Answers
The expression that represents the number of football cards that Frankie has is given as follows:
F = J + 65.
How to model the situation?The situation can be modeled by a system of equations, in which the variables are given as follows:
Variable F: number of football cards that Frankie has.Variable J: number of football cards that John has.Frankie has sixty-five more football cards than his friend John, hence the expression that represents the number of football cards that Frankie has is given as follows:
F = J + 65.
As the term sixty-five more means that the number 65 is added to the amount of cards that John has, which is symbolized by J, to obtain the amount F, which is the number of football cards that Frankie has.
Missing InformationThe problem asks for the expression of the number of cards that Frankie has.
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Related Questions
The function f(x) = 5one-fifth is reflected over the y-axis. which equations represent the reflected function? select two options.
Answers
The correct option D. f(x) = 5(5)ˣ and E. f(x) = 5(1/5)⁻ˣ, for the reflected function over the y-axis.
Explain the term reflected over the y-axis?The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be an additive inverse.We are aware of:
f(x) = 5(1/5)ˣ
Positive x-values and negative x-values are switched by a reflection over the y-axis, which also swaps the values of x and x.
Therefore:
f(ax) = f(x)
The following will be the value of the supplied function's y-axis reflection:
(Remember to swap out positive and negative x-values.)
f(x) = 5(1/5)⁻ˣ
A comparable form will be:
f(x) = 5(1/5)⁻ˣ
f(x) = 5(1/5)⁽⁻¹⁾⁽ˣ⁾
f(x) = 5[(1/5)⁻¹]ˣ
f(x) = 5(5)ˣ
Therefore
The following equations depict the reflected function:
f(x) = 5(5)ˣf(x) = 5(1/5)⁻ˣTo know more about the reflected over the y-axis, here
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The complete question is-
The function f(x) = 5(1/5)ˣ h is reflected over the y-axis. Which equations represent the reflected function? Select two options.
A. f(x) = One-fifth
B. f(x) = One-fifth.One-fifth.One-fifth
C. f(x) = 5One-fifth
D. f(x) = 5(5)ˣ
E. f(x) = 5(1/5)⁻ˣ
A radioactive isotope has a half life of 1 month. It begins with 500 grams. After 8 months, how many grams would it have. Round to the nearest two decimal places.
Answers
Answer:
t1/2=1m => 30days
A0=500g =0.5kg
t=8m = 240days
A=?
λ=ln2÷t1/2
λ=0.6931÷30
λ=0.0231033333
A=A0×e^-λ×t
A=0.5×e^-0.0231033333×240
A=1.953125grams
Which of the following is not a type of matrix?
A. square matrix
B. scalar matrix
C. trace matrix
D. term matrix
Answers
Term matrix is not a type of matrix among the given options.
A matrix is a rectangular array of numbers or other mathematical objects for which operations such as addition and multiplication are defined.
There are several types of matrices, including:
1. Square Matrix: A square matrix is a matrix in which the number of rows is equal to the number of columns.
2. Scalar Matrix: A scalar matrix is a type of matrix in which all the elements are equal to a single number (the scalar).
3. Trace Matrix: A trace matrix is a type of matrix in which the trace (sum of the diagonal elements) is a scalar multiple of the identity matrix.
4. Identity Matrix: An identity matrix is a type of matrix in which all the elements on the main diagonal are 1s and all other elements are 0s.
5. Symmetric Matrix: A symmetric matrix is a type of matrix in which the elements above and below the main diagonal are equal.
6. Diagonal Matrix: A diagonal matrix is a type of matrix in which all the elements outside the main diagonal are 0s.
7. Triangular Matrix: A triangular matrix is a type of matrix in which all the elements above or below a specific diagonal are 0s.
8. Orthogonal Matrix: An orthogonal matrix is a type of matrix in which the product of two matrices is the identity matrix.
9. Singular Matrix: A singular matrix is a type of matrix in which the determinant is 0.
10. Inverse Matrix: An inverse matrix is a type of matrix in which the product of the matrix and its inverse is the identity matrix.
Therefore, the answer is D. Term Matrix, as it is not a type of matrix.
