Answer:
the equation 10 = x - y
Step-by-step explanation:
Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.
We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.
We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.
Therefore, the initial value of the investment was $50.
there are 12 levels in Zoe new video game suppose she plays the same number of levels each day what are all the possibilities for the number of days Zoe could play the game show your work. Its about multiples and factors
Let no of level in one day is x. So, Zoe can play x= 12 level in a day.
What is probability?The likelihood might be between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. In a sample space, each occurrence has a probability of one overall. the possibility that two or more events will follow one another. Since there are two or more of them, the events are either dependent or independent events. A dependent event—also referred to as a conditional event—is one in which the occurrence of the first event affects the occurrences that follow. The total number of outcomes will differ.
Write formula for the probability.Probability = Possible outcomes/total outcomes
Factors of 12 can be written as:
1 * 12 = 12
2 * 6 = 12
3 * 4 = 12
For this question look for factors of 12-These would be
1 and 12 (1 x 12 = 12)
2 and 6 (2 x 6 = 12)
3 and 4 (3 x 4 = 12)
Hence Zoe could either play
1 level each day for 12 days
2 levels each day for 6 days
3 levels each day for 4 days
4 levels each day for 3 days
Or...
12 levels in one day
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what is 1/4 divied by 2 and 2/3
Answer:
3/32
Step-by-step explanation:
When dividing fractions, we use keep change flip.
We keep the 1/4, change into multiplication, and flip 2 and 2/3.
First, we want to change 2 and 2/3 into improper fraction form, which is 8/3.
Our equation is now :
1/4 divided by 8/3
Now, we apply keep change flip.
1/4 * 3/8
Multiply numerator by numerator and denominator by denominator.
3/32
3/32 is your final answer. It cannot be simplified further.
8 An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.
(a) Work out the gradient of the straight line.
(b) What does the gradient of this line represent?
The gradient of the line is 4/30 and it means that the amount for each unit of electricity used is 4/30
(a) How to determine the gradient of the straight line.From the question, we have the graph that can be used in our computation:
From the graph, we have the following ordered pairs
(0, 0) and (30, 4)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (30, 4)
The gradient of the line is then calculated using the following slope equation
gradient = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (30, 4)
Substitute the known values in the above equation
So, we have the following equation
gradient = (4 - 0)/(30 - 0)
Evaluate
gradient = 4/30
Hence, the gradient of the line is 4/30
(b) What does the gradient of this line represent?Generally, slope or gradient means rate
This means that the gradient of this line represent the rate
i.e. the amount for each unit is 4/30
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Two-fifths of the students in the music class of twenty students were boys. How many boys are in the music class?
Answer:
8
Step-by-step explanation:
the answer is 8
Answer:
8
Step-by-step explanation:
total students=20
boys=2/5×20
=8
Pam bought different drinks for a party she was throwing. After the party, she had the following drink amounts left over.
\dfrac1{2}
2
1
start fraction, 1, divided by, 2, end fraction liter of soda
\dfrac15
5
1
start fraction, 1, divided by, 5, end fraction liter of water
\dfrac8{10}
10
8
start fraction, 8, divided by, 10, end fraction liter of apple juice
Which statement correctly compares the amounts of 2 left over drinks?
Choose 1 answer:
(Choice A)
A
Pam had less water left over than apple juice.
(Choice B)
B
Pam had more soda left over than apple juice.
(Choice C)
C
Pam had less soda left over than water.
Answer:
A) Pam had less water left over than apple juice.
Step-by-step explanation:
Given amounts of drinks left over:
[tex]\dfrac{1}{2}\; \sf liter \;of \;soda[/tex][tex]\dfrac{1}{5}\; \sf liter \;of \;water[/tex][tex]\dfrac{8}{10}\; \sf liter \;of \;apple\;juice[/tex]To compare the amounts of drinks left over, convert the fractions into equivalent fractions that have the same denominator.
The denominators of the three fractions are 2, 5 and 10.
The lowest common multiple of the denominators is 10.
Therefore, rewrite the first two fractions so that their denominators are also 10.
[tex]\textsf{Soda}: \quad \dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]
[tex]\textsf{Water}: \quad \dfrac{1}{5}=\dfrac{1 \cdot 2}{5 \cdot 2}=\dfrac{2}{10}[/tex]
Therefore, as:
[tex]\dfrac{2}{10} < \dfrac{5}{10} < \dfrac{8}{10}[/tex]then:
water < soda < apple juiceTherefore, Pam had less water left over than apple juice.
