A) the z-critical value associated with a 99% confidence interval is 2.58. B) the z-critical value associated with a 95% confidence interval is 1.96. C) the z-critical value associated with a 90% confidence interval is 1.64. D) the z-critical value associated with an 80% confidence interval is 1.28.
Describe z- critical value?The z-critical value (or the critical z-value) is the number of standard deviations from the mean that corresponds to a given level of significance in a two-tailed z-test. It is used in statistical hypothesis testing to determine whether to reject or fail to reject the null hypothesis.
A) For a 99% confidence interval, the area in each tail is (1-0.99)/2 = 0.005. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 2.58
Therefore, the z-critical value associated with a 99% confidence interval is 2.58.
B) For a 95% confidence interval, the area in each tail is (1-0.95)/2 = 0.025. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 1.96
Therefore, the z-critical value associated with a 95% confidence interval is 1.96.
C) For a 90% confidence interval, the area in each tail is (1-0.90)/2 = 0.05. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 1.64
Therefore, the z-critical value associated with a 90% confidence interval is 1.64.
D) For an 80% confidence interval, the area in each tail is (1-0.80)/2 = 0.10. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 1.28
Therefore, the z-critical value associated with an 80% confidence interval is 1.28.
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Match the following equation to the correct situation.
A + A(9%) = A(1.09)
A.
The amount Ryan paid for two shirts, one was full price for A, the other was discounted 9%.
B.
The amount donated by a company which gives 9% of A dollars collected at a charity banquet.
C.
The amount Tonya owes after putting 9% down on an A home.
D.
The amount Jess owes Julie from borrowing A with 9% interest.
A + A(9%) = A(1.09) is matching with the amount Jess owes Julie from borrowing A with 9% interest.
What is interest?
In the study of finance and economics, interest is the predetermined amount that a borrower or deposit-taking financial institution pays to a lender or depositor above and beyond the principal amount. It differs from any fees the borrower may be required to pay the lender or another entity.
Suppose here A is 100
We put the value of A in the equation
A + A(9%) = A(1.09)
100+ 100*9/100 = 100*1.09
Or,100+9=100*109/100
Hence the correct answer is D, amount Jess owes Julie from borrowing A with 9% interest.
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Answer:
Step-by-step explanation:
deuyfheuf
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). 6y'' + y' − y = 0; y1 = ex/3
So, in response to the above question, we can state that The differential equation has a second solution, which is this.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical.
When we differentiate y2(x) with regard to x, we obtain:
[tex]y2'(x) = v'(x)y1(x) plus v(x)y1' (x)\\v"(x)y1(x) + 2v'(x)y1'(x) + v(x)y1" = y2"(x) (x)\\y2'(x) - y2(x) = 6y2"(x)\\[v"(x)y1(x), 2v'(x)y1'(x), and v(x)y1'(x)] [v(x)y1'(x) + v'(x)y1(x)] - v(x)y1(x) = 0\\3 + 2ex/3)v'(x) + 6v"(x) = 0\\[/tex]
A first-order linear differential equation in v' is shown below (x).
[tex]e(x/2 + (2/9)e(x/3)) = u(x)\\3 + 2ex/3 + 6u(x)v"(x)\\u(x)v'(x) = 0\\6u(x)v'(x) = C1[/tex]
where C1 is an integration constant. Calculating v'(x), we obtain:
[tex]v'(x) = C1/(6u(x))[/tex]
the expression [tex]v(x) = C1e(-x/2 - (2/9)e(-x/3)) dx/6[/tex]
[tex]y2(x) = y1(x)e(-P(x) dx)e(-P(x) dx)y1(x)e(-2) dx[/tex]
where P(x) = (3 + 2ex/3)/6 is the differential equation's coefficient for y'(x). When we replace y1(x) = ex/3 and P(x), we obtain:
y2(x) = (ex/3)
∫e^(-∫(3+2ex/3)/6 dx)
[tex](e^{(-2x/3)/9)} ex/3 e(x/2 - (2/9)e(x/3)) dx y2(x) =[/tex]
[tex]y2(x) = C1y1(x) (x)[/tex]
[tex]"e" (-x/2 - (2/9)e" (-x/3)") dx/6[/tex]
where C1 is an integration constant. The differential equation has a second solution, which is this.
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Odds 7 Megan is flying a kite that is 60 yards above the ground. The length of the kite string is 100 yards. 100 yd A 120 yd B 60 yd C 240 yd D 80 yd 60 yd What is the distance from Megan to the point on the ground directly below the kite?
