Answer:
Step-by-step explanation:
Jonathan invests $4100 in two different accounts. The first account paid 4 %, the second account paid 13 % in interest. At the end of the first year he had earned $299 in interest. How much was in each account?
$ _____________ at 4 %
$ _____________ at 13 %
The amount invested in the account that paid 4% interest is $2,600
The amount invested in the account that paid 13% interest is $1,500.
What are the simultaneous equations that represent the equation?a + b = 4100 equation 1
0.04a + 0.13b = 299 equation 2
Where:
a = amount invested in the account that paid 4% interest
b = amount invested in the account that paid 13% interest
How much was invested in each account ?
The first step is to multiply equation 1 by 0,04
0.04a + 0.04b = 164 equation 3
Subtract equation 3 from equation 2
0.09b = 135
b = 135 / 0.09
b = $1500
a = 4100 - 1500 = $2,600
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if i compare 0.10__0.01 what would the answer be?
The answer will be 0. 10 > 0. 01 . Option B
How to compare the valuesGiven the values as;
0.100.01Turn the values into proper fractions
a. 0. 10 = 10/ 100
Reduce to simpler terms
= 10/ 100
= 1/ 10
b. 0. 01 = 1/ 100
a = 1/ 100
b = 1/ 100
This means that both decimals are not of equal proportion and thus a is greater than (>) b
Thus, the answer will be 0. 10 > 0. 01 . Option B
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The dose of posaconazole in the treatment of oropharyngeal candidiasis is 100 mg twice a day on the first day and then 100 mg once a day for the next 13 days. Posaconazole oral suspension (posaconazole, 40 mg/mL) is available in 4-fluidounce bottles. How many bottles should be dispensed to meet the dosing requirements?
The number of 4-fluidounce bottles that should be dispensed to meet the dosing requirements for the treatment of oropharyngeal candidiasis is 37.5 bottles.
How is the number of bottles determined?To determine the number of 4-fluidounce bottles, we apply mathematical operations of addition, subtraction, division, and multiplication.
First, the total dosage is determined as 1,500 mg.
Since 40 mg/mL is available in 4-fluidounce bottles, the total dosage is divided by 40 mg/mL to determine the number of bottles required.
Data and Calculations:Dose of posaconazole for the first day = 100 mg twice
= 200 mg (100 mg x 2)
The total number of days for the dosage = 14
Dose for next 13 days = 1,300 mg (100 mg x 13)
Total dosage = 1,500 mg (200 mg + 1,300 mg)
40 mg/mL = 4-fluidounce bottle
1,500 mg = 37.5 bottles (1,500/40)
Thus, the number of 4-fluidounce bottles is 37.5 bottles.
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I don’t understand, can someone help me :)
I think you are supposed to add the the numbers in that row and if it's more that 18 and less that 37 that's the answer. exapmle:
2,8,3,9,5
Add those together and get 27. 27 is less than 37 and more that 18 so it would be one of the answers.
I could be wrong but I'm pretty sure that is what you do
Select the values that make the inequality -b < 8 true. Then write an equivalent inequality, in terms of b. (Numbers written in order from least to greatest going across.)
Answer:
true
Step-by-step explanation:
Answer: true
step by step explanation:
Answer this question please
The correct option is option B) which is that the statement is true for all real numbers.
According to the question we have been given the inequality equation as
|2s-7| ≥ -1
We know that for b<0,
if |a| ≥ b then all real numbers.
Here we have been given,
|a| = |2s-7|
b = -1 <0
As it is fulfilling the above condition and also all the absolute values are non-negative. Therefore the statement is true for all real numbers.
Hence the solution of the |2s-7| ≥ -1 is true for all real numbers that is option B) is the correct option.
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the middle term of the expansion
[tex] (ax + ay)^{n} [/tex]
is
[tex]14580x ^{3} y^{3} [/tex]
find the value of a and the value of n, where a, n are elements of N.
Answer:
Hello,
a=3
Step-by-step explanation:
Since the middle term is x^3y^3 ==> n=6
Coefficient of x^3y^3 is 20 (triangle de Pascal)
So a^6= 14580/20=729 ==> a=3
Solve for x
3x-1=11
Answer: x = 4
Step-by-step explanation:
Given:
3x - 1 = 11
Add 1 to both sides of the equation:
3x = 12
Divide both sides of the equation by 3:
x = 4
What number n is four times as close to 10 as it is to2?
