A) The data modelling is an exponential function.
B) The explicit funciton that will be used to represent the data is;
f(n) = 2(2)^(n - 1)
C) The average rate of change here is; 7
How to model a function?A) We are given the coordinates as;
(1, 2), (2, 4), (3, 8), (4, 16)
From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.
Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.
B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:
f(n) = ar^(n - 1)
Since first term ; a = 2
and common ratio r = 2, then we can say that;
f(n) = 2(2)^(n - 1)
C) The formula for average rate of change here is;
dy/dx = (y₂ - y₁)/(x₂ - x₁)
The coordinates of the 2nd and 4th day are;
(2, 4) and (4, 16)
Thus;
dy/dx = (16 - 4)/(4 - 2)
dy/dx = 14/2 = 7
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Sketch the graph of each line
The straight line y = x -1 is shown figure
Sketching graph of a line:
To plot straight-line graphs we need to take values of x and y values to make a value table and to work out the graph.
Take x values as -1, 0, 1, etc. to make our work easy and clearer, and from that find the values of y.
After calculating the coordinates, use the resultant points to plot the line as a graph.
Here we have a line
y = x -1
To sketch the graph we need to make a value table as given below
First take x values as, -1, 0, 1 from that find the values of y
At x = -1 => y = -1 - 1 = -2
At x = 0 => y = 0 - 1 = -1
At x = 1 => y = 1 - 1 = 0
From the above calculations, the value table is
x -1 0 1
y -2 -1 0
Use the above value and Sketch the graph
[ the resultant graph is shown below ]
The straight line y = x -1 is shown figure
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Gabriel has a stack of nickels that is 2 inches tall. The thickness of a nickel is
0.08 inch. How many nickels does Gabriel have?
Show your work.
Answer: Gabriel has
nickels.
Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
As given in the question,
Gabriel has 2 inches tall stack of nickel
Thickness of each nickel = 0.08inch.
Let 'n' be the number of nickels Gabriel has .
Required equation to get the number of nickel is equal to :
0.08 × n = 2
⇒ n = 2 / 0.08
⇒ n = 200/ 8
⇒ n = 25
Therefore, Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
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Answer 0.04
Step-by-step explanation:
because 0.08 divided by two is 0.04
solve the absolute value inequality.
|-3x|-7≥ 11
Answer:
x ≥ 6
Step-by-step explanation:
|-3x| - 7 ≥ 11 The absolute value of -3x is 3x
3x - 7 ≥ 11 Cancel the 7 by adding it on both sides
3x ≥ 18 To get x by itself divide 3 on both sides
x ≥ 6
Need asap! Write the expression as a power and evaluate it. The expression as a power is __. The value is__.
8•2^7 and 16•32
The expression as power is written as 2¹⁰ and 2^9
The values are
2¹⁰= 1024 2^9 = 512How to write expression as a powerpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.
8• 2^7
= 2 * 2 * 2 * 2^7
= 2^10
= 1024
16•32
2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2^9
= 512
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round this number to the hundredth 3.6432
Mia is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 15 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 18^{\circ}
∘
, and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^{\circ}
∘
. If her eyes are 1.75 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters
How to find the distance between the pointsinformation given in the question
Mia stands at a horizontal distance of 15 meters from the building
The angle of elevation from her eyes to the roof ((point AA)) is 18
the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^
her eyes are 1.75 meters from the ground
The direction of movements describes a right angle triangle of
opposite = height of antenna + height of the building
adjacent = 15 meters
The distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The the height of the antenna is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only
tan 53 = opposite / 15
opposite = 15 * tan 53 = 19.906 meters
opposite = 15 * tan 18 = 14.266 meters
Height of the antenna
= 19.606 - 14.266
= 5.34 meters
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q(x) = -x-2
r(x) = x² + 2
Find the following.
(r∙q)(-5) =
(q∙r)(-5) =
Answer: 5q-5r -5q+5r
Find the value of k such that the system of linear equations is inconsistent.
6x-12y = -7
2x + ky = 14
For the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
As given in the question,
Given system of linear equations are as follow:
6x-12y = -7 ____(1)
2x + ky = 14 _____(2)
Form equation (1) we have,
6x -12y = -7
⇒3 ( 2x -4y) = -7
⇒ 2x - 4y = -7 /3 ____(3)
From equation (2) and (3) we have,
2x + ky = 14
2x - 4y = - 7/3
Value of k so that the given system of equations are inconsistent is given by:
k = -4
For inconsistent there is no solution.
Therefore, for the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.
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Find the value of the expression:
3x^0 for x=2.6
Answer:
1
Step-by-step explanation:
We don't even need to calculate 3 x 2.6 considering any number raised to the power of zero equals 1.