The distance from Megan to the point on the ground directly below the kite would be = 80yd
How to calculate the distance from Megan to the point on the ground?To calculate the distance, the Pythagorean formula should be used such as follows;
c² = a² + b²
a = 60yd
C= 100yd
b = ?
That is;
100² = 60² + b²
make b the subject of formula;
b² = 10,000 - 3600
b² = 6400
b= √6400
b = 80yd
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sal translates the graph of the function shown in the box 3 units to the left
f(x)=(x-2)^2 +1
what is the function g(x) of the new graph
The solution is, the function is g(x) = (x -5)² + 1
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
we know that,
The vertex form of a quadratic equation is: y = a(x - h)² + k where
"a" is the vertical stretch
-a is a reflection over the x-axis
h is the horizontal shift (positive = right, negative = left)
k is the vertical shift (positive = up, negative = down)
given that,
f(x) = (x-2)² + 1
now we have,
Given: 3 units left --> h = -3
so, we get,
g(x) = (x - 2- 3)² +1
=(x-5)² + 1
Hence, The solution is, the function is g(x) = (x -5)² + 1.
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The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F Question 7(Multiple Choice Worth 1 points) (05.06 MC) A class trip to a ski resort has been planned for your senior trip. The mountain only allows skiing when the temperature is between −10 degrees and 35 degrees. There is room for 38 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip. −10 < x < 35 and 0 < y ≤ 38 x < 35 and y > −10 0 < x ≤ 38 and −10 < y < 35 x > −10 and y < 35 Question 8(Multiple Choice Worth 1 points) (05.06 MC) A company dyes two sizes of rugs. A small rug requires 2 hours for dyeing, and a medium-size rug requires 3 hours for dyeing. The dyers need to make at least 15 rugs, and they must do it in less than 60 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 15 to create a system that represents this situation? 2x + 3y < 60 3x + 2y < 60 2x + 3y > 60 3x + 2y > 60 Question 9(Multiple Choice Worth 1 points) (05.06 MC) Solve the following systems of inequalities and select the correct graph: 2x − y < 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. a dashed line g of x rising left to right that is shaded below and a dashed line f of x that is falling left to right that is shaded above a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above a dashed line
The point that is a solution to the system of inequalities y < −2x + 10 and y < 1/2x − 2 is point E at (4, -2). This is because point E satisfies both inequalities.
When we plug in the x and y values of point E into the first inequality, we get -2 < -2(4) + 10, which simplifies to -2 < 2, which is true.
When we plug in the x and y values of point E into the second inequality, we get -2 < 1/2(4) - 2, which simplifies to -2 < 0, which is also true. Therefore, point E is a solution to the system of inequalities.
For question 7, the correct answer is −10 < x < 35 and 0 < y ≤ 38. This is because the temperature must be between -10 and 35 degrees, and there must be between 0 and 38 people on the trip.
For question 8, the correct answer is 2x + 3y < 60. This is because a small rug requires 2 hours for dyeing and a medium-size rug requires 3 hours for dyeing, and the total time must be less than 60 hours.
For question 9, the correct answer is the graph with a dashed line f of x rising left to right that is shaded above and a dashed line that is falling g of x left to right that is shaded above.
This is because the solution to the system of inequalities is the area where both inequalities are true, which is the area where they have shading in common. In this case, it is the area above both dashed lines.
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Someone help me ASAP. What is the period and frequency.
The period of the sine function is given as follows:
2π.
Hence the frequency is given as follows:
0.5/π Hz.
How to define the sine function?The standard definition of a sine function is given as follows:
y = Asin(Bx + C) + D.
The parameters are given as follows:
A: amplitude.
B: the period is 2π/B.
C: phase shift.
D: vertical shift.
From the function defined in this problem, the parameter B is given as follows:
B = 1.
Hence the period of the function is given as follows:
P = 2π/1 = 2π.
The frequency is the inverse of the period, hence it is given as follows:
f = 1/p
F = 1/(2π)
F = 0.5/π Hz.
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The conjugate of 145+ 145/3
Answer:
193 1/3
Step-by-step explanation:
First, we need to convert [tex]\frac{145}{3}[/tex] into a mixed number.
[tex]\frac{145}{3}[/tex] = [tex]48[/tex] [tex]\frac{1}{3}[/tex]Now, we can add them together:
[tex]145 +48\frac{1}{3} = 193 \frac{1}{3}[/tex]Therefore, the answer is [tex]193\frac{1}{3}[/tex].
which of the following represents the area of a rectangle whose length is x-6 and whose width is x-8?
Answer:
48.
