Ken invested $5,700 in the 6% account, and the other $4,300 in the 4% account.
How much money was invested in each account?Let's define the variables:
x = amount of money on the 4% account.y = amount of money on the 6% account.We know that Ken invested $10,000 in total, so:
x + y = 10,000
And the interest in one year is:
x*0.04 + y*0.06 = 514
Then we have a system of equations:
x + y = 10,000
x*0.04 + y*0.06 = 514
To solve it we start by isolating one of the variables in one of the equations, isolating x we will get:
x = 10,000 - y
Replacing that in the other equation we get:
(10,000 - y)*0.04 + y*0.06 = 514
400 - y*0.04 + y*0.06 = 514
400 + y*0.02 = 514
y = (514 - 400)/0.02 = 5,700
Then Ken invested $5,700 in the 6% account, and the other $4,300 in the 4% account.
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Gind the greatest common factor for the list of terms.
98ab^3, 84a, 140b, 112ab
Answer:
14
Step-by-step explanation:
You want the greatest common factor of the terms {98ab^3, 84a, 140b, 112ab}.
Common factorsThere are no variables that are common to all terms. 'a' and 'b' are each common to 3 of the 4 terms, but not all.
The greatest common factor of the constants cannot be larger than the smallest difference of the constants. That difference is ...
98 -84 = 112 -98 = 14
Since 14 is a divisor of all of the constants, 14 is the greatest common factor.
__
Additional comment
Factoring out the greatest common factor, we have ...
= 14{7ab³, 6a, 10b, 8ab}
Solve the equation, 3|2x|+4=12.
Answer:
x=|4/3|
Step-by-step explanation:
3|2x|=12-4
|2x|= 8/3
x=4/3
GIVEN The area of the rectangle in front = 15x5 = 75cm² Determine the area of the rectangle on the left side of the rectangular prism. Determine the area of the rectangle at the bottom of the rectangular prism
Height =15cm
Width=2cm
Length=5cm
The area of the rectangle Infront =15×5=75cm ²
1 determine the area of the rectangle on the left side of the rectangular prism
2 determine the area of the rectangle at the bottom of the rectangular prism
3 determine the total surface area (TSA) of the rectangular prism.
The area of rectangle at left is 30 cm²The area of rectangle at the bottom of the rectangular prism is 10 cm².The total surface area (TSA) of rectangular prism is 230 cm²
Step-by-step explanation:
Given that
Height = 15 cmWidth = 2 cmLength = 5 cmThe area of the rectangle in front = 15x5 = 75cm²To find
The area of the rectangle on the left side of the rectangular prism.The area of the rectangle at the bottom of the rectangular prismThe total surface area (TSA) of the rectangular prism.So, according to the question
Let's assume,
height = h = 15cm
length = l = 2cm
width = w = 5cm
So, from question,
Area of rectangle in front = 15 cm x 5 cm
That's mean
Rectangle in front have h = 15cm and l = 5cm.
We know the width from question w = 2cm.
So,
Area of the rectangle to the left = h x w
= 15 x 2
= 30 cm²
Also,
There is no height to the rectangle at the bottom.
So, l and w make up the bottom rectangle.
Now,
the area of rectangle at the bottom = l x w
= 5 x 2
= 10 cm²
Now,
The total surface area (TSA) of the rectangular prism = 2(lw + wh + lh)
= 2 ( 75 + 10 + 30)
= 2 x (115)
= 230cm²
So,
Answer:
The area of rectangle at left = 30 cm²The area of rectangle at the bottom of the rectangular prism is 10 cm².The total surface area (TSA) of rectangular prism = 230 cm²To learn more about Surface area and Area of rectangle, please click on the link:
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HELP PLEASE!
Find the measurement of the angle indicated for each trapezoid.
Answer:
m∠B = 53°
Step-by-step explanation:
You want the measure of the acute angle, given that consecutive interior angles of the trapezoid have measures (32x-1) and (14x-3).
SetupConsecutive interior angles between the bases of a trapezoid are supplementary:
(32x -1) +(14x -3) = 180
SolutionSimplifying the equation, we get ...
46x -4 = 180
46x = 184 . . . . . . add 4
x = 4 . . . . . . . . divide by 46
The smaller angle is ...
14(4) -3 = 56 -3 = 53
The measure of angle B is 53°.
__
Check
The measure of angle C is 32(4) -1 = 127. This is the supplement of the measure of angle B, as it should be.