Answer:
I think 3.
Step-by-step explanation:
3*4=12 near 10
Write the equation in point-slope form of the line that passes through (-8, 2) and has the slope of −34 .
Answer:
y = -34x - 270
Step-by-step explanation:
m = -34, y = 2, x = -8
y = mx + b
2 = -34(-8) + b
b = 2 - 272
b = -270
y = -34x - 270
The equationnnnnnnnnnnnnn
Answer:
Step-by-step explanation:
9 ( 3 + 4) - 8 / 4 =
( use BIDMAS)
first step is brackets:
9 (7) - 8 / 4 =
next step is division:
63 - (8 / 4) =
63 - 2 = 61
hope that helps :)
Answer:
35
Step-by-step explanation:
thx for the pionts loolllll
Graph the line with slope
-1/2
passing through the point (-1,-4)
Equation of the line with slope -1/2 passing through the point (-1,-4) is x + 2y = -9
Given,
the slope of the line = -1/2
the line passes through the point (-1,-4)
=> s = -1 and t = -4
The following equation can be used to find the line's equation:
( y - t ) = slope ( x - s )
We get by substituting the values in the equation
=> y + 4 = - 1/2 * ( x + 1 )
=> x + 2y = -1 - 8
=> x + 2y = -9
Therefore, by using the formula for equation of line, we get the equation of the line with slope -1/2 passing through the point (-1,-4) as x + 2y = -9
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each day a bobcat drinks about 3 times as much water as a canada goose drinks. how much water can a bobcat drink in 1 day?
The water that a bobcat drink in 1 day will be 3x.
How to calculate the value?Let the amount of water be represented by x.
From the information, it was stated that each day a bobcat drinks about 3 times as much water as a canada goose drinks.
Let the water that the Canada goose drank be represented as x
Therefore, the water that a bobcat drink in 1 day will be 3x.
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El 32%de 125 cual es la respuesta
Answer:
40
Step-by-step explanation:
=125x32
=4,000÷100
=40
one fifth times w equals negative one eight what is w
If one fifth times w equals negative one eight then w = -5/8
What is Rational numbers?
A rational number is any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero. In other words, a rational number can be expressed as p/q, where p and q are both integers and q ≠ 0.
given that one fifth times w equals negative one eight
we have to find the value of w
one fifth = 1/5
one fifth times w = (1/5)* w
negative one eighth = - 1/8
now according to the question
one fifth times w equals negative one eight
(1/5) *w = -1/8
now solve the equation , we get
w= (5) * (-1/8)
= -5/8
Hence ,if one fifth times w equals negative one eight then w = -5/8
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ow:
(7-21)-(4+ 8) =
Answer:-26
Step-by-step explanation:
Answer:-14-12=-26
Step-by-step explanation: PEMDAS. You do the first parentheses which is 7-21, which will get you -14. Then you do the second parentheses, 4+8. That will get you 12. Then since there’s no multiplication/division, you go to addition/subtraction and since there’s a subtraction symbol in between the parentheses, that’s what you do. -14-12 which will get you -26.
Hope this helps!
Btw PEMDAS stands for (for those people who don’t know or don’t remember)
Parentheses
Exponents
Multiplication*
Division*
Addition’
Subtraction’
*do both together, whichever one comes first when reading it
’do both together, whichever one comes first when reading it
Find the value of B in the following equation if you know it
goes through the point (-4,1).
5x - 3y = B
B =
Answer:
17
Step-by-step explanation:
We can substitute x = -4 and y = 1 since the point lies on the line.
[tex]5(-4)-3(1)=B \\ \\ B=17[/tex]
Question
Simplify: (-12az² — 2z³) + (-2a³ +7a²z) − (−4a²z + 8az²),
Write
17/100
as a decimal number.
Answer: 0.17
Step-by-step explanation:
Plug the equation into a calculator (17 divided by 100).
You can also think of the problem like this; move both decimal places to the left twice since, in 100, there are two 0's.