Step-by-step explanation:
Area of a rectangle formula is [tex]l[/tex]·[tex]w[/tex]
Plug in know lengths.[tex]6[/tex] · [tex]8[/tex] [tex]= 48[/tex]
Thus, the area of the rectangle equals 48.
Suppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see whether they are defective (let D = defective and N = not defective). The chance experiment terminates as soon as a nondefective bettery is obtained.a. Give five possible outcomes for this chance experiment.b. What can be said about the number of outcomes in the sample space?c. What outcomes are in the event E, that the number of battery examined is an number?
Answer:
a. Possible outcomes for this chance experiment are:
NDNDDNDDDNDDDDN(Here, D means a defective battery, and N means a nondefective battery.)
b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.
c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.
Kristina paid mortgage interest of
$6,320.00 and Medical Expenses of
$19,500.00 during 2022. Her
GROSS INCOME was $32,500.
18. If $89.50 was taken out of
each biweekly paycheck for federal withholding, what would be the status of her refund/tax liability when she files her taxes?
A) Refund of $1,011.75
B) Pay $1,011.75
C) Refund of $1,415.25
D) Pay $1,415.25
To determine Kristina's refund or tax liability, we need to calculate her total tax liability and compare it to the total amount of federal withholding that was taken out of her paychecks throughout the year.
From the previous question, we know that Kristina's federal tax liability for the year is $668.00.
To calculate her total federal withholding, we need to multiply the amount taken out of each biweekly paycheck by the number of pay periods in a year. If $89.50 was taken out of each biweekly paycheck, then the total federal withholding for the year would be:
$89.50 x 26 = $2,327.00
To determine Kristina's refund or tax liability, we subtract her total federal withholding from her total tax liability:
$2,327.00 - $668.00 = $1,659.00
Since the result is a positive number, it means that Kristina will have a tax liability when she files her taxes. Specifically, she will need to pay $1,659.00 in federal taxes for the year.
Therefore, the answer is option B) Pay $1,011.75.
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls,x. The probabilities corresponding to the 14 possible values of x are summarized. Find the probability of selected exactly three girls
0.022
0.122
0.001
0.061
The probability of selected exactly three girls is A 0.022
How to explain the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
In this case, the probability of an event us usually represented as a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
In this situation, the probability of selected exactly three girls is 0.022. This can easily be seen in the table.
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Difference Quotient Problem
The difference quotient expression for the given function is
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
Difference Quotient Formula:The expression in single-variable calculus is usually referred to as the difference quotient.
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
When taken to the limit as h gets closer to zero, h frac f(x+h)-f(x)h, which gives the derivative of the function f.
The slope of a secant line passing through the curve of f(x) is measured by the difference quotient.
Consider the difference quotient formula,
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
Evaluate the function at x = x + h
replace the variable x with (x + h) in the given expression
[tex]f(x+h)=\sqrt{(x+h)^2-1}[/tex]
simplify the result ,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
find the components of the definition,
[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]
[tex]f(x)=\sqrt{(x+1)(x-1)}[/tex]
plug in the components,
[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]
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Noise in a quiet room is 500 times as intense as the threshold of sound. What is the decibel measurement for the quiet room?
The decibel measurement for the quiet room is 54 dB.
To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.
Next, we can use the formula for decibel measurement:
dB = 10 log (I/I0)
where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.
Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:
dB = 10 log (500/1)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.
To correct this mistake, we need to use the formula for decibel measurement with the correct values:
dB = 10 log (500 * I0/I0)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.
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We encounter three persons, P1, P2, and P3. We know that each one belongs to a different type. They give us the following statements: ➢ P1: I belong to type A. ➢ P2: P1 does not belong to type B. ➢ P3: P2 does not belong to type B. Find the type each person belongs to, given the above information
The types for each person are:
P1 belongs to type A
P2 belongs to type C
P3 belongs to type C
What is Statements?
Facts regarding a mixed company are key statements to add in the objective summary.
Let's assume that there are three possible types: A, B, and C. Then, we can use a process of elimination to determine the type of each person based on the given statements.
First, we know that P1 claims to belong to type A. Therefore, we can eliminate type A as a possibility for P2 and P3.
Next, P2 claims that P1 does not belong to type B. Since P1 has already claimed to be type A, we can eliminate type B as a possibility for P1. Therefore, we know that P1 belongs to type A and P2 does not belong to type B.
Finally, P3 claims that P2 does not belong to type B. Since we have already determined that P2 does not belong to type B, we can eliminate type B as a possibility for P3. Therefore, we know that P3 belongs to type C.