The table below shows the masses of some pears in a crate. If one of the pears is chosen at random from the crate, what is the probability that it has a mass of more than 120 g? Give your answer as a fraction in its simplest form.
PLS
The probability that it has a mass of more than 120 g is 13/40.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.
Given,
frequency = 5 9 13 7 6
sum of frequency = 40
P(120<m<=180) = 13/40
P(180<m<=240) = 7/40
P(240<m<=300) = 6/40
Probability that it has a mass of more than 120 g = [P(120<m<=180) + P(180<m<=240) + P(240<m<=300) ]
⇒ 13/40 + 7/40 + 6/40
= 26/40
= 13/20
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Look at the digits below.
1,1,2,2,3,3
Using these digits, create a six digit number where the ones are separated by one digit, the twos are separated by two digits, and the threes are separated by three digits.
Answer:
131232- This is the answer
Answer:
3,1,2,1,3,2
Step-by-step explanation:
3,1,2,1,3,2
You are a first-year police officer in NYC. You make $3,541.67 monthly. Next year, you are given a raise to 47,000. How much more per month will you earn your second year.
Answer:
374.99 or rounded up to 375
Step-by-step explanation:
First we need to take 47,000 and divide it by 12 to find the monthly income.
47,000/12 is 3916.66
now subtract 3541.67 from 3916.66
log 5 = 0.69897, log 3 = 0.47712 and log 2 = 0.30103. evaluate log 4 and log 15
Answer: log4=0.60206 log15=1,17579
Step-by-step explanation:
[tex]log4=\\log2^2=\\2log2=\\2(0.30103)=\\0.60206\\\\log15=\\log(3*5)=\\log3+log5=\\0.47712+0.69897=\\1.17579[/tex]
A rubber band is 1 1/8 inches unstretched and 4 1/2 inches when it is fully stretched. How much does it stretch? Write your answer as an improper fraction. inches
The stretch length is 27/8 inches
How to determine how much it stretches?The given parameters are
Unstretch = 1 1/8 inches
Stretch = 4 1/2 inches
The length of stretch is calculated using
Length = Stretch - Unstretch
So, we have
Length = 4 1/2 - 1 1/8
Evaluate the difference
Length = 3 3/8
Express as improper fraction
Length = 27/8
Hence, the stretch length is 27/8 inches
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Use identities to determine the six trigonometric function values for the given angle and given information.
Give exact values for answers.
sin (0) = //
and cos (0) < 0
Rema
 If a student has a GPA of 3.0, the student gets the “good student discount”, which is a discount of 20%. Write a function that represents the discount on the monthly premium for a “good student”. call this function S.
S(x) + 0.20(x/12) = 0
S(x) = -0.20(x/12) it is a function that represents the discount on the monthly premium for a “good student.
From the question,
A student has a GPA of 3.0 gets good student discount of 20%
Write a function with ‘S’ that represents the discount of the monthly premium for a good student.
S(x) = -0.20(x ÷ 12)
S(x) is a function and student got a discount of 20%.
i.e., 20/100 = 0.20
The function that represents the discount on the monthly premium so x/12
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Hence, it s a function that represents the discount on the monthly premium for a “good student.
S(x) + 0.20(x/12) = 0
S(x) = -0.20(x/12)
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$15,000 is invested for 6 months at an annual simple interest rate of 2%.
(a) How much interest will be earned?
(b) What is the future value of the investment after 6 months?
Step-by-step explanation:
u find 2 percent of 15000 which is 2/100×15000 to find the annual interest then divide it by 2 to find 6 months 300 is the yearly interest so 6 months will be 150
(b) here u add the 150 gotten from a to 15000 giving u 15150
Jakob is working on his math homework. He decides that the sum of the expression? 1/3+6
No, jacob is not correct.
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We are given that;
Expression= 1/3 + 6sqrt5/7
Now,
The sum of the expression 1/3 + 6sqrt5/7 is not rational, even though it is a fraction. A rational number is a number that can be written as the ratio of two integers, such as 1/3 or -4/5. An irrational number is a number that cannot be written as the ratio of two integers, such as sqrt2 or pi.
The expression 1/3 + 6sqrt5/7 contains an irrational term, 6sqrt5/7. This term cannot be simplified to the ratio of two integers, because sqrt5 is irrational. Therefore, adding this term to 1/3 does not make it rational. The sum of a rational and an irrational number is always irrational.
Therefore, by the fraction the answer will be No.
