Answer:
$16,000
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = Interest accruedP = Principal amountr = Interest rate (in decimal form)t = Time (in years)Let investment 1 be the bond that pays 5.75% simple interest.
Let investment 2 be the bond that pays 7.25% simple interest.
Given:
P₁ + P₂ = $28,000r₁ = 5.75% = 0.0575r₂ = 7.25% = 0.0725t = 1 yearCreate two equations for the interest from both investments.
Interest from Investment 1
[tex]\implies \sf I_1=P_1 \cdot 0.0575 \cdot 1[/tex]
[tex]\implies \sf I_1=0.0575\:P_1[/tex]
Interest from Investment 2
[tex]\implies \sf I_2=P_2 \cdot 0.0725 \cdot 1[/tex]
[tex]\implies \sf I_2=(28000-P_1)0.0725[/tex]
[tex]\implies \sf I_2=2030-0.0725\:P_1[/tex]
Given that the sum of the interest from both investments is $1,790:
[tex]\implies \sf I_1+I_2=1790[/tex]
[tex]\implies \sf 0.0575\:P_1+2030-0.0725\:P_1=1790[/tex]
[tex]\implies \sf -0.015\:P_1=-240[/tex]
[tex]\implies \sf P_1=16000[/tex]
Therefore, $16,000 should be invested in the 5.75% bond.
Check:
[tex]\implies \sf I_1=16000 \cdot 0.0575 \cdot 1 = 920[/tex]
[tex]\implies \sf I_2=12000 \cdot 0.0725 \cdot 1 = 870[/tex]
[tex]\implies \sf I_1+I_2=920+870=1790[/tex]
Which graph represents an exponential function?
In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of ther- mal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.
Ğ¢ÑÑеп ni xi si
Graded 42 0.486 0.187
No-fines Ñ 42 0.359 0.158
Assume that the conductivity for each sample of concrete is independent of that of all the others. Our interest is in determining if the mean conductivity for the graded concrete is significantly different than the mean conductivity for the no-fines concrete?
Required:
a. Formulate the above in terms of a hypothesis testing problem.
b. Give the test statistic and its reference distribution (under the null hypothesis).
c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.
Step-by-step explanation:
Given - In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of thermal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.
Type ni xi si
Graded 42 0.486 0.187
No-fines 42 0.359 0.158
To find - a. Formulate the above in terms of a hypothesis testing problem.
b. Give the test statistic and its reference distribution (under the null hypothesis).
c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.
Proof -
a.)
Hypothesis testing problem :
H0 : There is significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
H1 : There is no significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
b)
Test statistic :
[tex]Z = \frac{x_{1} - x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1}} + \frac{s_{2}^{2} }{n_{2}} } }[/tex]
[tex]Z = \frac{0.486 - 0.359 }{\sqrt{\frac{0.03496 }{42} + \frac{0.02496 }{42} } }[/tex]
[tex]Z = \frac{0.127 }{\sqrt{0.001468}}[/tex]
[tex]Z = \frac{0.127 }{0.0377}[/tex]
⇒Z(cal) = 3.3687
Z(tab) = 1.96
As Z (cal) > Z(tab)
So, we reject H0 at 5% Level of significance
p-value = 0.99962
Hence
There is significant difference in mean conductivity at the two materials.
The graph of a linear function
is shown on the grid.
What is the rate of change of y with respect to x for this function?
Record your answer in the space below.
What is 7/10 × 2 5/6
Answer:
1.983 or about 1 1/6
hope this helped!
A can of tuna has a diameter of 4 Inches and a helght of 3 inches. What is the volume of the can of tuna? (Use 3.14 for
TT.)
37.68 in 3
150.72 in. 3
56.52 in 3
113.04 in. 3
Answer:
37.68 Inches cubed (A)
Step-by-step explanation:
The formula for a cylinder is:
πr^2(h)
First, let's find the radius, which is:
4/2 = 2
Now, we can plug in the values:
3.14(2)^2(3)
Do exponents first:
3.14(4)(3)
Multiply left to right:
12.56(3)
Again:
37.68 Inches
So, the answer is:
37.68 Inches cubed (Or A)
Hope this helps!
