Answer
Amount invested at 6% interest = 17,000
Explanation
The simple interest on an invested principal (P), at a rate, R, for a period of time, T, is given by
Simple Interest = (PRT/100)
Let the amount invested at 6% be x
Let the amount invested at 7% be y
Sum of these amounts is $41,000
x + y = 41000
Simple Interest on x for 1 year
SI = (x × 6 × 1/100) = 0.06x
Simple interest on y for 1 year
SI = (y × 7 × 1/10) = 0.07y
Sum of annual interest = $2,700
0.06x + 0.07y = 2700
Now, we have a simultaneous equation
x + y = 41000
0.06x + 0.07y = 2700
Solving this simultaneously,
x = 17,000
y = 24,000
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A is the point (-6, 5) and B is the point (-2,-3). (a) Find the equation of the straight line, I, that passes through point A and point B. Give your answer in the form y=mx+c.
The linear equation that passes through the point (-6, 5) and B is the point (-2,-3) is:
y = -2x - 7
How to find the linear equation?
A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
In this case, we have the points (-6, 5) and (-2,-3), then the slope is:
s = (-3 - 5)/(-2 + 6) = -8/4 = -2
Then we have:
y = -2*x + c
To find the value of the constant we use one of the points, I will use (-2, -3) to get:
-3 = -2*(-2) + c
-3 = 4 + c
-3 - 4 =c
-7 = c
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You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company offers a salary of $ 270 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good?
One needs to sell $6750 worth of goods to make the straight commission be at least good to the secondary offer
Straight offer = 6% commission on the sales
Second offer = $270 + 2% of the sales
For the straight offer to be competitive with the second offer it should be able to cover the fixed income of $270
Let x be the sales made in the week
Formulating the equation we get the following:
6% of x = 270 + 2% of x
6/100x = 270 + 2/100x
4/100x = 270
x = 6750
So, for sales up to $6750, the second job offer is good, while for sales more than $6750 the first job offer is good
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use the distribution method to solve the system of equations. enter your answer as an ordered pair. y=7x+6 and y=x+20
y = 7x+6
y = x + 20
Substituting the value of y of the second equation into the first equation, we get:
x + 20 = 7x + 6
20 - 6 = 7x - x
14 = 6x
14/6 = x
7/3 = x
Replacing this value into the first equation, we get:
[tex]\begin{gathered} y=7\cdot\frac{7}{3}+6 \\ y=\frac{49}{3}+6 \\ y=\frac{49+6\cdot3}{3} \\ y=\frac{67}{3} \end{gathered}[/tex]The solution as an ordered pair is (7/3, 67/3)
The graph of a function g is shown below.
Find g (-4)
a different ratio that is equivalent to 3 over 5
Answer:
6 over 10
Step-by-step explanation:
You can use any number, but I used 2. You can multiply both numbers by any whole number, me using 2. I timed 3 by 2 which is 6. And 5 times 2 is 10. So, we have 6 over 10. And we can use 3, 4, 5, 6, and so on, it doesn't matter it is still the same. Just, make sure you multiply both numbers by the same number.
find x=___°please help
Step 1: We have two triangles with the following information:
• Upper Triangle has two known angles: 29 and 52 degrees
,• Lower Triangle has one known angle: 33 degrees and two unknown: x and the third angle
Step 2: Let's find the third angle of the upper triangle, as folllows:
Third angle = 180 - 29 - 52
Third angle = 99
Step 3: Now we can see that the angle we just found on Step 2 is a congruent angle with the third angle from the lower triangle, which means they are equal.
Therefore, we know two angles of the lower triangle:
99 and 33
With these measurements, we can calculate x, as follows:
x = 180 - 99 - 33
x = 180 - 132
x = You can calculate the difference now
Write in terms of the cofunction of a complementary angle.
given the expression
[tex]sin(\frac{\pi}{15})[/tex]since
[tex]sin(\theta)=\frac{1}{csc(\theta)}=cos(\frac{\pi}{2}-\theta)[/tex]then
[tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{\pi}{2}-\frac{\pi}{15})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{(15-2\pi)}{30})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=cos(\frac{13\pi}{30})[/tex]ten the correct answer is
Option C
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 17 HCF of water is $32.13 and the cost for using 35 HCF IS 61.83. . What is the cost for using 19 HCF of water?
If the cost for using 35 HCF IS 61.83. . the cost for using 19 HCF of water is :$68.31.
