Answer:
$3100 at 12%$2800 at 6%Step-by-step explanation:
Let x represent the amount on deposit at 12%. Then 5900-x is the amount deposited at 6%, and the total interest earned is ...
12%·x +6%·(5900 -x) = 540
0.06x + 354 = 540 . . . . . . . . eliminate parentheses
0.06x = 186 . . . . . . . . . . . . . . subtract 354
x = 3100 . . . . . . . . . . . . . . . . . divide by 0.06
Scott invested $3100 at 12% and $2800 at 6%.
_____
Quick sanity check
The average interest earned is $540/$5900 ≈ 0.0915 ≈ 9.15%. This is more than the average of 12% and 6%, which is (12+6)/2 = 9 percent. Hence more than half of the money must be deposited at 12%.
what is the probability of rolling a dice at most 3 times until a 6 occurs
Answer:
Probablity of getting six in at most three roll= 0.199.
Step-by-step explanation:
Given: Dice rolled at most 3 times untill a 6 occurs.
First, finding the probablity of getting 6 in a dice if rolled once.
Probablity= [tex]\frac{chances\ of\ occurance}{Total\ number\ of\ event}[/tex]
We know, dice have six side, therefore, total number of event will be 6.
∴ Probablity of getting six in one roll= [tex]\frac{1}{6}[/tex]
As given, Dice is rolled at most 3 times.
Now, finding the probablity of getting 6 in a dice if rolled 3 times.
∴ Probablity of getting six in three roll= [tex]\frac{1}{6}+(\frac{1}{6})^{2} +(\frac{1}{6})^{3}[/tex]
⇒ Probablity of getting six in three roll= [tex]\frac{1}{6}+\frac{1}{36} +\frac{1}{216}[/tex]
Taking LCD 216
⇒Probablity of getting six in three roll= [tex]\frac{1\times 36+ 6\times 1+1}{216}[/tex]
⇒Probablity of getting six in three roll= [tex]\frac{43}{216}[/tex]
∴Probablity of getting six in three roll=0.199
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the sum of a finite geometric series.
Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. If this process continues for 5 generations after Amanda,
people other than Amanda will know the art of quilling.
Answer:
4096
Step-by-step explanation:
4*4=16
16*4=64
64*4=256
256*4=1024
1024*4=4096
if this doesn't work, try the other products
Answer:
1,024
Step-by-step explanation:
Five generations after Amanda.
So, Amanda would be considered generation 0.
1st Generation- 4^1=4
2nd Generation-4×4=16
3rd Generation-16×4=64
4th Generation-64x4=256
5th Generation-256×4=1,024
Roger wants to buy 58 tennis balls. Estimate how many canisters he would have to buy if there are 3 tennis balls per canister by rounding the total number of tennis balls to the nearest tens place.
20 canisters
Step-by-step explanation:
Long divide the 58 by 3 to get 19.3 repeating. Then round off to 20. Hope this helps!
Final answer:
After rounding 58 tennis balls to the nearest ten, Roger would need to buy approximately 20 canisters, with each canister containing 3 tennis balls.
Explanation:
Roger wants to buy 58 tennis balls and needs to estimate how many canisters he would have to buy if there are 3 tennis balls per canister. To estimate, we round the total number of tennis balls to the nearest tens place. Rounding 58 to the nearest ten gives us 60. To find the number of canisters needed, we divide the rounded number of tennis balls by the number of balls per canister:
60 ÷ 3 = 20 canisters
Therefore, Roger would need to buy approximately 20 canisters to have around 60 tennis balls.
A mother is three times as old as her son, and in 11 years she will be just twice his age. Find their present ages
Answer:The kid is 11 and the mother is 33
Step-by-step explanation:
do the math
Step-by-step explanation:
Let the present age of son be x years
Therefore, mother's age = 3x years
11 years after:
Son's age = (x + 11) years
Mother's age = (3x + 11) years
According to the given condition:
3x + 11 = 2 (x + 11)
[tex] \therefore \: 3x + 11 = 2x + 22 \\ \therefore \: 3x - 2x = 22 - 11 \\ \therefore \: x = 11 \\ \implies \: 3x = 3 \times 11 = 33 \\ thus \\ Present \: age \: of \: mother = 33 \: years \\ Present \: age \: of \: son= 11 \: years \\ [/tex]
Write an expression with two terms. 1 term should have a coefficient with a variable and the other term should be constant. Name the coefficient, the variable, and the constant in the expression. Then write a word phrase for your expression.