Answer:
a) Pam had less water than apple juice.
★ Water < Soda < Apple juice
Step-by-step explanation:
Converting the fraction into decimals,
→ Soda left = 1/2 = 0.5 litres
→ Water left = 1/5 = 0.2 litres
→ Apple juice left = 8/10 = 0.8 litres
Let's order them in ascending order,
→ 0.2 < 0.5 < 0.8
→ 1/5 < 1/2 < 8/10
→ Water left < Soda left < Apple juice left
Now the applicable options is,
→ Pam had less water than apple juice.
Hence, option (a) is correct answer.
15) How many terminal zeros does the integer equal to
80 power to the 16 times 75 power 8 have?
HELP ME ASAP!!!!
I NEED THIS ANSWERED RIGHT NOW!!!!!!
Answer: The bisector of [tex]\angle BAC[/tex]
Step-by-step explanation:
This is a standard construction.
Jerry builds 5 shelves complete the equations to show the area of shelf A
The area of the shelf A is 30 square feet
How to determine the area of the shelf AFrom the question, we have the following parameters that can be used in our computation:
Dimensions = 3 ft and 2 ft
The above parameters mean that
Length = 3 ft
Width = 2 ft
Number of shelves = 5
The area of the shelf A is then calculated as
Area = Number of shelves * Length * Width
Substitute the known values in the above equation, so, we have the following representation
Area = 5 * 3 * 2
Evaluate the products
So, we have
Area = 5 * 6
Evaluate the products
So, we have
Area = 30
Hence, the area is 30 square feet
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"Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)"
The compound interest is 61.342 years
What is compound interest ?
The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
Formulas for Compound Interest
Formula for Monthly Compound Interest.
Compounded Quarterly Formula: Interest compounded monthly is calculated 12 times a year. Four times a year are used to calculate interest that is compounded quarterly.
Formulas for compound interest are available on a daily, annual, and other basis.
A = 1700
P = 500
r = 2%
n = 4
r = R/100
r = 2/100
r = 0.02 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.02/4)] )
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.005)] )
t = 61.342 years
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Write the equation of the line in fully
simplified slope-intercept form.
12
11
10
96
8
7
6
-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
5
4
3
2
1
-2
2 3 4 5 6 78 0
y
-9
-10
-11
-12
1
2 3 4 5 6 7 8 9 10 11 12
X
Answer:
y=5/2x-4
Step-by-step explanation:
y=mx+b
5/2 is the slope
-4 is the y intercept
The following data represent the monthly cell phone bill for a person's phone for six randomly selected months.
$35.34, $42.09, $39.43, $38.87, $43.39, $49.26
Compute the mean, median, and mode phone bill. (Round to the nearest cent as needed)
The mean of the data is x(bar) = 41.396
The Median of the data is $40.76
The mode of all the values are appearing once and therefore there is no mode for the phone bill.
Now, According to the question:
Given the data:
$35.34, $42.09, $39.43, $38.87, $43.39, $49.26
Mean is the average of the data computed as x(bar) = Σ[tex]x_i[/tex] /n where [tex]x_i[/tex]
are the data points and n is the number of data points
x(bar) = 35.34 + 42.09 + 39.43 +38.87 +43.39 + 49.26 / 6
x(bar) = 248.38 /6
x(bar) = 41.396
The median is the data point that lies in the middle of the data set when the data is arranged in ascending or descending order.
Thus,
Ascending order:
$35.34, $38.87, $39.43, $42.09, $43.39, $49.26
The median lies between $39.43 and $42.09 and to get it, we find the average of the two numbers
Median = (39.43 + 42.09)/ 2
Median = $40.76
→ Mode is the value in a data set that is repeated most frequently. In the given data, all the values are appearing once and therefore there is no mode for the phone bill.
Hence, The mean of the data is x(bar) = 41.396
The Median of the data is $40.76
The mode of all the values are appearing once and therefore there is no mode for the phone bill.
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Evaluate
16 ÷ (2 + 1/2 ) ²
A) 2 14/25
B) 4 1/4
C) 6 2/5
D) 8 1/4
Answer:
A) 2 14/25
Step-by-step explanation:
This is a question of order of operations, which PEMDAS helps describe.
P- parentheses
E - exponents
M, D - multiplication, division
A, S - addition, subtraction
In your problem, you'd start with P, what's in the parentheses.
