Answer:
about 11 years
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=?\ years\\ P=\$4,000\\ A=\$8,000\\r=9\%=9/100=0.09[/tex]
substitute in the formula above
[tex]8,000=4,000(1+0.09t)[/tex]
solve for r
[tex]2=(1+0.09t)[/tex]
[tex]0.09t=2-1[/tex]
[tex]0.09t=1[/tex]
[tex]t=11.1\ years[/tex]
plz someone help me 7(2m−1)−35m=65(4−3m)
Solve for m.
Enter your answer in the space provided. Enter only your answer.
Answer:
Step-by-step explanation:
1. m = -1/5
2. c = -9.75
3. q = 0
Answer:
m = 89/56 = 1 33/56
(Can be simplified to 1.58)
17 divided by 768 in long Division
Answer:
45 remainder 3.
Step-by-step explanation:
Write the expression: the sum of the quantity h and 3 divided by 6.
A) h/6 + 3
B) h/3 + 6
C) h+3/6
D) 6/h+3
The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6 so option (C) is correct.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
The sum of the quantity h and 3 = h + 3
It is divided by 6 so, (h + 3)/6
Hence "The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6".
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Triangle ABC has vertices at A(-3,4)B(4,-2)C(8,3).The triangle is translated 4 units down and 3 units left . Which rule represents the translation? After the translation, what are the coordinates of vertex C
Answer:
see explanation
Step-by-step explanation:
A translation of 4 units down means subtract 4 from the y- coordinate of the original point and a translation of 3 units left means subtract 3 from the original x- coordinate, thus translation rule is
(x, y ) → (x - 3, y - 4 )
Thus
C(8, 3 ) → C'(8 - 3, 3 - 4 ) → C'(5, - 1 )
7.08 × 26
Estimate and then find the exact answer.
Answer:
184.08
Step-by-step explanation:
83%
18)
Suppose two parallel lines are cut by a transversal. Which angles MUST be supplementary?
vertical angles
corresponding angles
alternate exterior angles
alternate interior angles
How much greater is the probability that a motorcyclist will die in a motor vehicle crash compared to the occupants of a car?
10 times greater
20 times greater
35 times greater
Answer:
My personal opinion to this question would be 20 times greater.
Step-by-step explanation:
This is because in a car, there is more safety as there is airbags for the driver and the passenger seat also if the people sitting on the back, lean forward from the crash, they would most probably hit their head on the headrest.
The two-way table represents data from a survey asking teachers whether they teach English, math, or both. A 4-column table with 3 rows. The first column has no label with entries math, not math, total. The second column is labeled English with entries 34, 40, 74. The third column is labeled not English with entries 22, 8, 30. The fourth column is labeled total with entries 56, 48, 104. Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent. 8% 21% 33% 38%
Answer:
b 21%
Step-by-step explanation:
good luck and hurry :)
The given 22 teachers from the total of 104 teachers in the survey gives
the teachers who teach math and not English as approximately; 21%
How can the joint relative frequency be obtained?
The relative frequency table is presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}&English&Not english & Total\\Math&34&22&56\\Not math&40&8&48\\Total&74&30&104\end{array}\right][/tex]
Required:
The joint relative frequency for teachers teaching math and not English
Solution:
The joint relative frequency is the ratio of the frequency of a given category to the total number of data points within the category.
The number of teachers that teach math but not English = 22
Total number of teachers in the survey = 104
Therefore;
[tex]The \ joint \ relative \ frequency = \dfrac{22}{104} \times 100\approx \mathbf{21\%}[/tex]
Therefore;
The joint relative frequency for the teachers that teach math and not English is approximately 21%Learn more about joint relative frequency here:
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86.4 is what percent of 192
Answer:45%
Step-by-step explanation:
I believe it’s 45%
Divide 86.4 by 192 and multiply the result by 100 to get the percentage, hence it is 45%.
A figure or ratio that may be stated as a fraction of 100 is a percentage.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
Here we have to find:
86.4 is what percent of 192
Divide 86.4 by 192:
86.4 / 192 = 0.45
Multiply the result by 100 to convert it into a percentage,
Therefore,
0.45 x 100 = 45%
Hence,
86.4 is 45 percent of 192.