________________________________________________________________________________________________________________________________________
Answer:
y = 2x + 5
Step-by-step explanation:
The 2 would be the coefficient with x as a variable, and the 5 would be the constant.
At the beginning of the day Jessica had 5 dollars (constant), and for every hour she worked (variable), she made 2 dollars (coefficient).
An example of an expression with two terms is 3x + 5, where 3 is the coefficient, x is the variable, and 5 is the constant. A word phrase for this expression is "Three times a number plus five."
An example of an expression with two terms where one term has a coefficient with a variable and the other term is constant is:
3x + 5
In this expression:
The coefficient is 3.
The variable is x.
The constant is 5.
A word phrase for this expression could be: "Three times a number plus five."
what is 176/14 simplified?
Answer:
12.57
Step-by-step explanation:
Answer:
12.57 i did on the calculator
Step-by-step explanation:
What number comes before 12 when you count by twos?
A 8
B 11
C 10
D 9
Answer:
c
Step-by-step explanation:
brainlist
If x/5+6=-14 then x equals
Answer:
x = - 100
Step-by-step explanation:
Given
[tex]\frac{x}{5}[/tex] + 6 = - 14 ( subtract 6 from both sides )
[tex]\frac{x}{5}[/tex] = - 20
Multiply both sides by 5 to clear the fraction
x = 5 × - 20 = - 100
The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?
The maximum height of the football is approximately 15.21 yards.
Explanation:The given equation for the path of the football is y = –0.04x^2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. To find the maximum height of the football, we need to determine the vertex of the parabolic function represented by the equation. The vertex represents the point where the function reaches its maximum or minimum value.
The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b/(2a). In this case, a = -0.04 and b = 1.56. Plugging these values into the formula, x = -1.56/(2*-0.04) = 19.5. Substituting this value back into the equation, we can find the corresponding y value which represents the maximum height of the football.
y = –0.04(19.5)^2 + 1.56(19.5) = -0.04(380.25) + 30.24 = 15.21 yards
completa:
1. un numero real es--------------------- si se puede escribir como la razon (cociente) [tex]\frac{a}{b}[/tex] de dos numeros enteros , donde b [tex]\neq[/tex] 0.
Answer:
un número real es una fracción o número racional
si puedes escribir como razón (cociente) [tex]\frac{a}{b}[/tex]
de dos números enteros, donde b [tex]\neq[/tex] 0
Step-by-step explanation:
un número real es una fracción o número racional
si puedes escribir como razón (cociente) [tex]\frac{a}{b}[/tex]
de dos números enteros, donde b [tex]\neq[/tex] 0
Question is in the problem, help please
Answer:
π units²
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ← r is the radius
Here diameter d = 2, thus r = 2 ÷ 2 = 1, thus
A = π × 1² = π × 1 = π units² ← exact solution
or A = 3.14 units² ← as a decimal
What is the answer to this 4×3^2?
Evaluate the expression.
Answer:
36
Step-by-step explanation:
The first thing to simplify is the Exponents
3^2 means 3 multiplied by it self 2 times
3×3=9
4×3^2
4×9
36
the measure of C if a=6 and b=9.
[tex]3 \sqrt{5} [/tex]
[tex]9 \sqrt{5} [/tex]
[tex]3 \sqrt{13} [/tex]
[tex]5 \sqrt{3} [/tex]
Answer:
[tex]c=3\sqrt{13}[/tex]
Step-by-step explanation:
Pythagorean Theorem: In the right triangle the square of longer side is equal to the sum of the squares of other sides.
[tex]c^2=a^2+b^2\\\\c^2=6^2+9^2\\\\c^2=36+81\\\\c^2=117\\\\c^2=3\times 3\times 13\\\\c=\sqrt{3\times 3\times 13}\\\\c=3\sqrt{13}[/tex]
Which number completes the inequality? Two-thirds less-than blank less-than StartFraction 7 over 9 EndFraction Three-fifths StartFraction 6 Over 9 EndFraction Three-fourths StartFraction 6 Over 7 EndFraction
Answer:
c
Step-by-step explanation:
Final answer:
To complete the inequality, we convert the fractions to decimal form or find a common denominator to compare them. The number that completes the inequality is three-fourths (0.75), as it is larger than two-thirds but smaller than seven-ninths.