(HELP ASAP) ABC Is Isosceles m
Answer:
m∠A = 55°-----------------------------
A and C are congruent angles opposite to congruent sides of the isosceles triangle.
m∠A = m∠C3x + 40 = x + 503x - x = 50 - 402x = 10x = 5Find the measure of ∠A
m∠A = 3×5 + 40 = 15 + 40 = 55Answer:
The angle A is 55°.
Step-by-step explanation:
We know that,
→ <A = <C
Now the value of x will be,
→ 3x + 40 = x + 50
→ 3x - x = 50 - 40
→ 2x = 10
→ x = 10/2
→ [ x = 5 ]
Then the value of m<A is,
→ A = 3x + 40
→ A = 3(5) + 40
→ A = 15 + 40
→ [ A = 55° ]
Hence, the answer is 55°.
NEED HELP ASAP!! ( NEED DONE WITHIN THREE MINS OF POSTING)
Answer: i am not positive but i think 2.5 on x and 9, and 27 on y
Step-by-step explanation: just want to help asap
The figure below is made up of a square with height, h units, and
a right triangle with height, h units, and base length, b units.
h
b
The area of this figure is 80 square units.
Write an equation that solves for the height, h, in terms of b.
Answer: $4x4x
Step-by-step explanation:
If the random variable Zhas a standard normal distribution, then P(1.17 S ZS 2.26) is
The value of P(1.17 <= Z <= 2.26 ) is 0.1091
From the question, we have
Z value for 1.17 is 0.8790
Z value for 2.26 is 0.9881
P(1.17 <= Z <= 2.26 ) = 0.9881 - 0.8790 = 0.1091
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be kilograms.
According to the scatter plot provided, the weight for someone who is 1.5 meters tall is predicted to be 45.45 kilograms.
What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical and analytical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the weight (in kilogram) would be plotted on the y-axis of the scatter plot while the height (M) would be plotted on the x-axis of the scatter plot.
From the scatter plot (see attachment) which models the relationship between data points in the table, a linear function for the line of best fit is given by:
Weight, kg = -114.3 + 106.5M
When M = 1.5 meters, we have:
Weight, kg = -114.3 + 106.5(1.5)
Weight, kg = -114.3 + 159.75
Weight, kg = 45.45 kg.
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Complete Question:
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be ____ kilograms.
A relation is shown: {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)} Which set of information is true about the relation shown?
The set of information that is true about the relation is:
Domain: {3, 4, 5, 6}
Range: {-8, -1, 2, 7}
The relation is not a function.
How to Determine a Relation that is a Function?A relation that represents a function will have each of its domain elements related to exactly one range element.
All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,
Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.
Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:
The domain of the relation is: {3, 4, 5, 6}
The range of the relation is: {-8, -1, 2, 7}
The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.
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Thelma and Patrick went to a cafe
for lunch. One of them is a
vegetarian. Thelma ordered a
turkey sandwich with extra
mustard. Who is the vegetarian?
Patrick is vegetarian and Thelma is non vegetarian.
What are vegetarian?
The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.
Main Body:
As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.
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Screenshot included in this work
The two blanks on the left side of the equation and the solution blank should be completed with the following ratios:
2050 kg/1 m³ × 2.2 lb/1 kg × 1 m³/35.3 ft³ = 127.76 lb/ft³.
What is a conversion factor?In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.
Conversion:
2050 kg/1 m³ × 2.2 lb/1 kg = 4,510 lb/1 m³
4,510 lb/1 m³ × 1 m³/35.3 ft³ = 4,510 lb/35.3 ft³
4,510 lb/35.3 ft³ = 127.76 lb/ft³.
Additionally, take note of the following units of conversion:
kg = kilograms.m³ = cubic meter.lb = pounds.ft³ = cubic foot.In conclusion, we can logically deduce that the crate's density is equal to 127.76 pounds per cubic foot.
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A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
The area of left over wrapping paper is 380 square inches
How to determine the amount left?The given dimensions are:
Box = 8 inches by 9 inches by 10 inchesWrapping paper = 2 feet by 3 feet.The surface area of the box is calculated as
Surface area = 2(lw + lh + wh)
This gives
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches
The surface area of the wrapping paper is calculated as
Wrapper = lw
This gives
Wrapper = 2 * 3 = 6 square feet
Express the area in square inches
Wrapper = 864 square inches
The area left is the difference between the areas calculated above
i.e. Amount left = Wrapper - Box
So, we have
Amount left = 864 square inches - 484 square inches
= 380 square inches
Hence, the amount left is 380 square inches
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Evaluate the power.
0.5² =
(Type a whole number or a decimal.)
-1/3v = -7 how do i solve this equation?
Answer: v=2.33333333333333.........
Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......
5. Simplify the complex fraction. a.-2/7
1 1/3
The simplification of the complex fraction is found as 11/14.
Define complex fraction/mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that. Step 1: Multiply the mixed fraction's denominator by the whole number component.Step 2: Increase the product from Step 1 by the numerator.Step 3: In the numerator/denominator form, write the improper fraction using the total from Step 2.For the given question, the expression is-
-2/7 + 1 1/3
To convert mixed fraction 1 1/3 i improper fraction, multiply 3 with 1 and add 1.