16 ÷ (2 1/2)²
Then do the exponent, E. It might help to convert 2 1/2 to 5/2.
16 ÷ 25/4
Then divide, D. When dividing fractions, you can flip the numerator and denominator and multiply.
16 x 4/25
= 64/25
Then simplify. 25 goes into 64 two times, and there is 14 left over.
= 2 14/25
Answer:
A
Step-by-step explanation:
Evaluate the sum in the brackets first to give 2.5 and square that to give 6.25
Divide 16 by 6.25 to get A
Last month, Lucy and Britney each read three books. The tables show the number of pages in each book and the time it took Lucy and Britney to read each book. Which of the tables, if any, represent a proportional relationship? Responses
The table that represents a proportional relationship is Table A.
What is a proportional relationship?A proportional relationship exists between two variables when their ratios are equal or equivalent.
With a proportional relationship, there is a constant rate of change between the comparable variables.
Proportions refer to ratios of equality between two or more variables.
Where there is a proportional relationship, we can determine the constant rate of change as the same quotient.
For instance, when the number of pages per book is divided by the reading time, a constant rate of change is established if the reading speed is the same for all three books.
Table A:Pages Lucas Read 208 156 234
Time (hours) 8 6 9
Reading speed 26 26 26 (234/9)
Table B:Pages Britney Read 168 120 348
Time (hours) 6 4 12
Reading speed 28 30 29 (348/12)
Thus, the constant rate of change or proportional relationship can be found in Table A and not in Table B.
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Question Completion:Table A:Pages Lucas Read 208 156 234
Time (hours) 8 6 9
Table B:Pages Britney Read 168 120 348
Time (hours) 6 4 12
Figure HEFG below is a parallelogram. If UH=19 and FH= 5x-7, find X
A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
The value of x is 5.2.
What is a parallelogram?
A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
UH and FH are the two sides of the diagonal.
UH and FH are equal.
UH = FH
19 = 5x - 7
19 + 7 = 5x
5x = 26
x = 5.2
Thus,
The value of x is 5.2.
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Bill is in a hot air balloon that has just taken off and is floating above its launching point.
Lillian is standing on the ground, 9 meters away from the launching point. If Bill and Lillian
are 15 meters apart, how high up is Bill?
meters
Submit
car is traveling at a steady speed It travels 1 1/2 miles in 2 1/4 minutes How far will it travel in 23 minutes? In ?
Answer:
15 1/3 miles in 23 minutes
(2/3)x in x minutes
Step-by-step explanation:
1 1/2=1.5
2 1/4=2.25
Convert to unit ratio
[tex]1.5/2.25=(2/3)/1[/tex]
2/3*23=46/3
Simplify
15 1/3 miles in 23 minutes
(2/3)x in x minutes
1. A taxi charges $2.00 for up to and including the first mile and $1.60 for each mile thereafter. Which equation best fits this situation, where x
represents the miles after the first mile and y is the total amount.
A)y=1.602 - 2.00
B)y=2.002 -1.6
C)y =2.00x + 1.60
D)y=1.60x+2.00
Answer:
D
Step-by-step explanation:
The taxi charges $2.00 for any distance less than or up to 1 mile.
Then for every mile after the taxi will charge you a fee of $1.60 dependent upon how many miles you go.
This can be modeled as:
y = 2.00 +1.60(x)
where x is the number of miles after the first mile.
At December 31, the records of Nortech Corporation provided the following selected and incomplete data:
Common stock (par $1; no changes during the current year).
Shares authorized, 500,000.
Shares issued, 2; issue price $12 per share.
Common Stock account, $100,000.
Shares held as treasury stock, 2,000 shares, cost $10 per share.
Net income for the current year, $24,500.
Dividends declared and paid during the current year, $14,700.
Retained Earnings balance, beginning of the year, $145,000.
Required:
Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par
value per share. (Round "per share" answers to 2 decimal places.)
1-a. Shares authorized
1-b. Shares issued
1-c. Shares outstanding
2. The balance in Additional Paid-in Capital would be
3. Earnings per share is
4. Dividends paid per share of common stock is
5. Treasury stock should be reported in the stockholders' equity section of the balance
sheet in the amount of
6. Assume that the board of directors approved a 2-for-1 stock split. After the stock split,
the par value per share will be
500,000
290,000
The solutions for the given questions are given below:
What is meant by income?Earnings from employment, investments, or company operations. Sam, for instance, had a weekly income of $770 after receiving $30 in bank interest, $700 from his employment, and an additional $40 from buying and selling veggies.
