanation:
When a point is dilated about the origin, each coordinate value is multiplied by the dilation factor. You seem to have ...
... -2x = 3 ⇒ x = -3/2
... -2y = 5 ⇒ y = -5/2
_____
In each case, you solve the linear equation by dividing by the coefficient of the variable.
Write an expression for
Answer: 6x - 18 (choice C)
Angle TSR is the same as angle RST. The order of the letters doesn't matter as long as the middle letter is the same (known as the vertex point).
Segment SQ bisects angle RST, so that means the two smaller pieces (angle TSQ and angle RSQ) are exactly half in measure compared to angle RST. Put another way, angle RST is twice that of angle RSQ
So,
angle RST = 2*(angle RSQ)
angle RST = 2*(3x - 9)
angle RST = 2*(3x) + 2*(-9)
angle RST = 6x - 18
Find a recursive formula for the sequence:
1, -1, -7, -25
[tex]a_n=3a_{n-1}-4[/tex]
Step-by-step explanation:Try the answers
You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.
a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works
b) -7 -2 = -9 . . . . ≠ -25
c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25
d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25
The formula that works is the first one.
_____
Derive it
All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...
[tex]a_n=p\cdot a_{n-1}+q[/tex]
Then, to get the second term from the first, we have
... 1·p +q = -1
And to get the third term from the second, we have
... -1·p +q = -7
Subtracting the second equation from the first gives ...
... 2p = 6
... p = 3 . . . . . . . this is sufficient to identify the first answer as correct
We can find q from the first equation.
... q = -1 -p = -1 -3 = -4
So, our recursion relation is ...
[tex]a_n=3a_{n-1}-4[/tex]
adult tickets to the fall play cost $8 and student tickets cost $4. The drama calss sold 20 more adult tickets than student tickets to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold?
Answer:
80 adult tickets were sold
Step-by-step explanation:
If you subtract the extra 20 adult tickets from ticket numbers and revenue, you get ...
equal numbers of $4 and $8 tickets were sold for a total of $720 collected
Since that is some number of ticket pairs worth $12 per pair, there must have been ...
$720/12 = 60 pairs of $4 and $8 tickets
The number of adult tickets is 20 more than this, so is
60 + 20 = 80 . . . . adult tickets sold
_____
If you feel better with an equation, rather than numerical reasoning, you can let n represent the number of adult tickets. Then n-20 is the number of student tickets and total revenue is ...
8n +4(n-20) = 880
12n -80 = 880 . . . . . simplify
12n = 960 . . . . . . . . . add 80
n = 80 . . . . . . . . . . . . divide by 12
_____
Comment on the different solutions
Using n for the number of adult tickets, we effectively chose a scenario where we added 20 student tickets to bring the total to $960 for some number of $12 pairs of tickets. That number is 80, the number of adult tickets.
In the "word solution" given at first, we effectively solved for the number of student tickets, then added 20 to get the number of adult tickets. The corresponding equation would be ...
4s +8(s+20) = 880 . . . s = number of student tickets sold
12s = 720 . . . . . . . . . subtract 160, the price of the 20 extra adult tickets
5x^6–3x^2+7–2x^6–3x^6+4x^2 for x=−10
Answer:
107
Step-by-step explanation:
These are easier to do if you simplify them first.
... = x^6(5 -2 -3) +x^2(-3 +4) +7
... = x^2 +7
For x = -10, this is
... (-10)^2 +7 = 100 +7 = 107
He daily milk production of guernsey cows is approximately normally distributed with a mean of 35 kg/day and a standard deviation of 6 kg/day. the producer is concerned when the mild production of a cow falls below the 5th percentile because the animal may be ill. the 5th percentile (in kg) of the daily milk production is approximatley:
Answer:
25.1 kg
Step-by-step explanation:
A suitable probability calculator can tell you the 5th percentile of this distribution.
In the figure, BCND is a rectangle and CGNR is a rhombus. The area of BCND is 90 and BC = 10. What is 3GR?
Answer:
[tex]3GR=27[/tex]
Step-by-step explanation:
Since area of rectangle BCND is given as 90 and one of its side is 10, the other side MUST be 9.
[tex]CN*BC=90\\CN*10=90\\CN=9[/tex]
In Rhombus CGNR, CN and GR are congruent (property of Rhombus). Hence GR = 9 as well.
Thus 3GR = 3(9) = 27
First answer choice is right.
Use the APR table in the Business Math Handbook to estimate the APR for the following installment purchase. You received a $2,000 rebate that brought the price of your car down to $20,000; the financing was for 48 months, and your total interest was $3,279.
7.65%
Step-by-step explanation:There are 200 times $100 in $20,000, so the interest amount per $100 is ...
... $3,279/200 = $16.395 per hundred
In the row of the given table corresponding to 48 months, the smallest amount of interest listed is $23.48 per $100. The APR on the loan of concern is clearly less than 10.75%.
A financial calculator says the interest rate on a loan of $20,000 with 48 monthly payments of ($20,000 +3,279)/48 = $484.98 is about 7.65%.
Someone please help I don’t understand
Answer:
D 2n+2
Step-by-step explanation:
We can check the slope of the function
m = (y2-y1)/(x2-x1)
= (10-8)/(4-3)
= 2/1
The slope is 2
We can use the point slope form of a line to calculate the equation for a line
y-y1 = m(x-x1)
y-2 = 2(x-2)
Distribute
y-6=2x-4
Add 6 to each side
y-6+6 = 2x-4+6
y = 2x+2
Brenda said that the number 2 is prime because it has only two factors. Carla said that the number 2 is composite because it is even, and all even numbers are composite. Who is correct? A) Brenda is correct. B) Carla is correct. C) Both of them are correct. D) Neither of them is correct.
Answer:
a) brenda is right
Step-by-step explanation:
five prime numbers: 2, 3, 5, 7 and 11. A prime number is an integer, or whole number, that has only two factors — 1 and itself
The table shows the total distance (d), in kilometers, a bicycle traveled after t hours.
Time in hours (t) Distance in kilometers (d)
(t) (d)
0 0
1 8
2 16
Which equation shows the relationship between d and t?
d=8t
d=16t
d=t+8
d=t+16
Answer:
d = 8t
Step-by-step explanation:
Neither of the "t + ..." answers work for t=0. The d=16t answer does not work for t ≠ 0. The only choice that works for all of the table values is ...
... d = 8t
Which number completes the Pythagorean Triple of 14, 48, x?
50
Step-by-step explanation:These numbers are double those of the (7, 24, 25) triple. 2×25 = 50.
You can also figure it out from ...
... x = √(14² +48²) = √(196 +2304) = √2500 = 50
m∥n, m∠1 = 50°, m∠2 = 48°, and line s bisects ∠ABC. What is m∠3?
49°
Step-by-step explanation:∠DEF = ∠1 +∠2 = 50° +48° = 98°
∠ABC = ∠DEF because they are alternate exterior angles, hence congruent.
∠3 = ∠4 because they are vertical angles.
∠3 = (1/2)∠ABC = (1/2)·98° . . . . . ∠4 is half of ∠ABC
∠3 = 49°