Explanation:
The student is asking which number fulfills the inequality between two-thirds and various other fractions. To determine the correct number that completes the inequality, we should consider the values of the fractions in decimal form or by comparing them to each other after finding a common denominator.
For example, two-thirds is approximately 0.666..., three-fifths is 0.6, seven-ninths is approximately 0.777..., three-fourths is 0.75, and six over nine is equivalent to two-thirds (as six-ninth simplifies to two-thirds).
Considering these values, the number that fills the gap should be bigger than two-thirds and smaller than the smallest fraction among the given options that is bigger than two-thirds. Therefore, three-fourths (0.75) fits the inequality because it is larger than two-thirds (approximately 0.666...) but less than seven-ninths (approximately 0.777...).
9. Abby walked 3 km west. Then she walked
twice as far going east. She continued east
for another kilometre, stopping 2 km east
of Lauren's home. When Abby started
walking, how far was she from Lauren's
home? Explain how you know.
Answer:
2km
Step-by-step explanation:
- Abby walked 3 km west: Abby is 3km west from her starting point.
- Then she walked twice as far going east: she walks 6km east so she's 3 km east from her starting point
- She continued east for another kilometre: She's is 4 km east from her starting point
- Stopping 2 km east of Lauren's home: She's currently 2 km east from Lauren's home and 4km east from her starting point. Therefore, Abby's starting point is 4km - 2km = 2km west from Lauren's home
2 + a/6 = -4 what is a?
Answer:
a= -36
Step-by-step explanation:
1. Subtract 2 from both sides
2 + a/6 -2 = -4 -2
2. Simplify
a/6 = -6
3. Multiply both sides by 6
6a/6 = 6(-6)
4. Simplify
a = -36
What is the factored form of 3x + 21x-24?
Answer:
factorize form of the equation is [tex]24(x-1)=0[/tex] , where [tex]x=1[/tex]
Step-by-step explanation:
Given Equation:
[tex]3x + 21x-24=0[/tex]
Adding the terms of 'x' and taking constants on the other side.
[tex]24x-24=0[/tex]
The sign of the constant will change on changing the side of it.
[tex]24x=24[/tex]
[tex]x=\frac{24}{24}[/tex]
[tex]x=1[/tex]
So, the value of 'x' is 1
The factorized form of the equation can be made by taking the common value from the equation i.e
[tex]24x-24=0\\[/tex]
[tex]24(x-1)=0[/tex]
A ticket at a movie theater costs $8.50. One night, the theater had $29,886 in ticket sales.
Which is the best estimate for the number of tickets sold?
2,000
30,000
3,000
4,000
Answer:
i would guess 3000
Step-by-step explanation:
this is because i rounded 8.50 to 10. and rounded 29886 to 30000
[tex]30000 \div 10 = 3000[/tex]
50 + 50 - 25 x 0 +2 + 2
Answer:
104
Step-by-step explanation:
Any expression multiplied by 0 equals 0
when adding or subtracting 0, the quantity doesn't change
Answer:
I think it is 4 or 104. There are 2 ways to look at it.
Way #1:
50 + 50 = 100
100 - 25 = 75
75 x 0 = 0
2 + 2 = 4
0 + 4 = 4
Way #2:
50 + 50 = 100
25 x 0 = 0
100 - 0= 100
2 + 2 = 4
100 + 4 = 104
Anton's family drove 216 mi to the lake averaging 48 mi/h . On the return trip home they averaged 54 mi/h .
What was the total time that Anton's family spent driving to and from the lake?
The total time that Anton's family spent driving to and from the lake is 8.5 hours
Solution:
Time taken is given by formula:
[tex]Time = \frac{distance}{speed}[/tex]
Anton's family drove 216 mi to the lake averaging 48 mi/h
⇒ Anton's family drove total distance = 216 mi les
⇒ Speed of Antony's family driving to lake = 48 miles per hour
[tex]Time = \frac{216}{48} = 4.5[/tex]
Therefore, time taken to drive to lake is 4.5 hour
On the return trip home they averaged 54 mi/h
[tex]Time = \frac{216}{54} = 4[/tex]
Therefore, time taken to return home is 4 hours
Total time = 4.5 + 4 = 8.5 hours
Thus the total time that Anton's family spent driving to and from the lake is 8.5 hours
Lesson 12 Homework
A rectangular garden has a total area of 48 square yards. Draw and label two possible rectangular
gardens with different side lengths that have the same area.
on the fifth figure in
See picture for solution to your problem.