Help me plzzzzzzzzzz I give u BRAINLY
The answer is
X= 3 and Y= -4
Answer:
If you are solving for substitution then the anwser is x+3, and y = -4 (3, -4)
Step-by-step explanation:
First you solve for x
x-2y=11 to x = 11 + 2y
Then you plug it in to the first equation.
-7 (11 + 2y)- 2 = -13 Then Simplify. -77 - 16y= -13
Solve for Y.
Add 77 to both sides. -16y= 64
Divide both sides by -16
y= -4
The Solve for X
x=11 + 2 x -4
X=3
Therefore the anwser is (3, -4)
A particular curve is represented parametrically by x=cost, y=−sint, t∈[0,2π]. (a) As t increases on [0,2π], in which direction is the point (x(t),y(t)) moving? the movement is clockwise (b) What is the corresponding Cartesian equation for this curve (the equation in x and y only)? Cartesian equation: functionsequation editor =0. Note! xyy=x2+1y−x2−1=0y−x2−1 (c) Give the smallest and largest values of y taken by this curve functionsequation editor ≤y≤ functionsequation editor .
Answer:
a) clockwise sense
b) x² + y² = 1
c) y ∈ [0,1]
Step-by-step explanation:
a) x = cos (t) y = -sin (t)
for t ∈ [ 0 , 2π ]
for t = 0 point P is x = cos (0) = 1 y = -sin (0) y = 0
The point is on the x axis
Now let´s see what happens for t = π/4
x = cos (π/4) x = √2/2 and y = - sin (π/4) y = - √2/2
Note π/4 is 45°
The coordinates of the new point P ´(t = π/4) are in the fourth quadrant
that means the point is moving clockwise sense.
b) x = cos(t)
y = -sin(t)
Squaring on both sides of each equation we get:
x² = cos²t
y² = sin²(t)
Adding side by side
x² + y² = cos²t + sin²t
x² + y² = 1
Values for y are y ( 0 , 1)
I am trying to find the answer to (in photo). But my calculator wont give me the answer. Does anyone know the answer to it? Or know how to calculate it without a calculator?
Answer:
[tex]\sqrt{13}[/tex] = 3.605551275......
Step-by-step explanation:
[tex]\sqrt{13}[/tex]
3.6
3 [tex]\sqrt{13}[/tex]
-9
36[tex]\sqrt{4}[/tex]00
do you need to know more... ??
9514 1404 393
Answer:
√13 ≈ 3.60555127546
"by hand": 3 4/7 or 398143/110425 or 3.6055 or 3 23/38
Step-by-step explanation:
Most on-line calculators, calculator apps for phone or tablet, and any spreadsheet can calculate this for you. The first attachment shows the result from the Go.ogle calculator.
Here, we describe 4 methods of approximating the root "by hand." That is, the calculations can be done with pencil and paper. They are easily within the capability of a 4-function calculator.
__
Method 1 -- Linear approximation
You can approximate it by hand in the following way.
√13 is between √9 = 3 and √16 = 4. As a first approximation, it is ...
3 + (13 -9)/(16 -9) = 3 4/7 ≈ 3.57 ≈ 3.6
This is a linear interpolation between √9 and √16.
_____
Method 2 -- Babylonian method
The "Babylonian method" can be used to refine this approximation. For the next guess, average this number and the quotient 13 divided by this number.
x = (3 4/7 + (13/(3 4/7))/2 = (25/7 + 13·7/25)/2 = (625 +637)/350 = 631/175
x = 3 106/175 ≈ 3.6057 . . . . . . good to 3 decimal places
One more iteration will double the number of correct decimal digits.
x = (3 106/175 + 13/(3 106/175))/2 = 398143/110425 ≈ 3.60555127915
(correct digits are highlighted)
_____
Method 3 -- "long division"
There is also a "long-division" method that develops the root one digit at a time. This is described in the second attachment, an extract from the NIST web site. For a number like 13, you would use 13.00 00 00 00 as the initial "dividend" to get a 4-digit root.
_____
Method 4 -- continued fraction
Once you realize that the root is between 3 and 4, you can write a "continued fraction" for the fractional part:
3 +x = √13 . . . . . . where x is the fractional part of the root
(3 +x)² = 13 . . . . . . square both sides
x² +6x +9 = 13 . . . expand the square
x(x +6) = 4 . . . . . . . subtract 9 and factor
x = 4/(6 +x) . . . . . . write as an iterator (continued fraction)
At this point, we can say x = p/q for some integers p and q. Then the next iteration is ...
p/q = 4/(6 +p/q) = 4q/(6q +p)
That is, successive approximations of x can be had by the transformation ...