17 -> 0.17
100 -> 1
This can also work with 17 and 1000, but you would have to move the decimal place three times.
17 -> 0.017
1000 -> 1
PLEASE HELP!!! 100 POINTS!
Solve the following system of equations for all three variables.
9x+y-3z=-9
10x-y+2z=8
-10x-y+4z=10
X = ___ , Y =___ , Z =___
Answer:
x = 0; y = -6; z = 1
Step-by-step explanation:
You want to find the solution to the system of equations ...
9x+y-3z=-910x-y+2z=8-10x-y+4z=10SolutionThis set of equations is conveniently solved using the matrix row-reduction features of a scientific or graphing calculator, spreadsheet, or any of a number of apps or on-line calculators.
The attachment shows the solution to be ...
(x, y, z) = (0, -6, 1)
__
Additional comment
Solving a system of three or more equations "by hand" often can be done by an ad hoc process. It can be done in systematic fashion using Gauss-Jordan reduction techniques, but that often gets messy. Similarly, Cramer's Rule can be used, but that math tends to involve more arithmetic operations than are really necessary.
Adding the first equation to the other two eliminates the y-variable and reduces the system to two equations in two unknowns.
(9x +y -3z) +(10x -y +2z) = (-9) +(8) . . . . adding [1] and [2]
19x -z = -1 . . . . simplified
(9x +y -3z) +(-10x -y +4z) = (-9) +(10) . . . . adding [1] and [3]
-x +z = 1 . . . . simplified
At this point, we could graph the two equations, or we can proceed algebraically.
Adding these two equations gives ...
(19x -z) +(-x +z) = (-1) +(1)
18x = 0 ⇒ x = 0
Using the second of the reduced equations, we find ...
-x +z = 1
0 +z = 1 ⇒ z = 1
And using the second of the original equations, gives us ...
10(0) -y +2(1) = 8
-y = 6 . . . . . subtract 2
y = -6 . . . . multiply by -1
Then the solution is (x, y, z) = (0, -6, 1), as above.
How do you perform the indicated operation, 8 x 10^16/4 x 10^11?
8 x 10^16/4 x 10^11
do exponents first
8 x 10,000,000,000,000,000/4 x 100,000,000,000
than multiply
80,000,000,000,000,000/4 x 100,000,000,000
than divide
20,000,000,000,000,000x 100,000,000,000
2,000,000,000,000,000,000,000,000,000
What is the value of the digit in the ones place in each number?431
Answer:
Step-by-step explanation:
400
30
1
400 FOR HUNDREDS
The width of a painting is 24 centimeters shorter than its length, x. The area of the painting is 4,081 square centimeters. Which equation could be used to find the dimensions of the painting?
We can't find dimension of the painting because length of painting is imaginary form.
WHAT IS A CUBOIDAL OBJECT ?
Six rectangles make up a cuboid, each of which is referred to as a face. The cuboid's six faces are denoted by the letters ABFE, DAEH, DCGH, CBFG, ABCD, and EFGH in the previous diagram.
A pair of opposing faces is formed by the top face ABCD and the bottom face EFGH. The opposing faces ABFE, DCGH, and DAEH, CBFG, have similar pairings. Adjacent faces are any two faces that are not opposite faces.
Consider the faces ABCD, ABFE, BCGF, CDHG, and ADHE that are close by.
CALCULATIONThe width of painting = x- 24
the length of painting = x
according to question
area of painting = 4081 [tex]cm^{2}[/tex]
i.e. [tex]x * (x - 24) = 4081[/tex]
[tex]x^{2} -24x-4081 = 0[/tex]
applying shridharacharya formula :
[tex]x = (-b ± √(b2 - 4ac)) / 2a.[/tex]
it has imaginary roots !!!
Roots: -12 + 62.745517768204i, -12 - 62.745517768204i
Root Pair: -12 ± √(3937)i
Factored: f(x) = (x + 12 + 62.745517768204i)(x + 12 - 62.745517768204i)
Discriminant: -15748
Vertex: (-12, 3937)
Sum of Roots (-b/a): -24
Product of Roots (c/a): 4081
∴ We can't find dimension of the painting because length of painting is imaginary form.