Wages is the amount of money obtained through employment; income is the entire amount of money obtained, which includes earnings, benefits, pensions, and other types of payments.
1.a 500000 shares have been authorized.
1/(210000) = 210000 shares issued Number of shares issued [Common stock account balance / par value of each share]
1-c) The number of shares outstanding is 210000 - 3100, or 206900 shares.
2) The APC Account Balance is $4620000, which is calculated as 210000 * (23 - 1).
3) Net income divided by the number of outstanding shares equals 165520 divided by 206900, or 0.8 per share.
4) The dividend per common share was paid at 53794/206900, or 0.26 per share.
5) 3100 * 21 = $65,100 should be stated for Treasury Stock in the Stockholders' Equity part of the Balance Sheet.
6) Following the stock split, the par value of each share is equal to 1 / 2 ($0.50 per share).
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A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line after x minutes.
f of x equals one fourth times x plus 10
f of x equals negative one tenth times x plus 4
f of x equals one tenth times x plus 4
f of x equals negative one fourth times x plus 10
The distance left after x minutes is modeled by the linear equation:
f(x)= 10 - (1/4)*x
The correct option is the last one.
Which equation models the distance after x minutes?We know that the total distance of the race is 10 kilometers, and the student runs 1 kilometer every 4 minutes, so the student's speed is:
S = 1km/4min = 0.25 km/min
The distance to the finish line is modeled by an equation of the form:
f(x) = total distance - speed*time
Here we know that:
total distance = 10kmspeed = 0.25km/mintime will be our variable, x.Then the equation is:
f(x)= 10 - (0.25)*x
We can rewrite the decimal as a fraction:
f(x)= 10 - (1/4)*x
The correct option is the last one.
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Identify all of the terms in the expression: 4x³ + x² + 3x + 6.
OA 6
OB 4, 3, 6
OC x³, x², x
OD 4x³, x², 3x, 6
Please help me
Answer:
OD 4x³, x², 3x, 6
Step-by-step explanation:
In the diagram, A is a point on the circumference of a circle with center O and radius r. A circular are with center A meets the circumference at B and C. The angle O A B is θ radians. The shaded region is bounded by the circumference of the circle and the are with center A joining B and C. The area of the shaded region is equal to half the area of the circle.
The area of the shaded region is equal to half the area of the circle.
What is the area of the circle?
The approximating parallelograms arbitrarily close and approximate the area of the circle by cutting it into ever-increasing slices.
The radius of the arc BC is |AB|=2rcosθ, and ∡AOB=π−2θ.
Dashed area= Area of sector BAC+ 2(Area of sector BOA−Area of triangleBOA)
= 1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)]
On the other hand, the area of the dashed surface is 1/2πr², then
1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)] = 1/2πr²
(2rcosθ)2(θ) + r²[π−2θ−sin(π−2θ)] = 1/2πr²
4θcos2θ+π−2θ−sin2θ = 1/2πr²
2θ(2cos2θ−1) = sin2θ−1/2π
2θcos2θ = (2sin2θ−π)/2
cos2θ = (2sin2θ−π)/4θ
Hence, the area of the shaded region is equal to half the area of the circle.
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Write an absolute value Inequality for the graph below. Use x for your variable.
The inequality is [tex]|x|\geq4[/tex].
What are the inequalities of a graph?
We can see the areas that satisfy one or more inequalities by visualizing them as inequalities on a graph. These inequalities can be represented using straight-line graphs in GCSE maths because they are frequently linear. You might need to draw lines and designate a region that fulfills the system of inequalities to find solutions to the inequalities, or you might need to use the graphs that have already been provided.
Here, in the graph given, we see that the points on and from 4 / -4 are highlighted. Since the interval has 0 in between, we write the variable as [tex]|x-0|[/tex]. Now, the graph excludes points from -4 to 4.
Therefore, we conclude that the absolute value inequality for the given graph is [tex]|x|\geq4[/tex].
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Absolute value is 7 or greater.
What is inequality?
In mathematics, an inequality is a statement that compares two values or expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). For example:
2 < 3 (2 is less than 3)
5 > 3 (5 is greater than 3)
2 ≤ 3 (2 is less than or equal to 3)
5 ≥ 3 (5 is greater than or equal to 3)
Inequalities can be used to describe a range of values that a variable can take on. For example, the inequality x > 0 describes all values of x that are greater than 0.