(p, q) ⇒ (4q, 6q+p)
Starting with the linear interpolation fraction x=4/7, the next refinements using this method are ...
(p, q) = (4, 7) ⇒ (28, 46) = (14, 23)* ⇒ (92, 152) = (23, 38)
At this point, you have approximated the root as 3 23/38 ≈ 3.6053, accurate in the third decimal place. Convergence is clearly much slower than using the Babylonian method.
__
* We have reduced the fraction p/q = 28/46 to 14/23 in order to keep the numbers as small as possible. Similarly, 92/152 is reduced to 23/38.
CAN SOMEONE HELP ME and please tell me the right answer this test means a lot to me :(
Please explain how you got the answer!
Answer:
16
Step-by-step explanation:
1250/ 80 = 125/8 ≈ 15.6 rounds up to 16
Find the area of the polygon to the nearest square inch.
Answer:
137 in.^2
Step-by-step explanation:
A = nsa/2
where
n = number of sides = 9
s = length of side = 4.7 in.
a = length of apothem = 6.5 in.
A = (9)(4.7 in.)(6.5 in.)/2
A = 137.475 in.^2
Answer: 137 in.^2
can someone show work and explain ??
Answer:
481 cubic inches
Step-by-step explanation:
Volume of the figure = Volume of the triangular prism + rectangular prism
Volume of the triangular prism = Base area * height
Volume of the triangular prism = (1/2*5*3) * 6
Volume of the triangular prism = 15/2 * 6
Volume of the triangular prism = 15 * 3
Volume of the triangular prism = 45in³
Volume of the rectangular prism = 16*7*3
Volume of the rectangular prism = 336in³
Volume of the figure = 45+336
Volume of the figure = 481 cubic inches
Which of the following is the logical conclusion to the conditional statements
below?
a = b
b=0
А. b=a
B. -as
C.boa
D. a =
Answer:
b
Step-by-step explanation:
Are these 4 questions correct? If anything is wrong, let me know and tell me what is correct.
Answer:
they're all correct
Step-by-step explanation:
I think, if it's wrong I'm very sorry, but I'm fairly sure they're right
hope this helps:)
What is the solution to this equation?
2X + 10=28
Answer:
x = 9
Step-by-step explanation:
2X + 10=28
Subtract 10 from each side
2X + 10-10=28-10
2X = 18
Divide each side by 2
2X/2 = 18/2
x = 9
Answer:
X=9
Step-by-step explanation:
28-10=18
2 x 9= 18
plz help me with this question and plz do NOT put links in when answers
Answer:
Remember to add up the 2 angles they give you and subtract it from 180. Then you will get the answer for each question.
5 x 100 + 4 x 10 + 6 x 1 + 2 x ( 1/10) + 8 x ( 1/1000) =?
Answer:
68276/125
Step-by-step explanation:
500+40+6+1/5+1/125
546+26/125
68276/125
Answer:
546.208
Step-by-step explanation:
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{\color{#c92786}{5}} \cdot {\color{#c92786}{100}}+4 \cdot 10+6 \cdot 1+2x(\frac{1}{10})+8x(\frac{1}{1000})
5⋅100+4⋅10+6⋅1+2x(101)+8x(10001)
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500+{\color{#c92786}{4}} \cdot {\color{#c92786}{10}}+6 \cdot 1+2x(\frac{1}{10})+8x(\frac{1}{1000})
500+4⋅10+6⋅1+2x(101)+8x(10001)
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500+40+{\color{#c92786}{6}} \cdot {\color{#c92786}{1}}+2x(\frac{1}{10})+8x(\frac{1}{1000})
500+40+6⋅1+2x(101)+8x(10001)
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500+40+6+{\color{#c92786}{2}}x \cdot {\color{#c92786}{\frac{1}{10}}}+8x(\frac{1}{1000})
500+40+6+2x⋅101+8x(10001)
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500+40+6+\frac{1}{5}x+8x(\frac{1}{1000})
500+40+6+51x+8x(10001)
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500+40+6+\frac{1x}{5}+8x(\frac{1}{1000})
500+40+6+51x+8x(10001)
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500+40+6+\frac{x}{5}+{\color{#c92786}{8}}x \cdot {\color{#c92786}{\frac{1}{1000}}}
500+40+6+5x+8x⋅10001
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500+40+6+\frac{x}{5}+\frac{1}{125}x
500+40+6+5x+1251x
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{\color{#c92786}{500}}+{\color{#c92786}{40}}+{\color{#c92786}{6}}+\frac{x}{5}+\frac{x}{125}
500+40+6+5x+125x
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{\color{#c92786}{546}}+\frac{x}{5}+\frac{x}{125}
546+5x+125x
Show less
Solution
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The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.