How to find the cost price?Straight line: y=mx+b, m=slope, b=y-intercept
Let y=cost of using 19 HCF water
Let x =amount of water used
m=∆y/∆x =(61.83 - 32.13) / (35-19)
m=∆y/∆x =29.7 /16
m=∆y/∆x = 1.85625
m=∆y/∆x = 1.86 ($/HCF) (approximately)
equation: y=1.86x+b
Solving for b using point (19, 32.13)
32.13 =1.86×19+b
32.13=35.34+b
b=35.34 -32.13
b=3.21
equation:
f(x)=1.86x+3.21
f(25)=1.86×35+ 3.21
= 68.31
Cost of using 35 HCF water= $68.31
Therefore the cost price is $68.31.
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what number is not part of the solution set for the inequality below?3x-18> 1210, 11, 15,8 _
First, let's solve for x in the inequality to find an interval, the options that are not included in the interval are not part of the solution set, we can do it by following these steps:
1. 3x-18> 12 , add 18 on both sides:
3x - 18 + 18 > 12 + 18
3x > 30
2. Divide both sides by 3:
3x/3 > 30/3
x > 10
So, to be a part of the solution, x must be greater than 10, then the interval that represents the solution is (10, ∞). From the given options, the only one that is not included in this interval is 8, because it is less than 10, then the answer is 8.
What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Answer: B. Symbolic - the "Queen" represents suppression and deceit.
The angle between 0° and 360° and is coterminal with a standard position angle measuring 1652° angle is ______ degrees.
Please help me find the answer for the blank.
Answer:
212°
Step-by-step explanation:
Keep subtracting 360 from 1652 until you get a number under 360
The weight of a goat increased by 12 pounds is 38 pounds. Which equation represents the situation?
Given that the weight of goat increased by 12 pounds to be 38 pounds.
It means that the weight became 38 pounds after attaining an extra 12 pounds to its initial weight.
Suppose that 'x' is the initial weight of the goat, then adding 12 to is will become 8,
[tex]x+12=38[/tex]Therefore, the third option is the correct choice.
perfect pizza has 16 Toppings
listed on their menu how many ways can a customer choose a piece of that contains five different toppings
Factorial five. Factorial 16-5. And the response to this question is 4368. There are therefore 4000 368 options for these pizzas with five toppings.
The sum of all positive integers less than or equal to n, indicated by the symbol n!, is the factorial of a non-negative integer n. Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1. The mathematical operation known as a factorial, denoted by the symbol (! ), multiplies a number (n) by each number that comes before it. The factorial function instructs you to multiply all the whole numbers starting at the selected number and going all the way down to one. In further mathematical terms, a number's factorial (n!) equals n (n-1)
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Which expression is missing from step 7?
OA.(d- e)²
OB. -2de
OC. (A+B)2
OD. A²+ B²
The correct option A. (d- e)², is the expression is missing from step 7.
What is termed as the Pythagorean theorem?The Pythagorean theorem, or Pythagorean theorem, tries to explain the relationship among the three sides of such a right-angled triangle. The square on the hypotenuse is equal to the total of the squares of the remaining two sides of a triangle, according to Pythagoras' theorem. According to Pythagoras' theorem, when a triangle has been right-angled (90 degrees), the square of the hypotenuse equals the sum of the squares of the remaining two sides.For the given question.
The missing value of the 7th term is -
(√1 + d²)² + (√e² + 1)² = (d- e)²
Such that the 8th terms becomes after squaring the both sides are;
(1 + d²) + (e² + 1) = d² + e² - 2de.
Thus, the missing term in the step 7 is (d- e)².
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I need to check my answer for number 1 I put C.
Given
[tex]f(x)=3(\frac{1}{2})^x[/tex]Find
Plot the graph
Explanation
To plot the graph we need points ,
let
[tex]undefined[/tex]A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x2−10x+25 yd2. Area of the flagpole plot: x2−10x+25 A plaza square with a small flagpole square in the middle. 100 yards100 yards Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.) The length of the base of the flagpole is
The area of the flagpole is:
[tex]x^2-10x+25[/tex]This represents a perfect square, because it can be represented as below:
[tex]x^2-2\cdot5+5^2[/tex]Therefore we can use the notable product, square of the difference to factor the expression:
[tex](x-5)^2=(x-5)\cdot(x-5)[/tex]Since the area of the flagpole is the product between it's length and width, then we know that the length and width are equal and are equivalent to:
[tex]\text{length}=\text{width}=(x-5)[/tex]How do I solve for the role of 0 in this equation?(x²-9)(x³-8)=0
Given the equation
[tex](x^2-9)\cdot(x^3-8)=0[/tex]you should have in mind that the expression x^2-9 and x^3-8 are "numbers" and that the product of two numbers is zero if and only if one of the numbers is zero. Then, by using this, you get the following auxiliary equations
[tex]x^2-9=0[/tex]which is equivalent to
[tex]x=\sqrt[]{9}[/tex]so x=3 o x=-3.