So the types for each person are:
P1 belongs to type A
P2 belongs to type C
P3 belongs to type C
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p(x)=-14+30x+26x^4 How many roots does this have
P(x) = -14 + 30x + 26x⁴ has four roots. The solution has been obtained by using properties of polynomials.
What is a polynomial?
The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
We are given a polynomial as P(x) = -14 + 30x + 26x⁴.
It is a polynomial of degree 4 as the highest power is 4.
We know that the number of roots is equal to the degree of the polynomial.
Here, since the degree is 4, so it has 4 roots.
Hence, P(x) = -14 + 30x + 26x⁴ has four roots.
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The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.
What fraction of the teams raised this extra money?
The fraction of the teams which walked as part of the fundraiser for the library, that raised extra money, is D. 1 / 3.
What fraction of the teams raised extra funds ?You must count the number of teams that were able to walk more than 50 laps in order to determine the percentage of teams that raised the additional funds. The distance walked by teams more than 50 laps were :
5363 6365 miles.There are 12 teams overall, which is equal to the number of leaves.
The fraction of teams that raised additional funds is:
= 4 teams / 12 total teams
= ( 4 ÷ 4 ) / ( 12 ÷ 4 )
= 1 / 3
In conclusion, the fraction of teams which raised extra money was 1 / 3.
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FILL IN THE BLANK a researcher who examines the causal relationship between amount of exercise (randomly assigned as 30 minutes per day or none) and memory abilities is using the ____ research design.
A researcher who examines the causal relationship between amount of exercise (randomly assigned as 30 minutes per day or none) and memory abilities is using the experimental research design.
What is experimental research design?The experimental research design involves the use of two sets of variables;
The constantThe controlled.It is the process of carrying out research in an objective and controlled way in order to achieve precision and specific conclusions are drawn from the hypothesis statement.
Ultimately, the purpose of experimental research design is to establish the effect that a factor has a dependent variable.
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I need help will award brainliest .
Answer:
Below
Step-by-step explanation:
Due to vertical angles:
5x+21 =9x -55 shows x = 19°
then WOZ = 9x-55 = 116 degrees
WOZ and WOY are supplemenrary (add to a 180 ° straight line)
116 + WOY = 180 so WOY = 64°
A rectangle is 1/2 feet long and 3/4 feet wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form
Answer: 3/8
Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.
Numerators first- 1x3Denominators second 2x4Prove the following statement by mathematical induction:
[tex]\sum_{i=1}^{n+1}{i*2^i = n * 2^{n+2} + 2}[/tex] for all integers n ≥ 0.
The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
What is mathmetical induction?Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.
The process involves two steps:
Base case: Prove the statement is true for some initial value, usually n = 1 or n = 0.Inductive step: Assume the statement is true for an arbitrary value of n, and use this assumption to prove that the statement is also true for the next value, n + 1.Here,
First, we need to prove the statement is true for the base case n=0,
When n=0, we have,
[tex]\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2[/tex]
and
[tex]n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2[/tex]
Therefore, the statement is true for n=0.
Next, we assume the statement is true for some arbitrary integer k, meaning:
[tex]\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2[/tex]
We want to show that the statement is also true for n=k+1,
[tex]\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2[/tex]
We can rewrite the left-hand side of the equation as,
[tex]=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2[/tex]
This last step used the assumption that the statement is true for n=k.
Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
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simplify:
• 4 cos² θ + 4 sin² θ
• tan² θ cos² - sin² θ
• 1 + tan² θ
Answer:
1. 4
2. [tex]cos^2(sin^2(0))tan^2(0)[/tex]
3. sec^2 theta
Hope it helped!
Which of the following best describes the expression 6(x + 10)? (1 point)
The sum of a constant factor 6 and a 2-term factor x + 10
The product of a constant factor 6 and a 2-term factor x + 10
The sum of constant factors 6 and x + 10
The product of constant factors 6 and x + 10
The best description of the expression 6(x + 10) is given as follows:
The product of a constant factor 6 and a 2-term factor x + 10.
How to describe the expression?The expression for this problem is defined as follows:
6(x + 10).
The 6 before the parenthesis means that the distributive property is applied, meaning that we have a product of two amounts, which are given as follows:
6.x + 10.Meaning that the second option is the correct option.
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HELP URGENT! LIMITED TIME TEST!!!
An ice cream truck tracks its sales for a year. They create a scatter plot using the data with the average monthly temperature temperature on the x-
axis and the sales along the y- axis.
The data in the graph (the photo added) suggest a linear association. Which of the functions best represents the equation of the line of best fit?