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on the way to the mousetrap car contest the judge drove from Exit 32 on the highway to exit 170 in 2 hours. exita 32 and 170 are 138 miles apart. did the judge follow the speed limit of 65 mph? explain
Answer: The judge did not follow the speed limit of 65mph because if she did she would have not gotten there in 2 hours. The judge was actually going at 85 mph.
Step-by-step explanation:
The cost of a dozen eggs is $2.50. At this store you must by them in packs by the dozen and they do not allow you to buy more than 6 dozen eggs at a time. State a reasonable domain for this situation.
The reasonable domain for this situation is { 1, 2, 3, 4, 5, 6 }.
What is a set ?A set is a well defined collection of objects.Set are represented by many forms two of them are set builder form and roaster form.
According to the given question The cost of a dozen eggs is 2.50 dollars.
At this store you must by them in packs by the dozen and they do not allow you to buy more than 6 dozen eggs at a time,So we can buy eggs in dozen from 1 dozen to 6 dozen.
This can be represented in roaster form by { 1, 2, 3, 4, 5, 6 }.
This can also be represented by set builder form as { x : x ∈ N and 1≤x≤6 }
where x represents no. of dozens of egg.
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There are N coins, each showing either heads or tails. We would like the number of coins showing heads to be equal to the number showing tails. What is the minimum number of coins that mmust be turned over?
Write a function:
int solution (vector &A);
that, given an array A consisting of N integers representing the coins,
returns the minimum number of coins that must be flipped.
Consecutive elements of array A represent consecutive coins, and contain either a 0 (heads) or a 1 (tails).
Examples:
1. Given array A = [1, 0, 0, 1, 0, 0], there are four coins showing heads and two showing tails. The function should return 1, as after reversing one of the coins showing heads, there will be three coins showing heads and three showing tails.
Array A = [1, 0, 0, 1, 0, 0], there are four coins showing heads and two showing tails.
def solution(A):
n = len(A)
dp = [[0 for x in range(2)] for y in range(n)]
if A[n-1] == 0:
dp[n-1][0] = 0
dp[n-1][1] = 1
else:
dp[n-1][0] = 1
dp[n-1][1] = 0
for i in reversed(range(len(A)-1)):
if A[0] == 0:
dp[i][0] = dp[i+1][1]
dp[i][1] = dp[i+1][0] + 1
else:
dp[i][0] = dp[i+1][1] + 1
dp[i][1] = dp[i+1][0]
return min(dp[0][0], dp[0][1])
An array of computer drives is a collection of two or more drives that operate as a single drive. For instance, in a RAID array, a user may make use of numerous drives that are mirror images of one another to help secure the data stored on the drives.
A data structure called an array consists of a set of elements (values or variables), each of which is identifiable by an array index or key. Depending on the language, additional data types that describe aggregates of values, such lists and strings, may overlap (or be associated with) array types.
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Maya is 12 years old and Sophia is 15 years older than Maya. In how many years will Sophia be twice has old as Maya
Sophia will be twice as old as Maya in 3 years
Solving equationsFrom the question, we are to determine the number of years when Sophia will be twice as old as Maya
From the given information,
"Maya is 12 years old"
and
"Sophia is 15 years older than Maya"
Thus,
Sophia is 12 + 15 years
Sophia is 27 years
Let the number of years when Sophia will be twice as old as Maya be x
Then,
27 + x = 2(12 + x)
Solve for x
27 + x = 24 + 2x
27 - 24 = 2x - x
3 = x
x = 3
Hence, Sophia will be twice as old as Maya in 3 years
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Write the following expression in simplest form. (6 + 12.5a) − (8 + 2.9a)
Answer:
15.4a + (-14)
Step-by-step explanation:
I had the same test :3
Zachary purchased a computer for $1,070 on a payment plan. Two months after he purchased the computer, his balance was $725. What is an equation that models the balance y after x months
An equation that models the balance y after x months y = 1070 - 172.5x.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
Zachary purchased a computer for $1070. The first step is to calculate the purchase he paid after 2 months.
= 1070 - 725
= $345
Then the purchase after 1 month is
= $345/2
= $172.5 per month
The equation can be written as:-
y = mx + c
y = 1070 - 172.5x.
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Help pls. I'll mark as brainlist.