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PLZ HELP I REALLY NEED IT
Answer:
Angle = 64 Degrees
Supplement of Angle = 116 Degrees
Step-by-step explanation:
Let the angle be "x"
We know
The complement of the angle is "90 - x"
and
The supplement of the angle is "180 - x"
From the statement given, we can write:
supplement is 12 LESS THAN twice the angle
The equation would be:
180 - x = 2x - 12
Now, we solve this for x:
[tex]180 - x = 2x - 12\\180+12=2x+x\\192=3x\\x-\frac{192}{3}\\x=64[/tex]
The angle is 64 degrees
The supplement of the angle is 180 - 64 = 116 degrees
will can jump rope at a rate of 8 jumps for every 10 seconds. find the unit rate
Answer:
The unit rate is 1.25 seconds per jump.
Step-by-step explanation:
Given:
Will can jump rope at a rate of 8 jumps for every 10 seconds.
Now, to find the unit rate:
So, by dividing we get the unit rate.
At the rate of 8 jumps Will takes 10 seconds.
Thus, for the rate of 1 jump he will take = [tex]10\div 8=1.25\ seconds.[/tex]
Therefore, the unit rate is 1.25 seconds per jump.
Which of the following matrix addition problems are possible?
Answer:
Option A
Step-by-step explanation:
When adding two matrices, they should be of the same sizes.
Option A:
Matrix [tex]\left[\begin{array}{c}2&3\end{array}\right][/tex] has 2 rows and 1 column.
Matrix [tex]\left[\begin{array}{c}3&4\end{array}\right][/tex] has 2 rows and 1 column too.
So, these matrices can be added.
The result will be
[tex]\left[\begin{array}{c}2+3&3+4\end{array}\right]=\left[\begin{array}{c}5&7\end{array}\right][/tex]
Answer:
A
Step-by-step explanation:
E2020
Simplify the square root of 30/20
Answer:
√6/2
Step-by-step explanation:
Aiden has three 20$ bills and two 10$ bills he wants to save a total of 95$ how much more money does he need what bills could they be
Answer:
$15.00
A $10.00 and a $5.00 dollar bill
Step-by-step explanation:
Answer:$80
Step-by-step explanation:
3 times 20=60
2 times 10=20
either 1, $10 and 1, $5, or 3, $5 or 15, $1
plz hurry!!!! thank you!!!!
Step-by-step explanation:
Since SP=TR, the differnce of PR and ST 24-15 divided by 2 is the length of PD (4.5)
Try to understand the rest from the attached picture
Explain what these ratios all have in common: 8:5,16:10,24:15 . Create a diagram to support your answer please and thank you
Answer:
Step-by-step explanation:
8:5, 16:10, 24:15
these can be written as 8/5, 16/10, 24/15
8/5
16/10 reduces to 8/5
24/15 reduces to 8/5
so basically, they are all the same ratio in simplest form
Convert Зcis 180° to rectangular form.
А. -3
в. -3i
с. з
D. Зі.
Answer:
-3
Step-by-step explanation:
[tex]3 cis(180^\circ)[/tex] means [tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
What is the [tex]x[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is -1.
What is the [tex]y[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is 0.
So this implies [tex]\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0[/tex].
[tex]3 cis(180^\circ)[/tex]
[tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]
[tex]3(-1+i (0))[/tex]
[tex]3(-1+0)[/tex]
[tex]3(-1)[/tex]
[tex]-3[/tex]
A retailer who sells fashion boots estimates that by selling them for x dollars each, he will be able to sell 70−x boots each week. Use the quadratic function R(x)=−x2+70x to find the revenue received when the average selling price of a pair of fashion boots is x. Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.
Answer: $35 is the selling price and $1225 is the maximum revenue.
Step-by-step explanation:
Since we have given that
[tex]R(x)=-x^2+70x[/tex]
We need to find the maximum revenue.
So, We will first derivative it w.r.t. x.
So, it becomes,
[tex]R'(x)=-2x+70[/tex]
Now, we will find critical points.