Finally, for the other case
[tex]x^3-8=0[/tex]So
[tex]x=\sqrt[3]{8}=2[/tex]so the three possible solutions for the equation are x=3, x=-3 and x=2
HELPPPPP. will give brainliest
Answer:
The maximum value is the same for both functions
Step-by-step explanation:
f(x) maximum is (0,5)
g(x) maximum is (2,5)
Answer:
The maximum value is the same for both functions.
Please give me brainlist!!!
help!!! please see image, thanks
The smallest whole numbers that makes the statement true are:
(a) 41 - 9 ≡ 2 (mod 5)
(b) 17 + 8 ≡ 4 (mod 7)
Let a, b and m be integers. Then a is said to be congruent to b modulo m if m divided a-b. That is,
a ≡ b(mod m) if and only if m divided a-b.
Also here, if b is the smallest integer satisfying this relation, then b is the remainder when a is divided by m.
(a) So for 41 - 9 ≡ (mod 5)
⇒ 32 ≡ (mod 5)
The smallest whole number satisfying this congruence is the remainder when 32 is divided by 5 which is 2.
That is, 41 - 9 ≡ 2 (mod 5)
(b) Similarly for 17 + 8 ≡ (mod 7)
⇒ 25 ≡ (mod 7)
The smallest whole number which makes this statement true is the remainder when 25 is divided by 7, which is 4.
Hence, 17 + 8 ≡ 4 (mod 7)
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Hypothesis p is false and conclusion q is false. So, the statement
∼q⟶p
True or false
If the Hypothesis p is false and conclusion q is false then the disjunction ∼q⟶p is false.
What is conjunction?In classic propositional logic, a conjunction is a binary operator, that is, used to connect two propositions. A conjunction between two propositions is always true if and only if each of the two propositions are also true, otherwise the compound proposition is false.
Logic Disjunction; consider p and q are propositions.
The dis-junction of p and q, is denoted by p ∨ q, is the proposition called "p or q".
The rule for the 'or' operation would be; If any of the propositions are true, then the result is true.
Thus, If the Hypothesis p is false and conclusion q is false then the disjunction ∼q⟶p is false.
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A pole that is 3.1 m tall casts a shadow that is 1.46 m long. At the same time, a nearby tower casts a shadow that is 38.5your answer to the nearest meter.long. How tall is the tower RoundIM
82 meters
Explanation
Step 1
Draw:
as the angle of the sun´s ligth is the same for both, we have two congruent trianges, then we can make a proportion
[tex]\text{ratio}=\frac{heigth}{\text{shadow}}[/tex]so
[tex]\begin{gathered} \text{ratio}_1=ratio2 \\ \text{replacing} \\ \frac{3.1}{1.46}=\frac{x}{38.5} \\ to\text{ solve, multiply both sides by 38.5} \\ \frac{3.1}{1.46}\cdot38.5=\frac{x}{38.5}\cdot38.5 \\ 81.74\text{ m=x} \\ \text{rounded} \\ x=82 \end{gathered}[/tex]therefore, the heigth of the tower is
82 meters
Find the surface area of the prism. 5 m 1 1 4646 om 13 m Not drawn to scale 195 m2 O 48 m2 780 m2 346 m2
Prism surface is formed by
2 rectangles x and 2 rectangles y ,2 rectangles z
then
Area of rectangles for x= 2x13x6 = 156 m2
. For y = 2x5x6= 60 m2
. For z = 2x13x 5 = 130 m2
Then now add all these results
Prism area = 156 + 60 + 130 = 346
Then answer is
OPTION D) 346 m2
The perimeter of a rectangular field is 338 yards. If the width of the field is 77 yards, what is its length?