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Option D is Answer. Compared with the given matrix, The Term matrix is not a type of matrix.
Term Matrix: It defines a document-term matrix as simply a matrix describing the frequencies of all terms occurring in the collection of text documents.
square matrix: A matrix which is having the same number of rows and columns. It is also called an n*n matrix.
Example:
[tex]\left[\begin{array}{ccc}1&2\\4&5\\\end{array}\right][/tex]
Scalar matrix: It is a type of square matrix, whose diagonal elements are equal and off-diagonal elements are zero. It is basically a multiple of the square identity matrix.
Example:
[tex]3I=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] =\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right][/tex]
Where I define the Identity matrix.
In a square matrix, the sum of elements of the principal diagonal is called the ‘trace of a matrix’. We denote the trace of the matrix A by ‘tr A’.
Example: If A =
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
, then tr A = 1 + 5 + 9 = 15.
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6.0 percent of a population are infected with a certain disease. there is a test for the disease, however the test is not completely accurate. 90.0 percent of those who have the disease test positive. however 3.1 percent of those who do not have the disease also test positive (false positives). a person is randomly selected and tested for the disease. what is the probability that the person has the disease given that the test result is positive?
Answers
Probability of the person has the diseases and the test result is positive = 1/90 = 0.011
What is probability?Probability refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.
How can we calculate probability?Given, percentage of people who have disease and test result positive =90
percentage of people who has not disease but test result positive =3.1
Suppose 6.0 percent of population are infected
Now, probability of a randomly selected person who has diseases and test positive
= 1/90
= 0.011
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find the value of x.
Answers
So… 76+49+x=180
= 125 + x = 180
= 125-125 + x= 180 - 125
=. x= 55°
Hope this helps :)
A rocket will launch in 3. 75 hour and the launch time i 11:20 am. What time i it now??
Answers
The time presently is 8:15 a.m, and the rocket will launch in 3.75 hours, at 11:20 a.m.
What is subtraction?Subtraction (represented by the minus sign) is one of four mathematical operations, the others being addition, multiplication, and division. Subtraction is the procedure of removing items from a collection. Subtraction may be thought of as the inverse of addition. Counting forwards helps children learn to add. To subtract, they just count backwards.
Here,
launch time=11:20 am
time left to launch=3.75 hour
=0.75*60
=45 minutes
= 3 hours 45 minutes
=11 hours 20 minutes-3 hours 45 minutes
=8 hours 15 minutes
=8:15 AM
The time right now is 8:15 AM when rocket will launch in 3. 75 hour and the launch time is 11:20 am.
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ts.
11. Given the financial transaction: "Having bought
a pair of shoes worth $85 and used them for a
month". Which of the following statements is
NOT TRUE?
[A] Your cash balance decreases.
[B] You are increasing your liability.
[C] Your wealth decreases.
[D] You are incurring an expense.
[E] You are acquiring (non-cash) asset.
Answers
The correct answer is [B] You are increasing your liability.
When you buy a pair of shoes for $85, your cash balance decreases by $85, which means that your wealth also decreases by $85. This is represented by [A] and [C].
[D] You are incurring an expense is also true, because you are spending money on the shoes.
[E] You are acquiring (non-cash) asset is also true, because you are obtaining an asset (the shoes) that you can use or sell in the future.
[B] You are increasing your liability is not true, because a liability is a debt or an obligation that you owe to someone else. In this case, you are not taking on any debt or obligation by buying the shoes, so your liability does not increase.
g there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join?
Answers
there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join is 120
A fractional factorial experiment utilizes subset of combinations that are gotten from the full factorial experiment. They are applicable when there are too many inputs to screen practically or cost or time would be excessive.
Also, using the fractional factorial experiment makes running the experiments faster and cheaper.
10C3 = 10! / (7!*3!)
= 10*9*8/6
= 120
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help plss and if u could plot the point as well thats better
TY
Answers
The linear functions defined in this problem are given as follows:
1. y = -x + 3.
2. y = x - 3.
3. y = 3x + 1.
4. y = -2x - 2.