So, R'(x) = 0
So, it becomes,
[tex]-2x+70=0\\\\-2x=-70\\\\x=\dfrac{70}{2}=35[/tex]
Now, to check whether it yields maximum revenue or not.
So, second derivative w.r.t. x, we get that
R''(x) = -2<0
So, At $35, it yields maximum revenue.
Amount of maximum revenue would be
[tex]R(35)=-(35)^2+70\times 35=-1225+2450=\$1225[/tex]
Hence, $35 is the selling price and $1225 is the maximum revenue.
1. If f(x) = log2 (x) and g(x) is the image of f(x) after a
translation five units to the left, which equation
represents g(x)?
1. g(x) = log 3 (x + 5)
2. g(x) = log 3 (x) + 5
3. g(x) = log 3 (x - 5)
4. g(x) = log 3 (x) - 5
Hi! The correct answer is 2. g(x) = log3 (x) + 5. Message me if you need further help.
The transformation of a function may involve any change. The correct option is 2. The value will be g(x) = log₂(x+5).
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k \times f(x)
Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)
As we know to shift a function towards the left horizontally, we need to add the number of units to the value of x. Therefore, the function of g(x) will be written as,
g(x) = log₂(x+5)
Hence, the correct option is 2. The value will be g(x) = log₂(x+5).
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y equals 4x to the 3rd power minus 3 plus 2x to the second power
please help thanks ❗
Answer:
see the explanation
Step-by-step explanation:
we know that
The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
Remember that if two triangles are congruent, then its corresponding angles and its corresponding sides are congruent
In this problem
PO≅SO ----> given problem
NO≅TO ----> because O is the midpoint NT
∠PON≅∠SOT -----> by vertical angles
so
two sides and the included angle of triangle PON are congruent to two sides and the included angle of triangle SOT
therefore
Triangles PON and SOT are congruent by SAS
hence
∠N≅∠T ----> by definition of congruence (corresponding angles are congruent)
graph a line with a slope of -5 that contains the point -3,-4
Answer:
The equation of the line is 5x + y + 19 = 0
Step-by-step explanation:
The equation of the line with slope 'm' and given a point (x₁, y₁) passing through it we use the Slope - one - point form which is given by:
y - y₁ = m(x - x₁)
The point given is: (-3, -4) and the slope is -5.
We get the equation of the line to be:
y - (-4) = -5(x - (-3))
⇒ y + 4 = -5(x + 3)
⇒ y + 4 = -5x - 15
⇒ 5x + y + 19 = 0. is the required equation of the line.
simplify c + 6 < -20
Answer:
Step-by-step explanation:
c + 6 < -20
Subtract 6 from both side
c +6 -6 < -20-6
c < -26
So value of c should be less than -26. Value of c = { - ∞ ...... -28, - 27 }
Eg:
If c = -27
-27 + 6 = - 21 . -21 is less than -20
At a farm ,Justin picks 3 bushels of fruits, the bushel weigh 8 1/4 pounds,6 1/2 pounds, and 6 5/8 pounds. What is the average weight per bushel
Answer:
7.125
Step-by-step explanation:
The average weight per bushel of fruits that Justin picked is calculated as the sum of all weights divided by the number of bushels, which comes out to be 7.125 pounds per bushel.
To calculate the average weight per bushel when Justin picks 3 bushels of fruits weighing 8 1/4 pounds, 6 1/2 pounds, and 6 5/8 pounds, we need to add up the weights of the bushels and then divide by the number of bushels. Here are the steps:
First, convert all fractions to decimals or common denominators for easier addition:
8 1/4 = 8.25 pounds
6 1/2 = 6.5 pounds
6 5/8 = 6.625 pounds
Add up the weights of the three bushels:
8.25 + 6.5 + 6.625 = 21.375 pounds
Finally, divide the total weight by the number of bushels to find the average:
21.375 pounds \/ 3 bushels = 7.125 pounds per bushel
The average weight per bushel that Justin picks is 7.125 pounds.
Which pair of ratios does not
form a true proportion?
