Step-by-step explanation:
Given the equation that modeled the total public debt D (in trillions of dollars) in the United States at the beginning of each year from 2000 through 2008 can be approximated by;
D = 0.032t^2 + 0.21t + 5.6, 0 ≤ t ≤ 8
We are to find the total public debt with the time interval;
when t = 0;
D = 0.032(0)^2 + 0.21(0) + 5.6
D = 5.6 trillion dollars
when t = 1;
D = 0.032(1)^2 + 0.21(1) + 5.6
D = 0.032+0.21+5.6
D = 5.842 trillion dollars
when t = 2;
D = 0.032(2)^2 + 0.21(2) + 5.6
D = 0.128+0.42+5.6
D = 6.148 trillion dollars
when t = 3;
D = 0.032(3)^2 + 0.21(3) + 5.6
D = 0.288+0.63+5.6
D = 6.518 trillion dollars
when t = 4;
D = 0.032(4)^2 + 0.21(4) + 5.6
D = 0.512+0.84+5.6
D = 6.952 trillion dollars
when t = 5;
D = 0.032(5)^2 + 0.21(5) + 5.6
D = 0.8+1.05+5.6
D = 7.45 trillion dollars
when t = 6;
D = 0.032(6)^2 + 0.21(6) + 5.6
D = 1.152+1.26+5.6
D = 8.012 trillion dollars
when t = 7;
D = 0.032(7)^2 + 0.21(7) + 5.6
D = 1.568+1.47+5.6
D = 8.638 trillion dollars
when t = 8;
D = 0.032(8)^2 + 0.21(8) + 5.6
D = 0.032(64)+1.68+5.6
D = 2.048+1.68+5.6
D = 9.328 trillion dollars
From the values gotten, we can see that the total public debt reached or surpassed 7 trillion dollars in 2005
To get the public debt in 2017, we can simply substitute t = 17 into the expression D = 0.032t2 + 0.21t + 5.6
D = 0.032(17)^2 + 0.21(17) + 5.6
D = 0.032(289)+3.57+5.6
D = 9.248+3.57+5.6
D(17) = 18.418 trillion dollars
Use the dot plot to find the MEAN.
Answer:
Step-by-step explanation: To find the mean of the dot plot, you will need to add all of the dots together.
For example: Above 2, there are 3 dots , so you would need to multiply 2 by three to get 6 dots above the number 2.
Do that for all of the numbers on the dot graph from 1 - 6, and you will have this equation:
1 + 6 + 18 + 20 + 15 + 12
Next, you will need to add all those numbers together and you will get 72.
Lastly, divide by how many numbers there are, and there are 6 numbers.
So, that will be 72/6 which is 12.
Your answer will be 12.
Simplify as much as possible (and only have positive exponents)
Vincent had both chocolate cake and coconut cake at his birthday party. There were 20
people at the party, and 6 of them picked chocolate cake. What percentage of the people at
the party picked chocolate cake?
Write your answer using a percent sign (%).
Answer:
30%
Step-by-step explanation:
Step 1:
6/20 Divide
Step 2:
3/10 Simplify
Step 2:
30/100 Multiply
Answer:
30%
Hope This Helps :)
Answer:
[tex] \huge \bf \: solution[/tex]
[tex] \sf \: total \: people \: = 20[/tex]
[tex] \sf \: people \: picked \: chocolate \: cake = 6[/tex]
[tex] \huge \tt \: \: percent \: = \frac{6}{20} [/tex]
[tex] \tt \: now \: \\ \tt \: \frac{3}{10} [/tex]
[tex] \tt \: 3 \times 10 = 30[/tex]
[tex] \large \boxed{30\%}[/tex]
A cone has height h and a base with radius r. You want to change the cone so its
volume is halved. What is the new height if you only change the height? What is the
new radius if you only change the radius? Explain.
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Answer:
a) h/2
b) r/√2 = (r√2)/2
Step-by-step explanation:
a) The volume of a cone is proportional to height. If the volume is halved, then the height will be halved.
The new height will be h/2.
__
b) The volume is proportional to the square of the radius. If the volume is halved, the square of the radius is halved. The new radius will be ...
(r')² = r²/2
r' = r/√2 = (r√2)/2 . . . radius of half-volume cone
if there is no number in front of a letter, it is really number 1
Answer: Yes, if there is no number in front of a variable(or letter, as you said), it is actually 1.
a = 1a
x^2 = 1x^2
2m + n = 0 means 2m + 1n = 0
Step-by-step explanation:
Wes had 4.75 in quarters and dimes if he had 25 coins how many of each did he have?