[Pay attention to the scale of the x and y axis]
Choose one,
y= 0.01x + 152
y= 0.5x + 100
y= x + 100
y = 30x - 159
A linear relationship between two quantities can be modeled using a mathematical function.
What is function?Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.
The form of the function is generally expressed as y = mx + b, where y is the dependent variable, m is the slope of the line, x is the independent variable, and b is the y-intercept. The slope of the line, m, can be calculated from two points on the line using the formula m = (y2-y1)/(x2-x1). The y-intercept, b, can be calculated by substituting any point into the equation y = mx + b and solving for b.
Once the slope and y-intercept are known, the equation can be used to predict the value of the dependent variable given a certain value of the independent variable. For example, if the equation is y = 3x + 4, then for any given value of x, the corresponding value of y can be calculated. For x = 5, the corresponding value of y is 19 (5 x 3 + 4 = 19). This equation can also be used to graph the linear relationship between the two variables; by plotting the equation, a straight line is produced.
By using a function to model a linear relationship between two quantities, it is possible to calculate the relationship between them and predict values for either one given the other. This can be a useful tool for understanding the data and for making predictions about the data.
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Write an equation in
point-slope form for the line
shown on the graph.
Use the right-hand point.
= 2
S
5
4
3
2
+
654321
+4
-2
-3
&
-5
€
123456
Submit
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The required point slope of the line shown in the graph is y + 4 = 2(x - 3).
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
From the graph, we have two points on the line (3, -4) and (6, 2)
The slope of the line, with the help of the two-point, is given as,
m = (y₂ - y₁) / (x₂ - x₁)
m = 2 + 4 / 6 - 3
m = 6/3
m = 2
Now,
The equation of the line having a slope of m = 2 and passing through (3, -4) is given as
y - y₁ = m (x - x₁)
y + 4 = 2(x - 3)
y = 2x - 6 - 4
y = 2x - 10
Thus, the required point slope of the line shown in the graph is y + 4 = 2(x - 3).
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please help, i inserted the photo below and i need the answer asap
By proportion formula and Pythagorean theorem, the length of line segment AB is equal to 8 units.
How to determine the length of a missing side in a system of similar triangles
Herein we find a geometric system formed by two similar right triangles, then we can determine the length of side BD by following proportion formula:
BD / AD = CD / BD
BD² = AD · CD
BD = √(AD · CD)
And the length of the line segment AB can be determined by Pythagorean theorem:
AB = √(BD² + AD²)
If we know that AD = 4 and CD = 12, then the length of the line segment AB is:
BD = √(4 · 12)
BD = √48
BD = 4√3
AB = √[(4√3)² + 4²]
AB = 8
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Need help with part C, pls, thx! :)
*Please show how u got it*
The percentage of amount paid toward principal is, 70.4%
And, the percentage of amount paid towards interest is,
⇒ 20.6%
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
An individual borrowed $95,000 at an APR of 5%.
Hence,
The percentage of amount paid toward principal can be calculated as;
Percent amount = 95,000/(450 × 25 × 12) × 100
= 95,000 / 135,000 × 100
= 70.4%
Hence, And the percentage of amount paid towards interest will be:
⇒ 100% - 70.4%
⇒ 20.6%
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What is the value of x?
Enter your answer in the box.
Answer:
x = 54
Step-by-step explanation:
See picture below :)
The area of the scale model of a garden is 15 square feet. The scale model is enlarged by a scale factor of 3 to create the actual garden. Which expression finds the area of the actual garden?
Answer:
15 x [tex]3^{2}[/tex]
Step-by-step explanation:
since each side is increased by 3, total enlargement of area will be [tex]3^{2}[/tex] times
15(5 + 7) = 15 x 5 + 15 x 7 what property is it? include of addition/ multiplication
This equation demonstrates the distributive property of multiplication
What is distributive property ?
In mathematics, the distributive property is a property of binary operations that applies to numbers, sets, or other mathematical objects. It governs how to perform the operation of multiplication over addition or subtraction. The distributive property states that for any numbers a, b, and c:
a × (b + c) = a × b + a × c (multiplication distributes over addition)
or
a × (b - c) = a × b - a × c (multiplication distributes over subtraction)
The property demonstrated in this equation is the distributive property of multiplication over addition. This property states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. In other words, a(b + c) = ab + ac.
In this case, 15 is being multiplied by the sum of 5 and 7, which is equivalent to multiplying 15 by 5 and 15 by 7 separately and adding the results. So, we have:
15(5 + 7) = 15 x 5 + 15 x 7
This equation demonstrates the distributive property of multiplication over addition.
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What is the x axis and the y axis