Inequalities can be solved by finding the values of the variable that make the inequality true. For example, the solution to the inequality x > 0 is all values of x that are greater than 0, such as 1, 2, 3, etc.
Inequalities can also be combined using the logical operators "and" (represented by the symbol ∧) and "or" (represented by the symbol ∨). For example, the inequality x > 0 ∧ x < 10 describes all values of x that are greater than 0 and less than 10, such as 1, 2, 3, etc. The inequality x > 0 ∨ x < 10 describes all values of x that are either greater than 0 or less than 10, which includes all values of x.
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What is the name of the point located at
(
4
,
3
)
?
A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point M is plotted 3 units above the origin. Point T is plotted 5 units above the origin. Point Y is plotted 1 unit to the right of the origin. Point Z is plotted 1 unit to the right and 4 units above the origin. Point N is plotted 1 unit to the right and 5 units above the origin. Point L is plotted 2 units to the right and 2 units above the origin. Point W is plotted 3 units to the right and 2 units above the origin. Point P is plotted 4 units to the right of the origin. Point X is plotted 4 units to the right and 3 units above the origin. Point O is plotted 5 units to the right and 4 units above the origin. Point S is plotted 5 units to the right and 5 units above the origin.
A.
Point M
B.
Point P
C.
Point W
D.
Point X
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
The name of the point located at (4, 3) is X.
Option D is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates of a point = (4, 3)
Point (4, 3) is located on the graph at point X.
(4, 3) means 4 is on the x-axis and 3 is on the y-axis.
The meeting point is point X.
Thus,
The name of the point located at (4, 3) is X.
Option D is the correct answer.
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what are the solutions of 2x^2 + 3x = -5
Answer:
No solution
Step-by-step explanation:
The square root of a negative number is not a real number
NO LINKS!! Please help me with these problems. Exponential.
Answer:
f(x) = 10400·(1/4)^x; table values: x = -1, f(x) = 162.5g(x) = 1.8·2.4^xIncorrect for b < 1.Step-by-step explanation:
You want to write exponential functions through the given points.
1. TableThe exponential function ...
f(x) = a·b^x
will have the values ...
f(0) = af(1) = ab ⇒ b = f(1)/f(0)Using these relations we can write the function from the table values:
f(x) = 10400·(2600/10400)^x
f(x) = 10400·(1/4)^x
Then your table is ...
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}[/tex]
2. PointsUsing the given points in the exponential function form, we have ...
4.32 = a·b^1
59.71968 = a·b^4
Dividing the second equation by the first, we find ...
59.71968/4.32 = b^3 ⇒ b = 2.4
Using this in the first equation, we get ...
4.32 = a·2.4 ⇒ a = 1.8
The equation of the function is ...
g(x) = 1.8·2.4^x
3. IncreasingThe exponential function ...
y = a·b^x . . . . . . a > 0, b > 0
will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.
Sarah's belief is incorrect.
Answer:
[tex]\textsf{1.} \quad f(x)=10400(0.25)^x[/tex]
(-1, 41600) and (3, 162.5)
[tex]\textsf{2.} \quad g(x)=1.8(2.4)^x[/tex]
