The equation which best shows the relationship between Davis' savings, y and the number of months passed, x is; y = 20 + 5x.
What is the relationship between Davis' savings and the number of months that have passed?It follows from the task content that the equation which represents the relationship between Davis' savings and the number of months passed be determined.
According to the task content;
Davis has $20 in his savings account, and he adds $5 every month.
Let the total amount of savings be; y andLet the number of months passed be; x.Therefore, we have;
y = 20 + 5x
This follows from the fact that the amount added after each month is $5.
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What is the answer to this question
Answer:
soda: 97
Hot dogs: 56
Step-by-step explanation:
S-sodas
H- hot dogs
S+H=153
41+H=S
Substitute equation
(41+H)+H=153
41+2H=153
-41. -41
2H=112
/2. /2
H=56
S+56=153
-56. -56
S=97
Hopes this helps please mark brainliest
which of the following fractions is smaller 4/9 or 1/5
Answer:
1/5
Step-by-step explanation:
these fractions are proper fractions
Answer: 1/
Step-by-step explanation:
what is the vertex of -2x^2 +12x -10
The vertex of the function f(x) = x^2 + 12x is (-6, -36).
How can the vertex be expressed?The concept that will be used here is the concept of Standard equation of a curve in vertex form.
The standard equation can be written as
f (x) = ax^2 + bx + c
Then the Vertex is the (h,k)
Then the X-coordinate of the vertex can be written as (h = -b/2a) where k = f(h)
If we compare the given equation with the standard form, then we have
a = 1, b = 12 and c = -10
Then we can input the values into the (h = -b/2a)
h =[ -12/2(1)] = - 6
Then we can substitute the value of h in f (x) which is f(x) = x2 + 12x
k = f(h)= f (-6) =[ (-6)2 + 12 (-6)]
= [36 - 72] = -36
In conclusion the vertex is (-6, -36).
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Find the surface area and volume of each triangular prism (base is a right triangle).
triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft
The surface area of a triangular prism = 108cm2
The volume of the triangular prism = 48cm3
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
Given that
The Triangle legs are 3 and 4 feet long, the hypotenuse is 5 feet long, and the prism height is 8 feet tall.
We have to determine the surface area and volume of each triangular prism
here a = 3ft b = 4ft c = 5ft and height h = 8ft
Surface area of triangular prism = ab + h(a+b+c)
= 3x4 + 8(3+4+5)
= 12 + 8(12)
= 12 + 96
= 108cm2
Volume of triangular prism = ½(abh)
= ½ (3x4x8)
=1/2(96)
= 96/2
= 48cm3
Therefore
The surface area of a triangular prism = 108cm2
The volume of the triangular prism = 48cm3
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the united nations stores data about the kilowatt-hours of wind power produced around the world. the following data set gives information of the united states for 25 years, from 1990 to 2014, in units of million kilowatt-hours. using a calculator or statistical software, find the linear equation of the first 11 years of data, from 1990 to 2000. round the slope to two decimal places and the y-intercept to the nearest whole number. provide your answer below:
The value that the linear equation predicts for the year 2001 is 4652.15
The discrepancy between the actual and anticipated value is 2173.85
Given data;
Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.
The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.
To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.
It will be written as y = m(x) + c.
where,
The dependent variable is y. (in our example is quantity)
The independent variable is x. (in our example is the year)
'm' is equal to the slope of the variable X.
'C' is a constant.
The fitted equation is provided as follows:
Quantity = 186.87 (year) - 369274.72
Now that the value for the year 2001 has been provided,
Quantity = -1868.87 -369274.72
Quantity = 4652.15
The value that the linear equation predicts for the year 2001 is 4652.15.
The precise figure for 2001 is 6806.
For the year 2001, the discrepancy between the actual and anticipated values is
6806 - 4652.15 = 2173.85
The distinction is 2173.85.
(2173.85/6806)*100 is the percentage difference.
As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.
Hence,
The value that the linear equation predicts for the year 2001 is 4652.15
The discrepancy between the actual and anticipated value is 2173.85
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Which of the following is not an isometry
A). Translation
B). Line reflection
3). Point reflection
4). Rotation
The option that is not an isometry from the given transformations is 3). Point reflection.
What is an isometry?An Isometry refers to a transformation that leads to the distance and length of a shape being preserved when it is transformed.
Translations and rotations preserve the shape of a figure during transformation which means they preserve length which makes them an isometry. The same is true of line reflections.
Point reflections on the other hand, will lead to a change in dimensions for the figure being transformed.
In conclusion, `a point reflection is not an isometry.
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Does the function y=x have an inverse? If so does it pass the horizontal line test?
Yes, y=x has an inverse.
Yes, y=x passes the horizontal line test.
If it didn't pass the horizontal line test, it would not have an inverse.
i really need help. Strawberries cost $2.13 per pound and Annie purchased 1.2 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?
Annie paid a total of $2.6 for 1.2 pounds of strawberries
How to determine the amount paid?In this question, we have the following parameters:
Unit cost per pound = $2.13 per pound
Number of pounds = 1.2 pounds
The amount paid for the number of pounds is represented by the equation
Amount paid = Unit cost per pound x Number of pounds
Substitute the known values in the above equation So, we have the following equation
Amount paid = 2.13 * 1.2
Evaluate the products
Amount paid = 2.556
Approximate
Amount paid = 2.6
Hence, the amount is $2.6
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Answer:
2.56
Step-by-step explanation:
suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. most airlines charge a fee for baggage that weigh in excess of 50 pounds. determine what percent of airline passengers incur this fee.
In most of the cases airlines charges a fees for baggage weigh in excess of 50 pounds. Then about 94.06% passengers incur this fees.
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Given That,
Mean (μ) = 45 pounds and Standard Deviation (σ) = 3.2
This means that μ = 46 , σ = 3.2
Since, Most airlines charges a fee for baggage that weigh in excess of 50 pound.
Then, As a proportion this is 1 subtracted by the P - value of Z when
X =50. So,
Z = X - μ / σ
⇒ Z = 50 -45/ 3.2
⇒ Z = 5/3.2
⇒ Z = 1.56
when Z = 1.56 has a P- value of 0.9406
Now, 0.9406 × 100%
= 94.06%
Therefor, 94.06% of airline passengers incur this fees.
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You have $18 and earn $0.25 for each cup of orange juice you sell. Write an equation that represents the total amount A (in dollars) you have after selling j cups of orange juice.
Answer:
A = 0.25*j + 1
Step-by-step explanation:
Answer:
[tex]A = 18 + \frac{j}{4}[/tex]
Step-by-step explanation:
A = 18 + j/4
A = Amount in $
Starting amount is 18 and a 1/4 dollar is earned for every cup of juice sold.
Help please
I need this by tomorrow
Answer:
I hope this will help. Tip: reuse the formula!
What is the next fraction
in this sequence?
Simplify your answer
5/14, 3/7, 1/2, 4/7 …
PLEASE HELP, QUESTION IN THE PICTURE
Step-by-step explanation:
AC is the combination of AB and BC.
so, AB + BC = AC
(2n - 1) + (4n + 5) = 10n - 12
2n - 1 + 4n + 5 = 10n - 12
6n + 4 = 10n - 12
4 = 4n - 12
16 = 4n
n = 4
Please help F(-1/2)=1 and f(0)=-4
Question:
Write a linear function f with f (- 1/2) = 1 and f (0) = -4
The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4
Let the equation in variables x and y can be written in the form y = mx + c
So f (- 1/2) = 1
this gives, 1 = -1/2m+c -----------eq 1
Also f (0) = -4
This gives -4 = c. --------------eq2
Now Putting the value of c in the equation in eq1 we get m=0.
So 1 = -1/2m+c
1 = -1/2m - 4
m = -5
Then we get;
y = -5x -4.
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Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies, what fraction of the cookies did she save?
Answer:
i think 2/15 of the cookies
Step-by-step explanation:
hope this helps
: in a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old?
the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243
the complete question is:
The demographic profile of Ecuador in 2018 is • 27.08% of the population are 0–14 years old • 18.35% are 15–24 years old • 39.59 are 25–54 years old • 7.53% are 55–64 years old • 7.45% are 65 years and older. In a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55–64 years old, 6 are 25–54 years old, 4 are 15–24 years old and 3 are 0–14 years old?
answer:
P(x) = P(x=2) + P(x=5) +p(x=6) +p(x=4) +p(x=3)
=20[tex]C_{2}[/tex][tex](7.45)^{2}[/tex][tex](2.55)^{18}[/tex]+20[tex]C_{5}[/tex][tex](7.53)^{5}[/tex][tex](2.47)^{15}[/tex]+20[tex]C_{6}[/tex][tex](39.59)^{6}[/tex][tex](0.41)^{14}[/tex]+20[tex]C_{4}[/tex][tex](18.35)^{4}[/tex][tex](1.65)^{16}[/tex]+20[tex]C_{3}[/tex][tex](27.08)^{3}[/tex][tex](2.92)^{17}[/tex]
P(x) = 0.2424
the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243
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what's the slope of 6x+13y= -18
Answer:
slope is the coefficient of x
so it is 6
good luck!!
sarah gets pocket money every week from the age of 5 until her 21st birthday and is given a choice of 2 options options .
option 1:get the same number of pounds each week as her age.
option 2 : get 5 pounds a week aged 5 and increasing by 15% a year.
which option should Sara choose ?
please help
The option that Sarah should choose is option 2.
Which option should Sarah choose?
Sarah would choose the option that give her the higher amount of money at her 21st birthday.
The amount that Sarah would earn each year with option 1 would increase at a linear rate. This is because she gets the same amount of money each year.
The form of a linear equation is y = mx + b
Where:
m = slope b = interceptThe amount that Sarah would earn each year with option 2 would increase at an exponential rate.
The general form of exponential equation is f(x) = [tex]e^{x}[/tex]
Where:
x = the variable e = constantThe rate of growth with an exponential function is faster than that of a linear function. It is for this reason that option 2 is the better option.
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Which of the following represents the series?
–12 + (–5) + 2 + 9 + 16
sum from k equals 0 to 4 of negative 19 plus 7 times k
sum from k equals 1 to 5 of negative 19 minus 7 times k
sum from k equals 0 to 4 of negative 12 plus 7 times k
sum from k equals 1 to 5 of negative 12 minus 7 times k
(image includes proper visuals for each option)
The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;
[tex]\sum\limits_{k = 0}^4-12+7\cdot k[/tex]What is an arithmetic series?An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.
The series in the question is; -12 + (-5) + 2 + 9 + 16
Each term in the series is obtained from the previous term by the addition of a 7The series in therefore a series of an arithmetic sequence
The equation of the series when the first term is -12 can therefore be presented as follows;
-12 + 7·k
Where;
-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1
When n = 1, k = 0, which gives;When k = 0, the expression, -12 + 7·k = -12 + 7 × 0 = -12When k = 1, -12 + 7·k = -12 + 7 × 1 = -5When k = 2, -12 + 7·k = -12 + 7 × 2 = 2When k = 3, -12 + 7·k = -12 + 7 × 3 = 9When k = 4, -12 + 7·k = -12 + 7 × 4 = 16The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4
The expression that represents the series is therefore the option;
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Image is the equation
Answer:
y = [tex]\frac{3}{4}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{3}{4}[/tex] , then
y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation
to find c substitute (- 4, 5 ) into the partial equation
5 = - 3 + c ⇒ c = 5 + 3 = 8
y = [tex]\frac{3}{4}[/tex] x + 8 ← equation of line
Wyatt says that both red lines are lines of symmetry. Is he correct? Why or why not?
Answer:
Step-by-step explanation:
There is only one line of symmetry:
because the one that is vertical is not representing symmetry.
find the middle side of each triangle. round your answers to the nearest tenth if necessary.
Step-by-step explanation:
using Pythagoras theorem.
37,
x² = 6² + 8²
x = √6²+8² = 10ft
38.
13²=12²+x²
169 = 144 + x²
√169 - 144 = x = 5cm
hope it helps. :)
Answer:
x = 10 and x = 5
Step-by-step explanation:
using Pythagoras' identity
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
(36)
x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )
x = [tex]\sqrt{100}[/tex] = 10
(38)
13² = x² + 12²
169 = x² + 144 ( subtract 144 from both sides )
25 = x² ( take square root of both sides )
[tex]\sqrt{25}[/tex] = 5 = x
x = 5
polynomial function
Answer: (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 )
Step-by-step explanation:
To write a polynomial in standard form, simplify and then arrange the terms in descending order. Expand (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 ) using the FOIL Method.
A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers. What is the total cost of 12 printers?.
The total cost of 12 printers is; $493.41
Cost of first printer; C1 = $54
Cost of second printer is; 95% × 54 = $51.3
Cost of third printer is; 0.95 × 51.3 = $48.735
Cost of fourth printer = 0.95 × 48.735 = $46.298
Now, let us apply same pattern using a calculator for the remaining costs and we will have them as follows;
Cost of 5th printer = $43.983
Cost of 6th printer = $41.784
Cost of 7th printer = $39.695
Cost of 8th printer = $37.710
Cost of 9th printer = $35.825
Cost of 10th printer = $34.033
Cost of 11th printer = $32.332
Cost of 12th printer = $30.715
Total cos is; 54 + 51.3 + 48.735 + 46.298 + 43.983 + 41.784 + 36.695 + 37.710 + 35.825 + 34.033 + 32.332 + 30.715 = $493.41
Therefore, the total cost of 12 printers is $493.41
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What is the answer to 4r - 9r - 11r + 7r
Answer:
-11r
Step-by-step explanation:
4r - 9r = -5r
-5r - 11r = -16r
-16r + 7r = -11r
If a gallon of paint costs $18 and covers 180 ft²,
how much does it cost to paint a 900 ft² wall
Answer:
$90
Step-by-step explanation:
180x5 equal 00
$18x5 equals $90
algebra 2 please help :)!
How do this?Help pls give answer
Answer:
Step-by-step explanation:
Ok! So apparently I think you are learning about pre algebra. So the questions are saying what times 1/4=8 in that case it would be x = 32. x is just a fancy way to say you don’t know what it is.
A cubic polynomial function f has a leading coefficient of 2 and a constant term of -5. When f(1) is zero and f(2) is three what is f(-5). Explain?
The value of f(-5) = -130
A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.
A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:
Ax3 + bx2 + cx +d = 0
For the given question the cubic equation will be:
2x3 + bx2 + cx - 5 = 0
Given
Leading coefficient (a) = 2
Constant (T) = -5
f(1) = 0
f(2) = 9
Therefore the equation formed will be:
2x3 + bx2 + cx - 5 = 0
Now f(1) = 0
2(1)3 + b(1)2 + c(1) - 5 = 0
2 + b + c -5 = 0
b + c = 3
b = 3-c -----(1)
On solving f(2) = 3
2(2)3 + b(2)2 + c(2) - 5 =3
16 + 4b + 2c – 5 =3
4b +2c = 3 – 11
4b + 2c = -8 ----(2)
Now substitute the b value in equation (2)
4(3-c) + 2c = -8
12 – 4c +2c = -8
-2c = -20
C =10
Now substitute the c value in equation (1)
b= 3 – c
b = 3 -10
b = -7
Now substitute the b and c values in the cubic equation
2x3 - 7x2 + 10x - 5 = 0
Now calculate f(-5)
2(-5)3 - 7(-5)2 + 10(-5) - 5
= -250 + 175 – 50 -5
= -130
Therefore the value of f(-5) = -130
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A family buys a studio apartment for 150,000. They pay a down payment of $22,500. a.Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $60,000 down payment be?
please help!!!