Answer:
Neither is correct
Step-by-step explanation:
Look at each side of the smaller figure and compare it to the larger figure. That will give you the scale: (Larger figure length)/(Smaller figure length)
Let's take the base
Smaller figure is 6 units
Larger figure is 9 units
Scale = 9/6 = 1.5
Take the vertical height
Smaller figure = 4
Larger figure = 8
So here the scale is 2
Scaling is inconsistent for different sides of the figure
So neither of them is right. For a figure to be scaled, all its sides must be scaled by the same number
Step-by-step explanation:
To know wgich scale factore the Original sketch was increased with Compare the measurements of the original sketch and the student's sketch.
HOW?
do the proportion with relations to each and every side to see by how much each side increased.
For the bases it will be>>>>>>> The base of the student's sketch/ The base of the Original sketch(distance)
=10/7
10/7Adjacent side of the Student's Sketch/Adjacent side of the Original sketch
10/7Adjacent side of the Student's Sketch/Adjacent side of the Original sketch=9/5
upper side os student's sketch / upper side of original sketch
upper side os student's sketch / upper side of original sketch =4/3
Before I go any further you can see that for any side there is no certain(constant) scale factor whuch was used to increase the original Sketch to the Student's Sketch. Fir each and every side the Scale factor keeps on Changing This brings us to a conclusion that NEITHER OF SASHA AND RANDY IS CORRECT.
HOPE THIS HELPS
6 to the 3rd power ÷ 4 + 2 x 9(32 x 8 – 17 x 4).
HELP
Answer:
6 to the 3rd power ÷ 4 + 2 ×9(256-17×4)
6 to the 3rd power ÷ 4 + 2 ×9(256-68)
6 to the 3rd power ÷ 4 + 2 ×9×188
216 ÷ 4 + 2 × 1692
216 ÷ 4 + 3384
54 + 3384
=3438
find the 53th term in the following arithmetic sequence
2,9,16,23
Answer:
It's 366. 53*7=371 | 371-5 because the 0th term is -5
Use the properties of exponents to simplify the expression ³√5 x ³√25.
Answer:
Step-by-step explanation:
we now that [tex]\sqrt[n]{x} *\sqrt[n]{y} =\sqrt[n]{xy}[/tex]
so:
[tex](\sqrt[3]{5} )(\sqrt[5]{25} )= \sqrt[3]{125} = 5[/tex]
what is 87,000,000,000,000 in scientific notation
Answer:
8.7*10^12
Step-by-step explanation:
Rewrite the expressions as a product of two factors 60m - 12n
Answer:
Step-by-step explanation:
12(5m-n)
Find the value of x the diagram is not a scale
○ 83
○ 97
○ 132
○ 41
Answer:
132
Step-by-step explanation:
.....................................
The table shows the items that come in an appetizer sampler at a family restaurant.
Small Sampler
4 chicken wings
2 loaded potato skins
2 mozzarella sticks
8 pretzel bites
The restaurant wants to create a larger appetizer sampler to accommodate larger groups of customers. They also
want to limit the number of pretzel bites to 20. If the ratio remains the same, how many mozzarella sticks will be in
the larger sampler?
The number of mozzarella sticks that will be in the larger sample will be 5.
How many mozzarella sticks will be in the larger sample?Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s). The sign used to express ratios is :.
The first step is to determine the ratio of mozzarella sticks to pretzel bites in the smaller sample. This can be done by dividing the quantity of mozzarella sticks by the number of pretzel bites.
Number of mozzarella sticks / number of pretzel bites = 2 : 8 or 1 : 4.
Now, divide the number of pretzel bites in the larger sample by the ratio of mozzarella sticks and pretzel bites in the smaller sample.
The ratio of mozzarella sticks in the larger sample = 20 / 4 = 5
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In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. What are the measures of its angles??
Answer:
every angle equals 60°
Step-by-step explanation:
the sum of angles of any triangle is 180 so the equilateral triangle have all angles equal so 180 ÷ 3 = 60
You deposit $3500 in an account that
earns 4% simple interest. How long will
you have to leave the money in the acount
to earn $350 interest?
Answer:
2years 6 months
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year.
I = P × R × T/100
Solving our equation:
$350 = $3500 × 4 × T /100
Let's solve your equation step-by-step.
350=(3500)(4)t/100
Step 1: Multiply both sides by 100.
350=(3500)(4)t/100
(350)*(100)=((3500)(4)t/100)*(100)
35000=(3500)(4)t
Step 2: Simplify both sides of the equation.
35000=14000t
Step 3: Flip the equation.
14000t=35000
Step 4: Divide both sides by 14000.
14000t/14000=35000/14000
t=5/2
t = 2.5 years
2.5 years = 2years 6 months
help me please its confusing