3. Sarah is incorrect.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question 1The y-intercept is when x = 0.
Therefore, from inspection of the given table, the y-intercept is 10400:
[tex]\implies a=10400[/tex]
Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:
[tex]\implies 2600=10400b^1[/tex]
[tex]\implies 2600=10400b[/tex]
[tex]\implies b=\dfrac{2600}{10400}[/tex]
[tex]\implies b=0.25[/tex]
Therefore, the equation of the function is:
[tex]\boxed{f(x)=10400(0.25)^x}[/tex]
Find the value of x when f(x) = 41600:
[tex]\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}[/tex]
Find the value of f(x) when x = 3:
[tex]\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}[/tex]
Therefore, the completed table is:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}[/tex]
Question 2Given points:
(1, 4.32)(4, 59.71968)Substitute the given points into the exponential formula g(x) = abˣ
[tex]\implies ab=4.32[/tex]
[tex]\implies ab^4=59.71968[/tex]
To find b, divide the equations:
[tex]\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}[/tex]
[tex]\implies b^3=13.824[/tex]
[tex]\implies b=\sqrt[3]{13.824}[/tex]
[tex]\implies b=2.4[/tex]
Substitute one of the points and the found value of b into the equation and solve for a:
[tex]\implies 2.4a=4.32[/tex]
[tex]\implies a=\dfrac{4.32}{2.4}[/tex]
[tex]\implies a=1.8[/tex]
Therefore, the equation of the function is:
[tex]\boxed{g(x)=1.8(2.4)^x}[/tex]
Question 3Sarah is incorrect. For an exponential function in the form a · bˣ:
If a > 0 and b > 1 then it is an increasing function.If a > 0 and 0 < b < 1 then it is a decreasing function.Marco uses 2 gallons of water while brushing his teeth. He uses 10 gallons of water to wash clothes. How many more cups of water does Marco use while washing his clothes than brushing his teeth? there’s are 16 cups in 1 gallon
Answer: 192 cups
Step-by-step explanation: there's 16 cups in 1 gallon so you would do 2×16=32 to get 32 cups. Then you would do 10×16=160 to get 160 cups. Now add 32+160=192 cups.
A light is on the top of a 12 ft tall pole and a 5’6’’ tall person is walking away from the pole at a rate of 2 ft/sec At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole? please give all solutions
Part a: the rate at which the shadow's tip moves away from the pole while the subject is 25 feet distant is 48/13 ft/sec.
Part b: the speed of the shadow from the speed of the man is 22/13 ft/sec.
Explain the term rate of change?Rate of Change: How quickly a parameter changes over a predetermined amount of time. It is frequently used while discussing momentum and is typically expressed as a proportion of one variable's change to another's corresponding change.A 5 feet 6 inch tall individual is going away from a 12 foot tall pole with a light on top at a 2 foot per second pace.
A) the speed at which the shadow's tip moves away from the pole while the subject is 25 feet distant;
Similar triangles allow us to say:
12/L = 55/(L - x)
Simpllifying,
12(l - x) = 5.5l
12l - 12x = 5.5l
6.5l = 12x
x = (6.5/12)l
Differentiate with respect to time;
dx/dt = (6.5/12)dl/dt or
dl/dt = (12/6.5)(dx/dt)
As, dx/dt = 2
dl/dt = (12/6.5)(2)
dl/dt = 24/6.5
dl/dt = 48/13 ft/sec
B: When a person is 25 feet from a pole, the point of the shadow travelling away from them at:
Subtract the speed of the shadow from the speed of the man.
Therefore,
48/13 - 2 = 22/13 ft/sec.
Thus, the speed of shadow from the speed of the man is 22/13 ft/sec.
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Please help - if could throw this out the window I would
The speed of the car will be 25.41 m/h
What is speed and velocity ?Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector quantity, whereas speed is a scalar quantity
According to the given information
d = [tex]\frac{s^{2} }{10}[/tex] + s
We are given that
distance is 90 feet
So, the expression becomes
90 = [tex]\frac{s^{2} }{10}[/tex] + s
[tex]s^{2}[/tex] + 10s - 900 = 0
which is quadratic in s
So applying the discriminant formula
[tex]$$[/tex]s [tex]=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]
[tex]$$[/tex]and then we input the values:
s [tex]=\frac{-10 \pm \sqrt{(10)^2-4(1)(900)}}{2(1)}$$[/tex]
and solve:
s [tex]=\frac{-10 \pm \sqrt{3700}}{2}$$[/tex]
It will have two answers
s = -35.41 m/h
s = 25.41m/h
Speed cannot be negative
So
The speed of the car will be 25.41 m/h
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If you draw a random card from a standard deck of 52 cards, what are the odds of drawing the jack, queen, king, or ace of clubs? Write your answer in the form a:b as a fully reduced ratio. Note: In a standard deck of cards, each of the four suites has three face cards.
Answer:
12:52
Step-by-step explanation:
almost every card game has 52 cards, you have a 23% chance to draw a face card of any kind.
There are a king, queen, and jack for each of the four different suits: hearts, spades, clubs, and diamonds. The four suits have 13 cards each, for a total of 52 cards. Therefore, your chance of drawing a face card out of a deck of cards upon choosing the card at random is 12 out of 52, or about 23%.
help meeeeeeeeeee pleaseee
Answer: 51.85
Step-by-step explanation: you use the formula given and plug is 25 for t because it is the number of years. So you get 200*e^(-0.054*25) = 51.85