How to define the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
The coefficients and their meaning are given as follows:
m is the slope, representing the rate of change of the output variable y relative to the input variable x.b is the y-intercept, representing the value of y when the graph of the function touches or crosses the y-axis.From the second bullet point above, the intercepts for each function in this problem are given as follows:
1. b = 3.2. b = -3.3. b = 1.4. b = -2.The slopes are given as follows:
1: m = -1, when x increases by 1, y decays by 1.2: m = 1, when x increases by 1, y increases by 1.3. m = 3, when x increases by 1, y increases by 3.4: m = -2, when x increases by 1, y decays by 2.Missing Information
The problem is incomplete, hence we just define the linear functions.
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A city has a 5% sales tax. What is the constant of proportionality?
Answers
Answer: 0.05
Step-by-step explanation:
The equation is k = y/x, which is a constant change rate
Take 5 divided by 100 = 0.05
5% = 0.05
So the constant of proportionality is 0.05
Which equation represents twenty-nine is one-third of the number n?
Answers
Answer:
29=n/3
Step-by-step explanation:
Answer:
29 = n/3
Step-by-step explanation:
[tex]29 = \frac{1}{3} of \: n \\ 29 = \frac{1}{3} \times n \\ 29 = \frac{n}{3} [/tex]
How would I solve this? I need steps..
Answers
Option 2 and option 4 are the respective answers.
what is a discriminant of a quadratic equation?The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
Given here -3x²+6x+2 = 0
therefore the discriminant is (6)² - ( -3×4×2) = 60
Thus the parabola formed by the curve would intersect the x-axis twice
Now for the second part of the answer, the equation is given as
3(2x-1) (x-4) = 3( 2x² - 9x + 4)
=6x² - 27x + 12
Applying the direct formula for root we get x = 27 + √(27² − 4×6×12)/12
Hence, option 2 is the correct answer for part 1, and option 4 is the correct answer for the latter question.
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when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5
Answers
When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13 degrees
The distance between point a to point b = 5.3 feet
The length of the top side = 3 feet
Therefore, it will form a right triangle
Here we have to use trigonometric function
Here adjacent side and the hypotenuse of the triangle is given
The trigonometric function that suitable for the given conditions is
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos θ = 3 / 5
θ = cos^-1(3 / 5)
θ = cos^-1(0.6)
θ = 53.13 degrees
Therefore, the value of θ is 53.13 degrees
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sqrt{ 45 Multiplyed bysqrt 10
Answers
Answer:
Step-by-step explanation:
a researcher at a major hospital wishes to estimate the proportion of the adult population of the united states that has high blood pressure. how large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 5%?
Answers
For the sample to be 99% confident and sample proportion to not differ more than 5% the sample size is 664 .
The term Sample Size is defined as number of observations that is used for determining estimations of a given population .
it is given that , sample proportion should not differ by 5% ,
that means , the Margin of Error (ME) = 0.05 .
Since , the prior information is unknown
we assume the sample proportion(p) = 0.05 .
and level of significance (α) ⇒ 0.01 ;
By using the z table ,critical value for 99% confidence interval is = 2.576
The sample size(n) can be calculated by the formula ,
n = p(1 - p)[(critical value)/ME]² ;
substituting the values of p , critical value and ME in the above equation ,
we get ;
n = 0.05×(1 - 0.05)×[2.576/0.05]²
n = 0.25 × 2654.3104
n = 663.5776
n ≈ 664
Therefore , the required sample size is 664 .
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A table of values of a linear function is shown below. Find the output when the input is n Type your answer in the space provided.
Input 1 2 3 4 n
Output -7 -9 -11 -13
Answers
Output of n= -15
The fraction 5/6 * i is equivalent to what percent ? Round your percent to the nearest tenth. 5/6 is approximately 96
Answers
It is approximately equal to 83.3%
What are percentages?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”
Given here, 5/6 thus in percentage terms it will be = 5/6 × 100
= 83.3%
Hence the answer is 83.3%
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-(12/5a-7x+31/6b)-3x+3a b
Simplify
Answers
Answer:
3ab-12a/5-31b/6+4x
Step-by-step explanation:
PLLEAASSEEE HELPP MEEEE DONT ANSWER IF U NOT GOING TO HELP PLS
Answers
On solving the provided question by slope intercept form, equation formed id=s 3x + 4y - 14= 0 .