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Jacob built a box with a volume of 90 cubic meters.
Choose all the boxes that Jacob could have built.
Answer:
A and D
Step-by-step explanation:
[tex]\sf \boxed{\text{\bf Volume of rectangular box = length * width * height}}[/tex]
A) Volume of the given box = 6 * 3 * 5
= 90 cubic meters.
D) Volume of the given box = 3 * 2 * 15
= 90 cubic meters
One liter of interior paint covers 100 square feet. How many gallons of paint does it take to cover 800 square meters of walls?
By doing some changes of units, we can see that we will need 22.61 gallons of paint to cover 800 square meters.
How many gallons does it take to cover 800 square meters of walls?
We know that with one liter of interior paint we can cover 100 square feet.
Remember the relation between square feet and square meeters:
1ft^2 = 0.092 m^2
Then with one liter we can cover:
100ft^2 = 100*0.092 m^2 = 9.2 m^2
So the number of liters of paint that we need to cover the 800 m^2 is given by the quotient:
L = 800m^2/9.2m^2 = 86.96
We need 86.96 liters of paint, and the relation between liters and gallons is:
1 L = 0.26 gal
Then we need:
86.96 L = 86.96*(0.26 gal) = 22.61 gal
We will need 22.61 gallons of paint to cover 800 square meters.
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I WIL VOTE BRAINLISET SOMEONE PLEASE HELP
Answer:
26.0 cm
Step-by-step explanation:
Given quadrilateral ABCD with diagonal BD forming triangles ABD and BCD, and angles A=90°, C=52°, ADB=35°, and CBD=52°, you want the length of CD to 3 significant figures.
Law of SinesThe law of sines tells you the relation between sides and opposite angles is ...
a/sin(A) = b/sin(B) = c/sin(C)
This lets us write two proportions that can be solved for the measure of CD.
In triangle ABD:
BD/sin(A) = AB/sin(D)
BD = AB·sin(90°)/sin(35°) = 12 cm/sin(35°) ≈ 20.921 cm
In triangle BCD:
CD/sin(B) = BD/sin(C)
CD = BD·sin(B)/sin(C) = 20.921 cm·sin(102°)/sin(52°) ≈ 25.969 cm
The length of CD is about 26.0 cm.
( m n ) (x) for x = −3
The value of the composite function (mn)(-3) is 9
How to determine the value of the composite function?The given parameters are:
m(x) = x
n(x) = -3
The composite function is given as
(mn)(x)
The above composite function is calculated as
(mn)(x) = m(x) * n(x)
Substitute -3 for x in the above function
So, the above function becomes
(mn)(-3) = m(-3) * n(-3)
So, the above function becomes
(mn)(-3) = -3 *-3
Evaluate the product in the above equation
So, we have
(mn)(-3) = 9
Hence, the value of the composite function (mn)(-3) is 9
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Complete question
If m(x) = x and n(x) = -3, calculate ( m n ) (x) for x = −3
The median for the given set of six ordered data values is 29.5
7 12 23 __ 41 50 What is the missing value?
Answer: 36
Step-by-step explanation:
Median of an even number data set, you would add the two middle numbers divided by 2. Answer is 36. See attached solution
Hunter measured the middle school and made a scale drawing. The scale he used was 1 inch : 10 feet. The gym is 7 inches wide in the drawing. How wide is the actual gym?
Answer:
70 ft
Step-by-step explanation:
You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.
Scale factorEach inch represents 10 feet, so 7 inches will represent ...
7 × 10 ft = 70 ft
The gym is 70 ft wide.
__
Additional comment
You can also write and solve an equation that shows the measures are proportional:
actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)
Multiplying both sides of this proportion by 7 in, we have ...
gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft
The function has a minimum or maximum. Looking for help with screenshot
Answer:
The function has a minimum of -1 at x = 3
The function is increasing on the interval: (3,∞)
The function is decreasing on the interval (-∞,3)
Step-by-step explanation:
Since our parabola opens upwards on the graph, the function has a minimum.
The minimum is the lowest x-value and y-value in the function.
From left to right, the function is moving downwards (decreasing) from x = -∞ to x = 3.
From left to right, the function is moving upwards (increasing) from x = 3 to x = ∞