Answer:it would be 15 quarters and 10 dimes
Step-by-step explanation:
15 quarters is 3.75 and 10 dimes is $1, add them up you get $ 4.75
Answer:
15 quarters and 10 dimes
Step-by-step explanation:
25x + 10(25-x) = 475
x = 225/15
x = 15
So that has to mean he has 10 dimes
Hope this helps!!!
The trapezoids are similar shapes. Find the lengths
1. Write the following as decimals
75
1
(a) 16% (b)
(c) 0.1% (d)
100
16
Answer:
the question isnt clear
Step-by-step explanation:
Answer:
a) 0.16
b) 100.00
c) 0.001
d) 16.00
Which one doesn't belong?Explain why
Answer:
6 or 33percent
Step-by-step explanation:
because he don't have a numerator
because he is not belong to the group the three is fraction and the first one is a percent
[tex]\huge\boxed{.6}[/tex]
Solution Steps:- Which doesn't belong -______________________________
- A rational number is a terminating or repeating decimal.
- An irrational number is when you can't write that number as a fraction.
Rational or Irrational: [tex]33[/tex]% = Rational number. ([tex]33[/tex]% = [tex]0.33[/tex], This is a terminating decimal.)[tex]\frac{1}{3}[/tex] = Rational number. ([tex]\frac{1}{3}[/tex] = [tex]0.3[/tex], This is a repeating decimal.)[tex]\frac{5}{3}[/tex] = Rational number. ([tex]\frac{5}{3}[/tex] = [tex]1.6[/tex], This is a repeating decimal.) [tex]\frac{}{.6}[/tex] = Irrational number. (You can't turn this into a true fraction, therefore it's irrational.)______________________________
Hope this helps!If you have anymore questions, or need help with anything else, feel free to ask!
235 people are at a summer camp. There are 35 more boys than girls, and 70 fewer adults than girls. How many people of each group are at the camp?
Answer:
125 boys, 90 girls and 20 adults
Step-by-step explanation:
Let the number of boys be x
Let the number of girls be y
Let the number of adults be z
If there are 235 people at the summer camp, then;
x + y+ z = 235 ..... 1
If there are 35 more boys than girls, then;
x = y + 35 .... 2
If there are 70 fewer adults than girls then;
y = z - 70
z = y - 70....3
Substitute 2 and 3 into 1;
x + y+ z = 235 ..
(y+35)+y+(y-70) =235
3y -35 = 235
3y = 270
3y/3 = 270/3
y = 90
Since x = y + 35
x = 90 + 35
x = 125
Also z = y - 70
z = 90+70
z = 20
There are 125 boys, 90 girls and 20 adults
Answer:
There are 90 girls, 125 boys, and 20 adults.
Step-by-step explanation:
Let x be the number of girls. How many boys were there?
x + 35
How many adults were there?
x - 70
We know that 235 people are at RSM summer camp. Use this to make an equation.
x + (x + 35) + (x - 70) = 235
x + x + 35 + x - 70 = 235
3x - 35 = 235
3x - 35 + 35 = 235 + 35
3x = 270
3x ÷ 3 = 270 ÷ 3
x = 90
x, x + 35, x - 70
90, 125, 20
The perimeter of the shape is 25.71 cm
Calculate the value of the radius
Take π to be 3.142
Answer:
The radius of the circle is: 4.09 cm
Step-by-step explanation:
Assuming the shape to be a circle.
The perimeter of a circle is called circumference and is given by the formula.
[tex]C = 2\pi r[/tex]
For the time being, we know
[tex]\pi = 3.142\\C = 25.71cm[/tex]
Putting the values in the formula we get: as x is the radius
[tex]25.71 = 2 * 3.142 * x\\25.71 = 6.284x\\x = \frac{25.71}{6.284}\\x = 4.09\ cm[/tex]
Hence,
The radius of the circle is: 4.09 cm
If a shirt manufacturer wanted to make shirts that fit most individuals, what characteristics would be better?
Answer:
a stretch shirt
Step-by-step explanation:
Find the present value that will grow to $1000 if the annual interest rate is 5.5% compounded quarterly for 10 years
Answer:
1708.14 rounded
Step-by-step explanation:
Y= a•b^x
5.5% = 0.055
1+0.055=1.055
Y= 1000•1.055^10
Y= 1708.14
A stop sign in the shape of a regular octagon is
resting on a brick wall, as shown in the
accompanying diagram.
STOP
X
What is the measure of angle x?
Answer:
45°
Step-by-step explanation:
First, find the measure of each interior angle of the octagon.