What is Slope Intercept Form?One of the most popular ways to express a line's equation is in the slope intercept form of a straight line. Given the slope of the straight line and the y-intercept, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). A line's equation is the equation that each point on the line fulfills. There are several ways to solve the equation for a straight line given as, - Slope-intercept form, Point slope form Two-point form and Intercept the form
slope = -3/4
points ( -2,5 )
equation,
(y - y1) = m(x - x1)
( y - 5) = -3/4(x+2)
4y - 20 = -3x - -6
3x + 4y - 14= 0
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True
False
ܘ ܗ
10
15-
f(x)
0
3
Answers
The range of the given function in the figure is R - {0, 1, 2, 3}.
What is the range of a function?The range of a function is represented by the set of output values for the given input values.A range for a function depends on the domain of the function. Where the domain is nothing but the set of input values to the function.If a function is given by y = f(x), then the range is given by R = {y: x ∈ D of f}D - the domain of the function; R - the range of the functionCalculation:The given mapping shows a function f(x).
There are 4 inputs to the function and 5 outputs.
So, the domain set for the given function is written as D = {0, 5, 10, 15}
And the range set for the given function is written as R = {0, 1, 2, 3}
(Since the 5th output is repeating, in the range it is considered only once).
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A shape has 7 non-congruent sides. If 6 of the exterior angles measure 310
degrees, and the remaining angle measures (6x + 2) degrees, what is the value
of x ?
Answers
The last remaining non - congruent side measure = 48°
what is non- congruent sides?Non congruent means "not congruent," i.e., not the same shape, and the sides. Congruent shapes are those that are copies of one another that have been rotated, reflected, and translated.
given
the sum of 6 exterior angles = 310°
remaining angle = ([tex]6x+2[/tex])
All sides of exterior angles sum= 360°
so , remaining angle + sum of all exterior angles=360°
[tex](6x+2)[/tex] + 310° = 360°
[tex](6x+2)[/tex] = 360° - 310C
[tex](6x+2)[/tex] = 50°
[tex]x[/tex] = 48°
The last remaining non - congruent side measure = 48°
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Determine the period.
Enter
Answers
Answer:
Your answer should be [tex]\frac{\pi }{7}[/tex]
Step-by-step explanation:
Looking at the x-axis we can say that is our b.
Period Formula: 2π/b.
x-axis is from 0 to 20.
b = 14 because of the rise to rise.
2π/14 = π/7
use the side-by-side boxplots shown to complete parts (a) through (e).
Answers
(a) The median of variable x is 70.
(b) The third quarterly of variable y is 94.
(c) Variable y has more dispersion.
(d) Shape of variable x is Symmetric.
(e) The shape of y variable is Skewed left.
a) The median of the variable x, which sits in the middle of the provided box plot, is 70 (roughly).
b) Variable Y's third quarterly value is 94. (approximately).
c) Because Q1 is farther away from the median than Q2, variable y has a higher inter quarterly range than variable x.
d) The shape of the variable x is symmetrical because both the left and right whiskers are roughly the same length and the median is located in the center of the box.
e) The left whisker of the y variable is longer than the right whisker, and the median is located outside the box's center.
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The complete question is given below:
One ector of a circle ha an area of 121 quare centimeter and an arc meaure of 36'. What i the area of the circle to the nearet
quare centimeter
Answers
The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]
Given in the question,
The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]
The measure of an arc = is 36 inches.
According to the attached figure,
Let us consider the arc length = L
Let radius = r
As per the question L = 36'
Let the radius be
To calculate the length of the arc we need to use the formula,
L = r x θ
36 = r x θ
θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1
Now according to the area of the sector of the circle,
A = [tex]r^{2}[/tex] x θ / 2
121 = [tex]r^{2}[/tex] x θ / 2
[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )
[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex] ----- equation 2
r = [tex]\frac{2 * 121 }{36}[/tex]
r = 6.72 cm.
