The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars)
t
years after 1995.
420
t
+
5750
Use this expression to predict what the total average credit card debt was or will be in the year 2006.
Answer: In the year 2006, the total average credit card debt for a U.S. household will be (or was)
dollars.
Answers
In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.
How to solve Exponential functions?
We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;
420t + 5750
where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;
t = 2006 - 1995
t = 11 years
Thus;
f(11) = 420(11) + 5750
f(11) = 10370 dollars
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Related Questions
Find the height of the tower using the information given in the illustration.
Answers
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
−3(−3x+1)=−6
What’s the answer to this
Answers
Answer:
x = -1/3
Step-by-step explanation:
the angle of elevation for the first Hill of a roller coaster is 55°. If the length of the track from the beginning to the highest point is 98 ft what is the approximate height of the roller coaster when it reached the top of the first Hill? options, 80 ft, 98 ft, 56 ft, 43 ft
Answers
Using trigonometric property in the figure,
\(\sin \theta=\frac{opposite\text{ side}}{hypotenuse}\)\(\begin{gathered} \sin \text{ }55^{\circ}=\frac{h}{98\text{ }} \\ h=98\times\sin 55^{\circ} \\ \cong80\text{ ft} \end{gathered}\)Here, h is the height of the hill.
Therefore, the approximate height of the of the roller coaster when it reached the top of the first Hill is 80 ft.
Option A is the answer.
y = f(x) = 5x
find f(x) when x = 3
Answers
The value of f(x) when x is 3 is 15
What is function?A Function in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
For example, if f(x) = x² +2x +5 , the value of f(x) when x is 2 is calculated as;
f(x) = 2² + 2(2) + 5
f(x) = 4 +4+5
= 13
This done by substituting the given value of x into the expression.
Similarly , if f(x) = 5x, the value of f(x) when x is 3 is calculated as;
f(x) = 5(3)
f(x) = 15
therefore the value of f(x) when x is 3 is 15
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The Fahrenheit temperature readings on 66 Spring mornings in New York City are
summarized in the table below. Construct and label a frequency histogram of the data
with an appropriate scale.
Temp (°F) Number of Days.
30-39
2
40-49
26
50-59
28
60-69
8
70-79
2
Graph answer Click and drag to make a rectangle. Click a rectangle to delete it.
Answers
To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.
The temperature ranges and their corresponding frequencies are as follows:
30-39: 2 days
40-49: 26 days
50-59: 28 days
60-69: 8 days
70-79: 2 days
To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.
Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.
Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.
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The quotient of a number and two, increased by five, is 3.
Answers
Answer:
the quotient is -4
Step-by-step explanation:
Starting from zero, zero divided by anything is 0. The main concept here is not to divide anything by 0 and just straight of add by 5 because there would be more than one answer for the quotient. I know that 2+3=5 but but I know that my quotient would be smaller than 0 but add up to 3 when I divide it in half and add 5. -4/2=-2 plus 5 is equal to 3. 5>-2 so my answer would be positive.
Please answer the two following questions.
Answers
The transformed graph is attached
The domain is (-∝, ∝) and the range is (-3, ∝)
How to transform the graph?From the question, we have the following parameters that can be used in our computation:
y = eˣ
To transform the graph to y = e⁻ˣ - 3, we make use of the following rules:
Reflect across the y-axisShift down by 3 unitsSee attachment for the graph of y = e⁻ˣ - 3
The domain and the rangeFrom the attached graph, we have:
The graph extends across the x-axis i.e. domain = (-∝, ∝)
The graph opens upward from y > -3 i.e. range = (-3, ∝)
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5. Determine the value of t4 in an arithmetic sequence given that t₁ = 11 and S9 = 243.
Answers
The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).
We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.