Measure of each interior angle of the octagon = [tex] \frac{(n - 2)180}{n} [/tex]
Where, n = 8.
Plug in the value of n into the formula
[tex] = \frac{(8 - 2)180}{8} [/tex]
[tex] = \frac{(6)180}{8} [/tex]
[tex] = \frac{1,080}{8} = 135 [/tex]
x = 180 - 135 (straight line theorem.)
x = 45°
evaluate 103 × 97 without directly multiplying
Answer:
9991
Step-by-step explanation:
103 × 97
(100 +3) (50+47)
get two number which you can add to get the value in the question
n then expand
100(50+47) +3(50+47)
5000+4700+150+141
9991
what is the remainder of 58,511 divided by 21, the quotient is 2,786 R
Answer:
the remainder is 5. 2,786 R 5
How can this be correct? 6>6 X+3+4=9
Answer:
its not
Step-by-step explanation:
because the x equals 4 so it will be 4+3+4=9 because 3+4 equals 5 so you add 4 and get 9
Which operation should you perform after (9 + 6) in the expression 12^2 + 10 × 2 − (9 + 6) ÷ 5?
Answer:
12²
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition SubtractionStep-by-step explanation:
Step 1: Define expression
12² + 10 × 2 - (9 + 6) ÷ 5
Step 2: Steps
We do parenthesis first, so (9 + 6) is the first thing we do.
The next thing we do is exponents (according to BPEMDAS), so we do 12².
Answer:
Following PEMDAS
Next step : Exponents
Next step : Multiplication
Next step : Division
Next step : Addition
Next step : Subtraction
Step-by-step explanation:
12²+10×2-(9+6)÷5
Open parentheses
12²+10×2-15÷5
Exponents : 12²= 144
144+10×2-15÷5
Multiplication : 10×2=20
144+20-15÷5
Division : -15÷5= -3
144+20-3
Add :144+20=164
164-3
Subtract
= 161
4+4
[tex]4 + 4[/tex]
Answer:
4+4 = 8.
Step-by-step explanation:
Or 44, depends on whether you're trolling. XD
Hope this helped...
[tex] \huge \: Your \: answer \: is \: 8[/tex]
Consider the sets A = fa; b; c; ; ; ; 1; 2; 3g, B = f ; ; ; ; ; g , C = f1; 2; 3; 4; 5; 6g and D = fa; b; cg. (a) List the elements of (A \ B)c (2 marks)
Answer:
hsad
Step-by-step explanation:
16. In the figure below, vertices D and F of ADEF lie on
CG, the measure of ZCDE is 148°, and the measure of
ZEFG is 140°. What is the measure of ZDEF?
E
?
140°
148°
D
C
F 720
G. 989
H. 100°
J. 108°
K. 116°
Answer:
J. 108°
Step-by-step explanation:
m<EDF = 180 - 148 = 32° (angles on a straight)
m<EFD = 180 - 140 = 40°(Angles in a straight line)
m<DEF = 180 - (m<EDF + m<EFD) (sum of triangle)
m<DEF = 180 - (32 + 40)
m<DEF = 180 - 72
m<DEF = 108°
A new LED light bulb uses 10 watts of power. Since energy = power × time , then the energy used for this light bulb can be found my multiplying the power times the time the bulb is lit. If the bulb is lit for one hour, the energy used will be 10 watt*hours or 10 Wh. If three 10 watt bulbs in one room are kept on for 5 hours, how many watt*hours of energy are used?
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Answer:
150 Wh
Step-by-step explanation:
We know the energy per bulb is 10 Wh per hour, so the total energy used by 3 bulbs in 5 hours is ...
(10 Wh/(bulb·hour))×(3 bulbs)×(5 hours) = 10·3·5 Wh = 150 Wh
A recipe for punch requires 8 quarts of orange juice concentrate, 2 quarts of cranberry juice, and enough water to make a total of 14 quarts of punch. How much water is needed for this recipe?
4,8and 12 find the LCM of each numbers
Answer:The LCM of 4, 8 and 12 is 24.
Step-by-step explanation:
Write an equation that passes through the point (1, 3) and is perpendicular to x – 2y = -8.
Answer:
y = -2x + 5
Step-by-step explanation:
Given:
Passes through point (1, 3)
Perpendicular to x – 2y = -8
Solve:
x – 2y = -8
y = 1/2x + 4
The slope is m = 1/2
The slope of the perpendicular line is the inverse of the slope of the original equation.
The slope of the inverse equation is m = -2.