Now if the radius is = 6.72 cm
Diameter = 2 x radius
= 2 x 6.72
= 13.44 cm
Area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi[/tex] x 6.72 x 6.72
= 144.87 [tex]cm^{2}[/tex]
Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]
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Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point
O and its radius is
units. The equation of this circle in standard form is
Answers
The equation of this circle in standard form is x² + y² - 8x - 16y + 73.75 = 0
How to determine the equation of this circle in standard formFrom the question, we have the following parameters that can be used in our computation:
Endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)
These endpoints represent endpoints of the diameter
So, we have the diameter to be
diameter = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
diameter = √[(4 - 4)² + (5.5 - 10.5)²]
Evaluate
diameter = 5
So, we have
radius, r = 5/2
The midpoint is
(a, b)= 1/2[(4 + 4, 5.5 + 10.5)]
So, we have
(a, b)= (4, 8)
The circle equation is calculated as
(x - a)² +(y - b)² = r²
Substitute the known values in the above equation, so, we have the following representation
(x - 4)² +(y - 8)² = 2.5²
This gives
x² - 8x + 16 + y² - 16y + 64 = 6.25
Evaluate the like terms
x² + y² - 8x - 16y + 73.75 = 0
Hence, the equation is x² + y² - 8x - 16y + 73.75 = 0
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Geometry: 6.7_Law of Cosines: 15 POINTS
Answers
The measure of side a is 4.1 unit.
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
c² = a² + b² - 2ab cos C
(c is opposite side to angle A)
In the given triangle ABC, we have sides BC = a, AB = b and AC = c
Now we know as per cosine rule for all three sides of the triangle.
c² = a² + b² - 2ab cosC
Where; b = 9 and c = 7 degrees
Angle A = 35 degrees
Plugging these values into the equation, we have;
a² = c² + b² - 2cb cos A
a² = 9² + 7² - 2(9)(7) cos (35)
a² = 81 + 49 - 126 x (-0.9036)
a = 4.1
Therefore, the side a is 4.1 unit.
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what is the slope of the line (5,-9) and (5,2)?
Answers
Answer:
The slope of a line is a measure of its steepness or incline. It is calculated by dividing the difference in the y-coordinates of two points on the line by the difference in their x-coordinates. In the case of the line (5,-9) and (5,2), the difference in the y-coordinates is -9 - 2 = -11 and the difference in the x-coordinates is 5 - 5 = 0. Since division by 0 is undefined, the slope of the line (5,-9) and (5,2) is undefined.
In general, when the x-coordinates of two points on a line are the same, the line is vertical and has no slope. This means that the line (5,-9) and (5,2) is a vertical line and has no slope.
The slope of a line is calculated as the rise over the run, which is the difference in the y-coordinates divided by the difference in the x-coordinates. In this case, the line has the same x-coordinate for both points, so the rise and run are both zero, and the slope is undefined.
the difference between the sample statistic and the population parameter when sampling is done correctly is referred to as what?
Answers
A sampling error is the difference between a population parameter and a sample statistic.
Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.
Thus, the difference is defined as sampling error.
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Rita has $1,000 in a savings account. The interest rate is 5% per year and is not compounded. How much interest will she earn in 1 year? Use the formula i = p x r x t, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
The interest earned is $50
What is simple interest?Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. Simple Interest=P×r×t
where:
P=Principal
r= interest rate per annum
t=Number of years
Given here, P = $1000 , r = 5% t=1
thus using the formula we get SI = 1000×5/100×1
= $50
Hence, the interest earned is equal to $50
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because of different units being used for various data series, which fit statistic can be used across different series that are in fact measured in different units?
Answers
The fit statistic that can be used across different series that are in fact measured in different units is; MAPE
What statistic can be used?There are different statistics models in this regards such as;
Mean Absolute Error (MAE)
Mean Absolute Scaled Error (MASE)
Accuracy Percent (Accuracy %)
Mean Squared Error (MSE)
Root Mean Squared Error (RMSE)
Mean Absolute Percent Error (MAPE)
Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.
The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.
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