2(l+b)=338 2(l+77)=338
154×l=338 l=338÷154=2ans
Answer:
The length is 92 yards.
Step-by-step explanation:
Just use the rectangle perimeter formula and substitute the given values.
P=2l+2w Rectangle formula
We know the perimeter and the width already.
So, 338=2L+2(77)
Now solve:
338=2L+154
338-154=2L
184=2L
184/2=L
92=L Answer
1. Think of a real-life situation, where knowing the percent error would be helpful.2. In a short paragraph, describe the situation and include the percent error. Explain why knowing the percent error is helpful.
SOLUTION:
The percent erroris helpsful in many situations. An example will be when conducting
Choose the function whose graph is given below. 1 į į NA 5 in A. Y= CSC X B. y= tan x O c. y = sec x OD. y = cotx
In the picture there is graph. The graph has a function is y=secx. The option c is correct.
Given that,
In the picture there is graph.
We have to find the graph has a function.
The graph is of y=secx.
Secant will not present at
x = - 5∏/2 , - 3∏/2 , -∏/2 , ∏/2, 3∏/2 , 5∏/2
At certain places, the graph will also include asymptotes. The graph of the secant on the range of - 5∏/2 is shown below. - 5 ∏/2
The graph also always has a value greater than 1 and less than -1. It shouldn't come as a huge surprise. Keep in mind that -1≤ cos (x)≤ 1. One will be more than one when divided by a number that is less than one. Additionally, 1 / ±1 = ±1, therefore we obtain the following secant ranges.
We can write as sec(x)≥1 and sec(x)≤-1
Therefore, the graph has a function is y=secx. The option c is correct.
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Are the following ratios equivalent?5cookies:9 glasses of milk and 3 cookies :12 glasses of milk
Answer:
No
Step-by-step explanation:
5:9 and 3:12 do not divide with the same number
For example:
3:6 and 9:18 would be equivalent as dividing 9:18 by 3 would give 3:6
Find the exact value of the indicated trigonometric function of θ.
cos θ = (2/5), tan θ < 0 Find sin θ.
The exact value of indicated trigonometric function, sin θ is -0.92
How to find a sine relation when a cosine relation is given?The sine relation is the ratio of the height to the hypotenuse. Meanwhile, the cosine relation is the ratio of the base to the hypotenuse.
The relation of sine and cosine is given as follows:
[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}[/tex]
It is given that cos θ = (2/5)
So, the sine value can be obtained from the given value.
[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}\\=\pm\sqrt{1-(2/5)^2}\\=\pm\sqrt{21}/5\\ =-0.92[/tex]
So, the sine value for the given cosine value is - [tex]\sqrt{21}/5[/tex] or -0.92.
Note that we omitted the positive value because it is given that the tangent value is negative, so the angle lies in the fourth quadrant, where the sine value is also negative.
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What is the rate of return when 12 shares of Stock
A, purchased for $22/share, are sold for $465? The
commission on the sale is $9.
Rate of Return = profit or loss
total cost
First, calculate the total cost.
Hint: 12 shares were purchased for $22
each. So first, we'll multiply 12 - 22.
12- $22= $[?]
The rate of return of the 12 shares purchased by A is 72.72%.
Here, we are given that A purchases 12 shares at $22 per share.
So the cost price of 12 shares will be = 12 × 22
= 264
A sold these shares at $465.
The commission on sale = $9.
Thus, the total cost of the shares will be = 264 + 9
= $273
Hence, the total profit of A will be-
465 - 273
= 192
The rate of return is calculated as-
Rate of return = profit/cost price × 100
Thus, here-
Rate of return = 192/264 × 100
= 0.7272 × 100
= 72.72%
Thus, the rate of return on these 12 shares purchased by A is 72.72%.
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Determine the intercepts of the line
Find the value of sin t if tan t = 1 and pi/2 < t < 3pi/2
The value of sin t = sin 135° = 1/√2
What are trigonometric functions?The trigonometric functions are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths. They are also known as circular functions, angle functions, or goniometric functions[1][2]. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given; tan t = 1
And the given condition is π/2 < t < 3π/ 2
this mean t lies in the 2nd quadrant because the value of t lies between 90 and 270 degrees.
This means tan t = tan (90 + 45)= cot 45 = 1
thus t = 235 degree
And thus sin t = sin 135 ° = sin (90+ 45) = cos 45 ° = 1/ √2
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