1500 bricks for $1,110.00
1300 bricks for $845.00
1300 bricks for $845.00
230 bricks for $170.20
230 bricks for $170.20
100 bricks for $75.00
100 bricks for $75.00
35 bricks for $25.90
Answer:
35 bricks for $25.90
35 bricks for $25.90
230 bricks for $170.2
Step-by-step explanation:
Cost per brick = number of bricks / price of bricks
1500/$1110 = $1.35
1300 / $845 = $1.54
230 / $170.20 = $1.35
100 / $75 = $1.33
35 / $25.90 = $1.35
Based on these calculations, the bricks that have the same cost per brick are :
35 bricks for $25.90
35 bricks for $25.90
230 bricks for $170.20
What is the circumference in centimeters of the circle? Use 3.14 for 7. Enter your answer in the box
24 cm
cm
Answer:
75.36
Step-by-step explanation:
24 cm x 3.14 = 75.36
Given the graph below, which of the following statements is true?
Answer:
A. the graph represent a one - to - one function because every x-value is paired with only y-value
Step-by-step explanation:
that's it
3186 people contributed to charity. this was an increase of 486 people over last year. Express the increase as a percentage.
Answer:
18%
Step-by-step explanation:
Given data
People that contributed the last year= 3186-486
=2700people
Hence the percentage change
=486/2700*100
=0.18*100
=18%
Hence the change in the number of people that contributed is 18%
Roman used 10% off coupon to buy a toaster that was originally priced at $18.48. Is the final amount cheaper or more expensive than the original price?
Correct answer gets Brainliest! Have an amazing day!! :)
what is the point in mulitplucation
Answer:
its good for life and career choices
Step-by-step explanation:
Multiply the numbers just as if they were whole numbers.
Line up the numbers on the right - do not align the decimal points.
Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
Add the products.
Four friends share 3 sheets of construction paper equally.
Value of x in this? Having trouble with this problem.
4. Which set of ordered pairs represents a function?
(1) {(0,4), (2,4),(2,5)}
(2){(6,0), (5,0),(4,0)}
(3) {(4,1),(6,2), (6,3), (5,0)}
(4) {(0,4),(1,4), (0,5),(1,5)}
Answer: (2) {(6,0), (5,0),(4,0)}
It is a function, where each value is associated with exactly one output.
Step-by-step explanation:
A relation is said to be a function if the first components of the ordered pairs are associated with exactly one value of the second components of the ordered pair.
(1) {(0,4), (2,4),(2,5)}
here 2 is associated with 2 different values of second component.
Thus it is not a function.
(2) {(6,0), (5,0),(4,0)}
It is a function, where each value is associated with exactly one output.
(3) {(4,1),(6,2), (6,3), (5,0)}
It is not a function as 6 is associated with 2 different values of second component.
(4) {(0,4),(1,4), (0,5),(1,5)}
It is not a function as 0 and 1 are associated with 2 different values of second component.
Helpppppppp math pls I need help asap
Identify the coordinates for point A. Type your answer in the form (# #), without spaces.
Answer:
(-4,3)
Step-by-step explanation:
Hope this helps. :)
14 in. = _____ ft
Plzzzzzzzz help
Answer:
1.2
Step-by-step explanation:
12 in= 1 foot
Answer:
1.16 feet
Step-by-step explanation:
12 inches in one foot so there are 14 inches in 1.16 feet.
URGENT HELP Graph f(x) = 3|x - 5| + 1 (please put picture of the answer graphed)
Answer:
Step-by-step explanation:
I uploaded a picture of the graph, but you can go to the site, Desmos. Just plug in your equation, and you will get the equation graphed.