Use the distributive property to create an equivalent expression to 7x divided by 56 use GCF
Answer:
x/8
Step-by-step explanation:
7x/56=x/8
A rectangular box of height 10 has a base with edges of length 10. What is the length of a diagonal of this box?
Answer:
The diagonal of the box is [tex]D=10\sqrt{3}\ units[/tex]
Step-by-step explanation:
Let
d ----> the diagonal of the base
D ---> the diagonal of the box
step 1
Find the diagonal of the base
Applying the Pythagorean Theorem
[tex]d^2=10^2+10^2[/tex]
[tex]d^2=200[/tex]
[tex]d=10\sqrt{2}\ units[/tex]
step 2
Find the diagonal of the box
In this part the legs of the right triangle are the height of the box and the diagonal of the base
so
Applying the Pythagorean Theorem
[tex]D^2=10^2+(10\sqrt2)^2[/tex]
[tex]D^2=300[/tex]
[tex]D=10\sqrt{3}\ units[/tex]
Fraction calculator 66 1/2 - 43=
Answer:
[tex]\frac{47}{2}[/tex]
Step-by-step explanation:
66[tex]\frac{1}{2}[/tex] - 43 = 47/2
Answer:
47/2
Step-by-step explanation:
3.14•8.7•8.7•14.7
Round to the nearest hundreds
Answer:
3493.70
Step-by-step explanation:
if you multipy all these in a calculator you get a long number, look at the third digit behind the decimal, if its 5+ then make the second digit behind the decimal one number higher. If its 4 or under than keep the number the same. To round, cut off all the digits behind the second digit thats past the secimal
What is the value of the function FX equals 4X +9 when X equals
nanci has a large fish tank that contains fish. The ratio of orange fish to black fish is 5:8. If nanci has a total of 20 orange fish, then how many black fish are inn the tank?
Answer:
32 black fish
Step-by-step explanation:
1. set up a ratio
[tex]\frac{5}{8} = \frac{20}{?}[/tex]
2. we know that we have to multiply by 4 to get from 5 orange fish to 20 orange fish. Therefore we multiply the 8 black fish by 4 as well to get 32 black fish
[tex]\frac{5}{8} =\frac{20}{32}[/tex]
Find the value of c such that the equation x^2 - c = 0 has 12 and –12 as solutions.
Answer:
c=144
Step-by-step explanation:
The given equation is [tex]x^2-c=0[/tex]
If this equation has 12 and -12 as roots, then the roots must satisfy the equation.
We substitute x=12 to obtain
[tex]12^2-c=0[/tex]
[tex]144-c=0[/tex]
Solve for c to get:
[tex]144=c[/tex]
This implies that:
[tex]c=144[/tex]
We could have also substitute x=-12 to get the same result.
2) The two rectangles shown are similar.
24 cm
9 cm
16 cm
What is the missing measurement?
Fx = 3 cm
G
x = 6 cm
H
x = 18 cm
J
x = 32 cm
Answer:
[tex]6\ cm[/tex]
Step-by-step explanation:
First Rectangle:
[tex]length(l_1)=24\ cm\\\\Width(b_1)=9\ cm[/tex]
Second Rectangle:
[tex]length(l_2)=16\ cm\\\\Let\ Width=b_2\ cm[/tex]
[tex]Since\ these\ two\ rectangles\ are\ similar\\\\\frac{l_2}{l_1}=\frac{b_2}{b_1}\\\\\frac{16}{24}=\frac{b_2}{9}\\\\16\times 9=24\times b_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cross\ multiplication\\\\b_2=\frac{16\times 9}{24}\\\\b_2=6\ cm[/tex]
I need someone help
Answer:
[tex]1\frac{4}{5}[/tex]
Step-by-step explanation:
Each is dived into 5 section. so section is 1/5