From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:
243 = (9/2)(2(11) + (9-1)d)
243 = 9(22 + 8d)
243 = 198 + 72d
45 = 72d
d = 45/72 = 5/8
Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:
tₙ = a + (n-1)d
t₄ = 11 + (4-1)(5/8)
t₄ = 11 + 3(5/8)
t₄ = 11 + 15/8
t₄ = 88/8 + 15/8
t₄ = 103/8
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Write an expression to represent the product of 6 and the square of a number plus 15. In your expression what is the value of the coefficient? A. 1 B. 6 C. 15 D. 2
Answers
Answer:
B) 6
Step-by-step explanation:
Let the number be x
Product of 6 and square of number plue 15 : (6x²) + 15
Coefficient of x² = 6
In the following image, segment BD bisects segment AC, and three triangles are similar: AABC~ AADB~ ABDC. Complete the two-column
proof of the Pythagorean theorem.
3: A. (AC)DC) + (AC)(CD) = (AC)AC) + (BC)BC)
B. (AC)(CD) + (AC)(AD) = (BC)BC) + (AB)AB)
C. (AB)(CB) + (AD)CD) = (AC)AC) + (BC)BC)
D. (AC)BC) = (AC)(AC) + (BC)BC)
5: A.angle bisector postulate
B. triangles
C. common line segment
D. segment addition postulate
Answers
1. The Fill ups are as follow:
AB² + BC² = AC. AD + AC. CD
2. Segment addition postulate
What is Pythagorean theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
Given:
BC/ AC = CD/ BC and AB/ AC = AD/ AB
Now, BC² = AC. CD and AB² = AC. AD
Using, Addition Property of Equality
AB² + BC² = AC. AD + AC. CD
and, AB² + BC² = AC (AD + CD) [factor]
AD + CD = AD (segment addition postulate)
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PLATO
i got it correct :)
-
3/1
213
- 3)
-
Simplify the expression
properties of operations used.
Cite the
5
(please help if you can and thank you so much!) hurry
Answers
Answer:
7/10 or 0.7
Step-by-step explanation:
-3/2 (1/3 - 4/5)
(-3/2) (1/3 + -4/5)
(-3/2)(1/3) + (-3/2)(-4/5)
-1/2 + 6/5
7/10
I think this PDF should assist you in the property of operations for fractions and also help you in solving future problems.
Simplify the following expression:
√-36+√-100+ 7
O A. 7+ 16i
OB. 7+√136i
O C. 16
C. 16 - 7i
O D. 23 + 0i
Answers
√-36 + √-100 + 7
To simplify this expression, we need to first remove the negative radicals. We can do this by squaring both sides of the equation:
√-36 = -6
√-100 = -10
Substituting these values back into the expression, we get:
-6 + -10 + 7 = -19 + 7 = -12
So, the simplified expression is:
-12
Since the expression is already in its simplified form, there is no need to factor it further.
Rose wants to buy a toy that costs $14. If she gives the cashier $20, which equation will tell you how much change Rose gets back?
Answers
Answer:
$20-$14=$6
Step-by-step explanation:
this is correct because if you give the $20 to them and the toy costs $14 then you subtract that from the amount you gave them then whatever is left is how much you get back.
brainliest?
a group of friends every time they play a game of marbles, they lose 5 marbles as it’s a big playground and they can’t be bothered to look for marbles that roll away somewhere. every time a game of marbles ends (each game takes 10-15 minutes), they collect all their marbles in a big box, hide it behind a tree, and go for a quick run. every time these kids hide all their marbles in a box behind the tree, a very intelligent squirrel sneaks up to the box, and if there are more than 12 marbles in it, the squirrel steals 3 marbles and runs off. if this group of kids started with 120 marbles in total, how many games can they play in total before they have less than 10 marbles left (given that they lose some marbles each time they play, and a squirrel steals some marbles each time they go for a run).
Answers
Answer:
14 gamesStep-by-step explanation:
Initial number of marbles = 120Lost at every game = 5Stolen by a squirrel = 3Left = less than 10Let the number of games be x
then lost marbles = 5xstolen marbles = 3xInequality:
120 - 5x - 3x < 10120 - 8x < 10110 < 8xx > 110/8x > 13 rounded downSince there should be more than 0 left, another inequality for it:
120 - 8x > 0120 > 8x x < 15So 13 < x < 15, which leaves us with 14
A bag contains 6 batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select 3 batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected
Answers
Answer:
there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.