A) 6:16 and 21:56
B) 2 to 10 and 15 to 75 C) 9/11=27/15
D) y = 5x
Answer:
C
Step-by-step explanation:
The cost of pumpkin seeds is proportional to their weight. A 24-ounce bag of pumpkin seeds costs $6.00. What is the unit rate for the pumpkin seeds?
$0.24 per ounce
$0.25 per ounce
$0.40 per ounce
$0.60 per ounce
Answer:
$0.25 per ounce
Step-by-step explanation:
Look at this and now tell me if my deleted answer was right
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Unit rate has to do with comparison or the proportionality of an item to its unit value or unit of measure.
The unit rate for the pumpkin seeds is $0.25 per ounce.
Based on this question, unit rate is the cost of 1-ounce of pumpkin seeds
From the question:
24-ounce of pumpkin seeds = $6.00
1- ounce of pumpkin seeds = ?
Cross Multiply
1 - ounce × $6.00 / 24-ounce
= $0.25
Therefore, unit rate for pumpkin seeds is $0.25 per ounce.
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Given f(x) = x - 7 and g(x) = x2.
Find g(f(4)).
g(f(4)) =
Answer:
Step-by-step explanation:
If we are looking to find the composition of g(f(4)), we start at the innermost part of the problem which is to evaluate f(4).
If f(x) = x - 7, then f(4) = 4 - 7. f(4) = -3.
Now take that -3 and evaluate the g(-3).
If g(x) = x^2, then g(-3) = (-3)^2 which is 9.
Therefore, f(g(4)) = 9
Answer:
9
Step-by-step explanation:
edg 2020
George invested a total of $5,000 at the beginning of the year in two different funds. At the end of the year, his investment had grown to $5,531. The money in the first fund earned 9%, while the money in the second fund earned 13.5%. Write a system of equations, then solve it to find out how much of the $5,000 was invested into each fund at the beginning of the year
Answer:
The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested at 9% (first fund)
5,000-x ----> the amount invested at 13.5% (second fund)
Remember that
[tex]9\%=9/100=0.09[/tex]
[tex]13.5\%=13.5/100=0.135[/tex]
The total interest earned is equal to
[tex]\$5,531-\$5,000=\$531[/tex]
we know that
The amount earned by the first fund at 9% plus the amount earned by the second fund at 13.5% must be equal to $531
so
the linear equation that represent this situation is equal to
[tex]0.09x+0.135(5,000-x)=531[/tex]
solve for x
[tex]0.09x+675-0.135x=531[/tex]
[tex]0.135x-0.09x=675-531[/tex]
[tex]0.045x=144[/tex]
[tex]x=\$3,200[/tex]
so
[tex]\$5,000-x=\$5,000-\$3,200=\$1,800[/tex]
therefore
The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800
missy sold between seven and 12 glasses of lemonade every hour at her lemonade stand. If she sold lemonade for two hours how many glasses could she have sold?
Answer:
"she could have sold between 14 and 24 glasses"
Step-by-step explanation:
7 to 12 glasses sold per hour
Min 7 glasses and Max 12 glasses
If she sold for 2 hours, her minimum would be:
7 * 2 = 14 glasses
and her max would be:
12 * 2 = 24 glasses
Hence,
she could have sold between 14 and 24 glasses
What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?
Answer:
z = x^3 +1
Step-by-step explanation:
Noting the squared term, it makes sense to substitute for that term:
z = x^3 +1
gives ...
16z^2 -22z -3 = 0 . . . . the quadratic you want
_____
Solutions derived from that substitution
Factoring gives ...
16z^2 -24z +2z -3 = 0
8z(2z -3) +1(2z -3) = 0
(8z +1)(2z -3) = 0
z = -1/8 or 3/2
Then we can find x:
x^3 +1 = -1/8
x^3 = -9/8 . . . . . subtract 1
x = (-1/2)∛9 . . . . . one of the real solutions
__
x^3 +1 = 3/2
x^3 = 1/2 = 4/8 . . . . . . subtract 1
x = (1/2)∛4 . . . . . . the other real solution
The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.
Answer:
x^3 +1
Step-by-step explanation: