Using Graphs to compare two quantities.
The area of a given triangle is 35 square meters. The height of the triangle is (g-11) meters and the base is (g- 8) meters.
area of triangle = (b × h) ÷ 2
where b is the base so (g - 8)m,
h is the height so (g - 11)m
and area is 35
35 = (g - 11) × (g - 8) /2
35 = g² - 19g + 88 / 2
35 = 1/2g² - 19/2g + 44
1/2g² - 19/2g + 9 = 0
use the quadratic formula to find the two values of g and you will get:
g = 18 and g = 1
if we use g as 1 we will get negative metres for the values for the base and height so we use g = 18 instead!
base = (18) - 8
= 10m
height = (18) - 11
= 7m
what is 8x8 divided by 4
Answer:
16 is the answer
Step-by-step explanation:
hope this helps
Answer:
16
Step-by-step explanation:
8 x 8 = 64
divide
64 divided by 4 = 16
PLEASE HELP!
A survey was conducted of 371 teenagers. Thirty-five percent of the teenagers said they occasionally smoked cigarettes.
A. Find the margin of error for this survey
B. Write a statement about the percentage of teenagers who occasionally smoke cigarettes
a. The margin of error for this survey is of: 4.85%.
b. The 95% confidence interval for the percentage of teenagers who occasionally smoke cigarettes is of:
(30.15%, 39.85%).
How to obtain the confidence interval?Confidence intervals for proportions are obtained using the z-distribution.
The bounds of the interval are given as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size and the estimate in this problem are given as follows:
[tex]n = 371, \pi = 0.35[/tex]
The margin of error is given as follows:
[tex]M = 1.96\sqrt{\frac{0.35(0.65)}{371}} = 0.0485[/tex]
As a percentage, it is of 4.85%.
Then the bounds of the interval are given by the estimate plus/minus the margin of error, hence:
Lower bound: 35 - 4.85 = 30.15%.Upper bound: 35 + 4.85 = 39.85%.More can be learned about the z-distribution at https://brainly.com/question/25890103
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What is the highest possible number of positive real zero/s does the polynomial function f(x) = x4 – 3x3 – 4x2 + 6x - 1 have?
a. 3
b. 1
c. 2
d. 4
Answer: The answer to the question is $\boxed{\text{(d)}\ 4}$. This is because a polynomial of degree 4 can have at most 4 zeros, and those zeros can be either real or complex numbers. Since the question asks for the maximum number of positive real zeros, the answer is $\boxed{\text{(d)}\ 4}$.
Step-by-step explanation: The maximum number of positive real zeros that a polynomial function of degree 4 can have is 4. This is because a polynomial of degree 4 can have at most 4 zeros, and those zeros can be either real or complex numbers. Since the question asks for the maximum number of positive real zeros, the answer is $\boxed{\text{(d)}\ 4}$.
A(n) ____ is formed by two adjacent sides of a triangle. A:Corresponding angles B:Corresponding Sides C:Included Angle D:Congruent triangles E:Included Side
Answer: Corresponding angles
Step-by-step explanation: The answer is corresponding angles or "corresponding internal angles" form when two jointed sides or adjacent sides of a triangle meet. Look in the attachment below to see a picture showing the example of corresponding angles.
Two students, Mattie and Pete agreed to display their work.
Their work is shown below.
Pete is correct because the student used multiplication as the correct function operation to simplify the expression.
f(-5)=5, f(0)=10, write a linear function f with the given values
Answer:
F(x)= x +10 (Cus when x is 0, Function is 10)
Answer:
y=x+10
Step-by-step explanation:
You first need to find the y intercept using the coordinates where x equal 0. Then you can figure slope by solving for m when you plug in the other points.
Solve for each variable
x = 2 , y' = 70 , x' = 30 : by using the property of SAS(side angle side) in ΔKMN and ΔKLI as they were similar polygon.
What is SAS property of triangle ?The property of a triangle whose two sides and the angle between these sides are stated is "SAS," which stands for "Side, Angle, Side". The SAS formula can be used to determine the area of a given triangle ABC with two known sides and an included angle between these sides.
Assume that the triangle's three sides are a, b, and c.
A SAS Triangle's perimeter
The following formula can be used to determine a triangle's area using SAS:
When sides "b" and "c" are known, along with angle A, the triangle's area is equal to: 1/2 bc sin(A)
The area of the triangle is equal to 1/2 ab sin(C) when sides 'b' and 'a' as well as included angle B are known
when sides "a" and "c" were added using SAS in triangle 1ΔMKN ~ ΔJKL
So, MN/KN = JL/KL
(x+1)/12 = (3x-2)/32
∴ 5x = 10 ⇒ x = 2
Using same property (SAS) in triangle 2
J = 80
∴ 30 = <x'
∵ in a triangle sum of angles is equal to 180° so, y' + <
J + 30 = 180
∴ <J = 80
then, y' = 70 and x' = 30
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{(8, 2), (4, -1), (0, -1), (-4, 2)}
D=
R =
Function?
Therefore , range of given function is R ={2,-1,2} and Domain is D={8,4,0,-4}
What is a function?A function from a set X to a set Y in mathematics assigns each object of X exactly one element of Y. The domain and codomain of the function are denoted by the sets X and Y, respectively.
Here,
Given:{(8, 2), (4, -1), (0, -1), (-4, 2)}
Thus , to find the domain
D={8,4,0,-4}
And to find the domain we check the last term of every bracket,{(8, 2), (4, -1), (0, -1), (-4, 2)}
R ={2,-1,2}
Therefore , it is many one function and onto function
Therefore ,It is many one - one function because two elements is connected with single element.
It is onto because of all elements of set B is connected with Set A.
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The ratio of aving and expene of Sheryl i 2 : 3. If Sheryl ave $4000, find her income. (Income mean total earning)
She makes $10,000 a year.
What is ratio?An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. An equation with two ratios set equal to one another is called a proportion.
Sheryl's savings to spending ratio is 2:3, and she has $4,000 available.
Let her earnings be X.
She rescued 2*X/5 = $4000
X = 5*$4000/2
X= 10,000
Consequently, she earns 10,000.
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There are 95 green balls and 90 red balls in a box. How many balls must be chosen to
be certain we have the following?
Three of each color?
To be certain of attaining the required result , 5 green balls must be selected.
We are informed that a box contains 90 red balls and 95 green balls.
To ensure that we have the items below, we must find the balls.
One red and one green
Consequently, take away the box's 90 red and 95 green balls.
95-90 = 5
Consequently, 5 green balls must be picked.
The unitary method , in its most basic form, is used to calculate the value of a single unit from a specified multiple. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.
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A theater has 41 rows of seats. If there are 22 seats in the 1st row, 26 in the 2nd row, 30 in the 3rd row . How many seats are there in total? Show and explain all work.
tim tebow had hit 2 hits in 7 attempts. if he continues this pattern how many hits will he have in 119 attempts?
Answer:
Step-by-step explanation:
it will be 22
What is an equation of the line that passes through the points (-3, -4) and
(-4, -6)?
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-3)}}} \implies \cfrac{-6 +4}{-4 +3} \implies \cfrac{ -2 }{ -1 } \implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +4 = 2 ( x +3) \\\\\\ y+4=2x+6\implies {\Large \begin{array}{llll} y=2x+2 \end{array}}[/tex]
A jar contains three marbles; 1 yellow (y), 1 orange (o), and 1 red (r). Which list shows all the possible outcomes for choosing two marbles at random from the jar if the first marble is replaced after it is drawn?
The list that shows all the possible outcomes for choosing two marbles at random is yy, oo, ro, yo, oy, ry, yr, or, rr
How to determine the list of possible outcomes?From the question, we have the following parameters that can be used in our computation:
Orange = o
Red = r
Yellow = y
From the question, we understand that the selection is with replacement
This means that it is possible to select a marble two times
So, we have the following representation
yy oo ro
yo oy ry
yr or rr
Hence, the list is yy, oo, ro, yo, oy, ry, yr, or, rr
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reteaching 5-4 proportions (PLEASE HELP)
The Answers are shown below:
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
1. 3 x 20= 60
10 x 6 =60
Yes, it is proportion.
2. 12 x 4 =48
24 x 2= 48
Yes, it is proportion.
3. 8 x 8= 64
5 x 16 = 80
No, it is not proportion.
4. 7/5, 21/15 is proportion
5. 16/3, 5/1 is not proportion
6. 12/9, 4/3 is proportion
7. 4/24, 2/6 is not proportion
8. 15/5, 6/2 is proportion
9. 9/3, 27/9 is proportion
10. 25/35, 5/7
or, 5/7, 5/7
The ratio is in proportion.
11. 15/3, 10/2
or, 3/1, 5/1
The ratio not in proportion.
12. 9/3, 12/4
or, 3/1, 3/1
The ratio is in proportion.
13. 2/5, 6/15
or, 2/5, 2/5
The ratio is in proportion.
14. 3.6/200, 1.8/100
The ratio is in proportion.
15. 6/12, 4/8
or, 1/2, 1/2
The ratio is in proportion.
16. 16/ 12 , 96/24
or, 4/3, 4/1
The ratio not in proportion.
17. 3/7, 2/5
The ratio not in proportion.
18. 2/22, 1/11
or, 1/ 11, 1/11
The ratio not in proportion.
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Which expression is represented by this model?
Responses
The correct option is 1/8 for the given expression.
What is fraction?
In Maths, a fraction is employed to represent the portion/part of the full issue. It represents the equal elements of the full. A fraction has 2 elements, particularly dividend and divisor. the quantity on the top is named the numerator, and therefore the range on the bottom is named the denominator.
Main body:
firstly , the model shows that it is divided into 4 parts
so the fraction becomes 1/4
as one part of 1/4 is divided into half so we can say
half of quarter which can be represented as
1/4*1/2 = 1/8
Hence the correct option is 1/8
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(c) Select all that describe ST.
ST describes the perpendicular bisector of PQ.
What is the perpendicular bisector?
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.
Here,
We have to find which statement describes the ST.
We concluded that ST describes the perpendicular bisector of PQ.
A perpendicular bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment.
Hence, ST describes the perpendicular bisector of PQ.
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Determine if each answer choice represents a proportional or not proportional linear relationship. drag each answer choices to the correct column. The order does not matter.
The proportional or not proportional linear relationship of the given options are;
a) y-intercept is not at the origin - non-proportional linear relationship.
b) Direct variation - proportional linear relationship
c) y = -7x - proportional linear relationship.
d) y = 5x + 1 - non-proportional linear relationship.
e) y = x - proportional linear relationship.
f) 4y = 2x - proportional linear relationship.
g) Non linear proportional relationship
h) Proportional linear relationship.
How to Interpret a Proportional Relationship?Proportional relationships are defined as relationships between two variables where their ratios are equivalent.
a) We are told that the y-intercept is not the origin. The equation of a line in slope intercept form is; y = mx + c
If c which is the y-intercept is not equal to zero, the this is a non-proportional linear relationship.
b) Direct variation is a proportional linear relationship because the two variables are directly related to each other.
c) y = -7x can be rewritten as; y/x = -7. Thus, this is a proportional linear relationship.
d) y = 5x + 1. As said in a above, this is also a non-proportional linear relationship.
e) y = x. can be rewritten as; y/x = 1. Thus, this is a proportional linear relationship.
f) 4y = 2x. can be rewritten as; y/x = 2/4. Thus, this is a proportional linear relationship.
g) This is a non linear proportional relationship because the rate is not directly proportional.
h) This is a proportional linear relationship as it is a defined rate.
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Rachel has a $10,000, three-year loan with an APR of 7.25%.
a. What is the monthly payment?
b. What is the total amount of the monthly payments?
c. What is the finance charge
Simple interest analysis reveals that
a) The installment was $321.53 per month.
b) The total amount of the payments is $11,575.
c) Interest was paid of $1,575.
How to find the Calculation?After t years, the amount of simple interest is calculated using:
A(t) = p(1 + rt)
that where:
The initial deposit is known as the primary, or P.
The interest rate in decimal form is r.
In this issue:
Hence, a $10,000 loan.
APR of 5.25%, which equals 3 years, therefore
Item c:
The result is A(3), so:
A(t) = P( 1 + rt)
A(3) = 10000[ 1 + 0.0525(3)]
A(3) = 11575
The total amount of the monthly installments is $11,575.
Item d:
I = A(3) - P = 11575 - 10000 = 1575
When interest is calculated, the principal is removed, so:
Interest was paid of $1,575.
Item b:
36 payments were made over a period of 3 years, or 3 x 12 months.
Item a:
11575/3 = 321.53
The amount due each month was $321.53.
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solve the system of equations?
7x+10=-4x-23
Answer:
x = -3
Step-by-step explanation:
7x+10 = -4x-23
11x+10 = -23
11x = -33
x = -3
Answer:
x= -33/4
Step-by-step explanation:
Which situation below represents a 30% decrease?
from 50 to 35 OR from 30 to 27
Answer: 50-35
Step-by-step explanation:
Because if you calculate it, 50x70% or 50x0.7 is 35. I multiply bt 70% not 30% because you are trying to find the amount after the 30% decrease, meaning it is 70% of the orginal value.
Answer:
50 to 35
Step-by-step explanation:
[tex]\frac{30}{27} =\frac{100}{y}[/tex]
30y = 2700
y = 90
27 is 90% of 30.
[tex]\frac{50}{35}=\frac{100}{y}[/tex]
50y = 3500
y = 70
35 is 70% of 50.
What is a residual for a multiple regression model and the data that is used to create it? select one.
The difference between the actual value of the response variable and the corresponding predicted value(regression error) using the multiple regression model is the correct option.
A residual is a measurement of the vertical distance between a point and the regression line. It is just the discrepancy between an actual value observed and a value that was projected.
To ensure that the requirements for making conclusions about the coefficients in a linear model have been met, one should always perform a residual analysis.
In regression analysis, a residual is the discrepancy between an observed value and a predicted value.
It is determined by,
Residual = Observed value – Predicted value
The residual is the discrepancy between the expected value and the actual value.
Observed value minus predicted value equals residual.
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To hire an accountant to prepare taxes costs a flat fee and an additional hourly rate. The amount the accountant costs can
be modeled by the function A(x) = 150 + 35x, where x represents the number of hours the accountant works to prepare the
taxes and 150 represents the flat fee. What is the value of A(220) and its interpretation?
OA(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
OA(220) = 7850; If the accountant takes 7,850 hours to prepare the taxes, the cost will be $220.
OA(220) = 2; If the accountant takes 220 hours to prepare the taxes, the cost will be $2.
2
OA(220) = 2; If the account takes 2 hours to prepare the taxes, the cost will be $220.
A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
Hence option (A) is correct.
What is a linear equation in one variable?
The linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
The cost function is A(x) = 150 + 35x
We have to find the value of A(220), so put x = 220 in the given cost function, we get
A(x) = 150 + 35x
A(220)= 150 + 35(220)
= 150 + 7700
= 7850 dollars
Hence, A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
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the rate of pay per hour of an employee who gets paid $627 for working 38 hours help
Answer:
16.5
Step-by-step explanation:
627 divided by 38 equals 16.5.
16.5 is the amount earned per hour.
In a rhombu, ide a equal 160 cm and angle alpha equal 60 degree. Calculate the ize of the diagonal
5√3 is of the diagonal of rhombus .
What is a rhombus, exactly?
A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal.
A rhombus's diagonals are right angles to one another, and all of its sides are equal in length. The term "rhombus" can also refer to a diamond or rhombus.
Since all the sides are equal, the altitude is
10 sin60° = 5√3
To see this, draw the rhombus ABCD and drop an altitude from D to AB.
Now you have a right triangle with hypotenuse=10 and base angle=60°
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the periodic interest rate for a loan with an annual interest rate of 15.98% compounded weekly is 0.3073%, rounded to four decimal places.
a. True
b. False
yes, the periodic interest rate for a loan with an annual interest rate of 15.98% compounded weekly is 0.3073%
How do you calculate periodic interest rate?The yearly interest rate is divided by the quantity of compounding periods to produce the periodic interest rate. Interest can be earned on or added to interest more frequently when there are more compounding periods.
What is a periodic monthly rate?The interest rate that is levied on a periodic basis, such as monthly or quarterly, is known as the periodic rate. A credit card with an annual percentage rate of 18% has a periodic rate of 1.5 percent per month. The periodic rate is calculated by multiplying it by the number of periods in a year.
according to the formula :
periodic interest rate is annual interest rate divided by the number of times per year interest compounds so,
we have;
Annual interest rate = 15.98%
no.of week in a year= 52
so ;
periodic interest rate=15.98%/52
=0.3073%,
so the given statement is true.
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The growth of outpatient surgeries as a percent of total surgeries at hospitals is approximated by
f(x)=1314+303 In x
where x is the number of years since 1900.
(a) What does this function predict for the percent of outpatient surgeries in 1996?
(b) When did outpatient surgeries reach 60%?
(a) What does this function predict for the percent of outpatient surgeries in 1996?
% (Round to the nearest percent as needed.)
(b) When did outpatient surgeries reach 60%?
(Round down to the nearest year.)
The percent of outpatient surgeries in 1996 is 68.99 % and outpatient surgeries reach is 1992.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
total surgeries at hospitals is approximated by
f(x)=1314+303 Inx
A) this function predicts for the percent of outpatient surgeries in 1996 IS
x = 1996-1900 = 96.
So f(96) = -1314 + 303 ln(96) =68.99 %
b) f(x) = 60
60 = -1314 + 303 ln(x)
ln x = (1314+60)/303 = 4.53
x = 92.75.
Hence, the percent of outpatient surgeries in 1996 is 68.99 % and outpatient surgeries reach is 1992.
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Please help me with this
The consequence of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ by composition is f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.
How to use composition between two functions
In this question we must use the definition of composition between two functions f and g, where the independent variable of the function f is substituted by function g. That is to say:
f ° g (x) = f [g(x)]
If we know that f(x) = (1 / 6) · ∛x and g(x) = 6 · x³, then the result of each composition is:
f [g (x)] = (1 / 6) · ∛(6 · x³)
f[g (x)] = (1 / 6) · ∛3 · x
g[f (x)] = 6 · [(1 / 6) · ∛(6 · x³)]³
g[f (x)] = 6 · (1 / 216) · (6 · x³)
g[f (x)] = (1 / 6) · x³
The results of the compositions of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ are f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.
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