1 1/3 = 1 x 3 + 1 /3
1 1/3 = 4/3 Put in main equation.
-2/7 + 4/3
Simplify the expression.
= -2 x 3 + 4 x 7/ (7 x 4)
= -6 + 28 / 28
= 22/28
Divide both with 2
= 11/14
Thus, the simplification of the complex fraction is found as 11/14.
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The correct question is
Simplify the complex fraction.
-2/7 + 1 1/3
Pls help 3z2-6z for z=5
Answer:
0
Step-by-step explanation:
to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.
Answer: 78
Step-by-step explanation:
3z2-6z for z=5
Solve the inequality4x + 13 ≥ 27
Work Shown:
4x + 13 ≥ 27
4x + 13-13 ≥ 27-13
4x ≥ 14
4x/4 ≥ 14/4
x ≥ 7/2
The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).
Note: 7/2 = 3.5
Given mn, find the value of x.
(2x+6) (x+9)"
Answer:
(2x+6) = (x+9) ; x = 3
Step-by-step explanation:
-x both sides ; 2x-x = x and -6 both sides which is x = 3
A model rocket is launched with an initial upward velocity of 235 feet the Rockets height H in feet after t seconds is given by the following
By assuming that the initial height of the rocket is the ground, we will get the height equation:
H(t) = -16*t^2 + 235*t
How to find the equation for the height?The height equation for any object near the surface of the heart that is not being subject to any other forces than the gravitational one is:
H(t) = -16*t^2 + v*t + h
Where:
t represents the time in seconds.
the first coefficient -16 is half of the gravitational acceleration in feet over squared seconds.
v is the initial velocity, which in this case is 235 ft/s
h is the initial height, in this case we assume is zero (the rocket is launched from the ground)
Replacing all that in the height equation, we will get:
H(t) = -16*t^2 + 235*t
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What is the image of (-9,12)(−9,12) after a dilation by a scale factor of \frac{1}{3} 3 1 centered at the origin?
The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
In the given question,
We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.
Since we have to find the image after a dilation.
So we learn about it now,
Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.
So the given point is (-9,12).
Scale factor is 1/3.
So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as
=(-9×1/3,12×1/3)
Simplifying
=(-3,4)
Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2y - 3x = 6
Equation of the line is y = 3/2x + 3.
Define slope intercept form.Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The "slope-intercept" form is one of the most popular methods. It is so named because it makes the slope and y-intercept of the equations in the equation more clear. The number that is placed before the x is the slope.
Given,
Slope intercept form:
Formula:
y = mx + b
Where m = slope
2y - 3x = 6
2y = 6 + 3x
Equation:
y = 3 + 3/2x
y = 3/2x + 3
Equation of the line is y = 3/2x + 3.
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mr colton needs 4.62 cups of flour to make 3 pound of dough.How many cups does she need to make 2 pounds of dough
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10
Let the number of cups be represented by x.
This will be expressed as:
2/3 = x/4.62
Cross multiply
3x = 2 × 4.62
3x = 9.24
Divide
x = 9.24 / 3
x = 3.08
Therefore, 3.08 cups are needed.
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Answer:
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
Step-by-step explanation:
Find the exact solutions of the given equation in the interval .
sin 4x= –2sin 2x
The exact solutions of the given equation in the interval are;
A: x = 0, π/2, π, ³/₂π
How to find the exact solutions of trigonometric equations?
We are given the equation as;
sin 4x = –2sin 2x
Writing the equation in standard form gives;
sin 4x + 2sin 2x = 0
Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;
2sin 2x cos 2x + 2sin 2x = 0
Factorize to get;
2sin 2x(cos 2x + 1) = 0
A. sin 2x = 0
The unit circle will give us 3 solutions for 2x as follows;
2x = 0
Thus; x = 0
2x = π
Thus; x = π/2
2x = 2π
Thus; x = π
B. cos 2x = - 1
The unit circle gives 2 solutions for 2x as;
2x = π
Thus; x = π/2
2x = 3π
Thus; x = ³/₂π
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Complete question is;
How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?
Ryan is going to spin the spinner 80 times.
(b)
Work out an estimate for the number of times he should expect the spinner to land on 2
The estimate for the number of times Ryan should expect the spinner to land on 2 is 13.
How to calculate the number of times?From the information, the spanner has numbers labeled 1 - 6 and Ryan is going to spin the spinner 80 times.
It should be noted that the fraction for getting a 2 is 1 out of 6. This will be 1/6.
Therefore, when it's spinned 80 times, the expected number will be:
= 1/6 × 80
= 13
The number of times is 13.
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Complete question
A spanner has numbers labeled 1 - 6. Ryan is going to spin the spinner 80 times. Work out an estimate for the number of times he should expect the spinner to land on 2