Making an inverse equation of y = -2x + a
Find a:
Use point, (1, 3) where (x, y):
3 = (-2)*(1) + a
a = 5
y = -2x + 5
Answer:
y=½x+5
Step-by-step explanation:
Passes through, (1,3)
Perpendicular to x-2y=-8.
Step 1
write the equation in form of y=mx+c
x-2y=8
-2y=-x+8
Dividing both sides of the equation by -2 we get;
y=-x/2+8
y=-½x+8
Thus the gradient is -½. Call it M1
Recall, The product of the gradients(slopes) of perpendicular lines is -1 i.e
M1 × M2= -1
Solve for M2
-½×M2=-1.
Dividing both sides by -½ we get
M2=-1×-2
M2=2Now, use this slope(M2) with the points (1,3) to find the new equation that is perpendicular to x-2y=-8
Note: Given two points (x1,y1) and (x2,y2) the the slope would be ∆x/∆y i.e (x1-x2)/(y1-y2).
Therefore, identify new point (x,y). Use this new point with point (1,3) and the slope M2 to get the new equation.
Slope=∆x/∆y
M2=(x-1)/(y-3)
but M2 is 2
2=(x-1)/(y-3)
2/1=(x-1)/(y-3) Note: 2= 2/1
Cross multiplying we get:
2(y-3)=1(x-1)
Open the brackets
2y-6=x-1
Solve for y so as to write the equation in form of y=mx+c
2y=x-1 +6
2y=x+5
Divide both sides of the equation by 2
y=x/2+5
y=½x+5solve cos(2x + 30) = 0.5 for -180≤x≤180
Answer:
x = 15°
x = 135°
x = -45°
x = -180°
Step-by-step explanation:
Trigonometric Equations
Solve
cos(2x + 30°) = 0.5 for -180° ≤ x ≤ 180°
Applying the inverse cosine function:
2x + 30° = arccos(0.5)
There are several angles whose cosine is 0.5. They are 60°, 300°, -60° and -300°, thus we have these candidate solutions:
2x + 30° = 60°
2x + 30° = 300°
2x + 30° = -60°
2x + 30° = -300°
Subtracting 30° to all the equations:
2x = 60° - 30° = 30°
2x = 300° - 30° = 270°
2x = -60° - 30° = -90°
2x = -60° - 300° = -360°
Dividing by 2 we have the complete set of solutions:
x = 15°
x = 135°
x = -45°
x = -180°
Pretty easy if you know what you’re doing lol please helpppp Bc idk what I am doingggy
PLEASE ANSWER QUICKLY!!! PLZZZZZ!!!!!!!
Step-by-step explanation:
each 20m miles takes 1g gallon.
Answer:
[tex]y=-\frac{1}{20} x + 20[/tex]
Step-by-step explanation:
The slope equation is always [tex]\frac{rise}{run}[/tex]. In this case, the gallons went down by 1- so we can call the rise -1. When it went down by 1, the miles went up by 20- so we can call the run 20. This gives us a fraction (the "m" value) to put in the slope equation [tex]y=mx+b[/tex]. To find the y intercept (the "b" value), you find out what y is when x = 0, which is given in the chart: 20.
Which is the better buy?
4-quart carton of fruit punch for $2.08
4-cup carton of fruit punch for $0.80
Answer:
$0.90
Step-by-step explanation:
1 quart = 2 pints
Write a proportion:
$1.80 / 4 pint = x / 2 pint
Cross multiply:
4x = 3.60
Divide:
x = 0.90
The price per quart is $0.90.
Answer:
4-quart carton of fruit punch for $2.08
Step-by-step explanation:
4-quart carton of fruit punch for $2.08
2.08 : 4 = 0.52
check your work: 0.52 x 4 = 2.08
so for the first offer you will be paying $0.52 per quart .
4-cup carton of fruit punch for $0.80
1 cup = 0.25 quarts
4 cups = 1 quart
0.80 : 1 = 0.80
for the second offer you will be paying $0.80 per quart of fruit punch. 4-quart carton of fruit punch for $2.08 is a better buy because you will be paying for each quart than in first offer.
hope this helps!
A farmer has a rectangular plot of land. There is a bother identical plot of land 100 yards east and 100 yards north. Find the combined area of the two plots of land
Answer:
Step-by-step explanation:
Area of a rectangular plot = Length × width
With the aid of the diagram attached below.
For plot 1:
The area = ( 60 - 20 ) × ( 80 - 20 )
Area = 40 × 60
Area = 2400 sq yard
For plot 2:
Area = (160 - 120 ) × ( 180 - 120 )
Area = 40 × 60
Area = 2400 sq yard
Therefore, the combined area of the two plots of land = 2400 + 2400
= 4800 square yards