Step-by-step explanation:
The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.
In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:
Select the first battery. There are 6 choices for the first battery.
Select the second battery. There are 5 choices left for the second battery, since we've already selected one.
Select the third battery. There are 4 choices left for the third battery.
Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:
6 x 5 x 4 = 120
Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.
CAN SOMEONE PLEASE HELP??????
Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in table #7.3.10 ("Maintaining balance while," 2013). Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level.
Table #7.3.10: Forward/backward Sway (in mm) of Elderly Subjects
19
30
20
19
29
25
21
24
50
Answers
Answer:
Reject H0 and conclude that adults sway more than the mean forward sway for younger people.
Step-by-step explanation:
H0 : μ = 18.125
H0 : μ > 18.125
Sample data: 19 30 20 19 29 25 21 24 50
Sample size, n = 9
Sample mean, xbar = Σx / n = 237 / 9 = 26.333
Sample standard deviation, s = 9.772 (calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (26.333 - 18.125) ÷ (9.772/√(9))
T = 8.208 / 3.2573333
T = 2.519 = 2.520
Decison :
Reject H0 ; If Pvalue < α
The Pvalue :
Degree of freedom, df = n - 1 ; df = 9 - 1 = 8
Pvalue(2.520; 8) = 0.0179
Since 0.0179 < 0.05 ; WE reject H0 and conclude that adults sway more than the mean forward sway for younger people.
The solution to -5 m = -20 is negative.
True False
Answers
Answer:
false
Step-by-step explanation:
This is because -5m=-20
m=-20/-5
m=4
Step-by-step explanation:
False
because there two - are cancelled
- ×- = +
Is there any number that when added to 0 is negative, and when subtracted by 0 is also negative?
Answers
Answer:
Adding with zero: 0 + a is just a. Zero doesn’t change the value of a. (This is also true for a + 0.)
Subtracting with zero: 0 – a = –a. Use the rule for subtracting signed numbers: Change the operation from subtraction to addition and change the sign of the second number. Likewise, a – 0 = a. It doesn’t change the value of a to subtract zero from it.
Therefore, if the equation is 0 - a, then it will have a negative outcome.
Find the product. 5.2 × 10.38
Answers
Answer:
The answer would be approximately 53.976
Step-by-step explanation:
Answer:
53.976
Step-by-step explanation:
5.2 × 10.38 = 53.976I hope this helps!
Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.
log√7 =
Log 23/6=
Answers
Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.
Logarithmic evaluationLog√7 = 1.659Log 23/6 = 0.862It is a rapid increase in the quantity of something over a period of time. Exponential growth can be seen in populations, investments, and other areas.It is characterized by a doubling or tripling of the original amount within a specified period of time.This type of growth is often caused by compounding, where gains from one period are reinvested in the next period, leading to a rapid increase in the overall amount.Exponential growth is often seen in the early stage of a business, when it is experiencing rapid growth due to investments or other factors.However, exponential growth can also lead to rapid decline if not managed properly.This is called logarithmic evaluation, which involves using logarithms to simplify complex expressions.To learn more about logarithmic evaluation refer to:
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Which of the following can divide into 756 with no remainder?
Select all that are correct. (Chapter 4)
Select
4
2
9
25
5
8
10
3
6
Answers
Answer:
4, 2, 9, 3, 6
Step-by-step explanation:
756/4= 189
756/2= 378
756/9= 84
756/25= 30.24
756/5= 151.2
756/8= 94.5
756/10= 75.6
756/3= 252
756/6= 126
Help me with maths, please.
Answers
Answer:
Find QS by Pythagoras theorem.
QS² = 14²-10²
QS = 9.7 cm
PQ²=5²+9.7²
PQ = 10.5 cm
My sister plans to sell more than 250 boxes of cookies.
C>250
c250
Ob
Ос
Od
CS250
C2250
Next Page
Answers
Answer:
x > 250
Step-by-step explanation:
we are to express the statement using an inequality expression
Since my sister plans to sell more than 250 boxes of cookies, the inequality sign to use will be a greater than sign (>), since my sister is not selling amount less. Hence the required inequality will be x > 250 where;
x is the amount of box of cookies
Which function has a greater maximum?
�
(
�
)
=
−
2
(
�
+
4
)
2
+
1
f(x)=−2(x+4)
2
+1f, left parenthesis, x, right parenthesis, equals, minus, 2, left parenthesis, x, plus, 4, right parenthesis, squared, plus, 1
A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens down. The function increases through negative four, negative five and negative three, negative two. It has a maximum at negative two, one, then the function decreases through negative one, negative two and zero, negative five.
Answers
The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.
1. The given function is f(x) = \(-2(x+4)^2\) + 1.
2. To find the maximum of the function, we need to determine the vertex of the parabola.
3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.
4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.
5. The x-coordinate of the vertex is given by h = -4.
6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.
7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.
8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).
9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.
10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.
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Jon was at a football match.
The match ended at 16:55
Jon got back to his car in the car park 15 minutes after the match ended.
He drove out of the car park 10 minutes later.
It then took him 45 minutes to drive home.
Did Jon get home before 18 00?
You must show how you get your answer.
Answers
Answer:
no he will make it home at 18:15
Step-by-step explanation:
\(4:55+15=5:10\\5:10+10=5:20\\5:20+45=6:15\)
a) complete the table in the answer space for the equation y=21/2x when x=2 and x=5b) using a scale of 2cm to 1 unit on the x-axis and 2cm to 2 unit on the y-axis, draw the graph of y= 21/2x for 0.5 ≤ x ≤ 7c) from the graph in (b) ,find:i. the value of y when x=4.5ii. the value of x when y= 7.6d) draw a suitable straight line on the graph in (b) to find the value of x which satisfy the equation 21/2x=15-2x for 0.5 ≤ x ≤ 7.State the values of x
Answers
For a)
x=2
\(y=\frac{21}{2(2)}=5.25\)x=5
\(y=\frac{21}{2(5)}=2.1\)b)
c)
We locate for each case the points
d)
First we need to solve the equation given
\(\frac{21}{2x}=15-2x\)We isolate the x
\(21=2x(15-2x)\)we simplify
\(21=30x-4x^2\)Then we make zero the equation
\(4x^2-30x+21=0\)Then we solve the second-degree equation.
The solutions are
\(\begin{gathered} x=0.781 \\ x=6.719 \end{gathered}\)Both solutions are inside the given interval
Therefore the lines are
Select the correct answer.
A figure shows the inscribed triangle ABC with center point O which bisects BO. An angle of C is 50 degrees.
In the diagram,
is a diameter of the circle with center O. If m∠
= 50°, what is m∠
?
A.
50°
B.
40°
C.
80°
D.
100°
Reset Next
Answers
Answer: C
Step-by-step explanation:
A cell phone is plugged in to be charged. The table shows the percent of battery power at some times
after it was plugged in.
Time
Percent charged
6:00 pm
2%
6:15 pm
10%
6:35 pm
21%
7:05 pm
38%
At what time will the battery be 100% charged? Use the data to find out and explain or show your
reasoning
Answers
Answer:7:45
Step-by-step explanation:
Find all values of m for which the equation has two real solutions.
3x² + 7x- (m + 1) = 0
Answers
2. Suppose the price of good x increased from 4 birr to 5 birr. Because of change price of good x, quantity demand of good y changed from 5,000 to 6,250. a. Find cross price elasticity of demand b. What types of goods (good x and good y) are?
Answers
Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.
Let's calculate the cross-price elasticity of demand using the given information:
a. Find the percentage change in quantity demanded of good Y:
Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100
Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%
b. Find the percentage change in the price of good X:
Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100
Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%
Now, we can calculate the cross-price elasticity of demand:
Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X
Cross-Price Elasticity of Demand = 25% / 25% = 1
b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:
If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.
Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.
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Answer:
Step-by-step explanation: