1)The regression equation is Age--26.7+809 LN [(1+(R/1))/(1-(R/L))]. Hence, the value of the regression coefficients by is-26.7 and by is 809
2)The forecasted value for 0.0901 LN [(1+(RL)) (1- (RL))) is 46.103.
3)The 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor is 41.013,51.193.
4)Yes, a man in Sherlock Holmes's neighborhood thought that the body because; the man's age comes under the age in years that is, the smaller age is 14 and the larger age is 69. Thus, this is the body of that man.
Exponential law=The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.
MINITAB procedure:
Choose Stat > Regression Regression
Step 2: In Responses, enter the column of Age (yrs)
Step 3: In Predictors, enter the column of LN [(1+(R/L))/ (1-(R/1))] Step 4: In Options, enter the value of Prediction interval for new observation as 0.0901
The regression equation Age (year 26,7 809 28(13+1/233/4-1-26.7252.025 -13.20 0.00025.61 31.37 0.000)
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Select the correct answer.
What is the circumference of this circle?
OA. 4 1/2 pi
B. 9 pi
c. none of the above
d. 2 1/4 pi
e. 20 1/4 pi
The circumference of this circle is 2π
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
The arc is the circumference.
C = 2πr
C = 2x πx 6
C = 12π
A circle is 360 degrees. The arc is covering 60 degrees
60/360 = 1/6
The arc is 1/6 of the circle, so it will be 1/6 of the circumference
1/6 C = 1/6 (12π)
arc = 2π
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08
En completes an exercise program at a fitness center The graph shown below represents
the percentage of her exerclee program 09 Erin has completed when she has exerched for
*minutes
Erin's Exercise Program
felpaydung
2882882822
100
0 8 10 15 20 25 30 35 40 45 50 558 00 08
Time (minutes)
Based on the graph what does the value of the y-coordinate represent when x = 15
A Bin has completed ON of her exercise program
8
Bin has completed 25% of her exercise program
0
Bin has completed 0 minutes of her exercise program
D. Ein has completed 28 minutes of her exercise program
The meaning of the y-coordinate of the graph when x = 15 is given as follows:
B. Erin has completed 25% of her exercise program.
What is shown by the graph?The graph is a relation that represents a function between two variables.
The variables for this problem are given as follows:
Variable x: time that Erin spent exercising.Variable y: percentage of the exercise program that Erin has completed, considering that she has been exercising for x minutes.One ordered pair for the graph in this problem is given as follows:
(15, 25).
This means that when Erin spends 15 minutes exercising, she has completed a percentage of 25% of her exercise program, and thus option B is correct.
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1. 50x2=
2. 60x3=
3. 75x8+3=
And then add then all together
Answer:
1. 50 x 2 = 100
2. 60 x 3 = 180
3. 75 x 8 + 3 = 603
603 + 180 + 100 = 883
Step-by-step explanation:
Just multiply and add.
Calculate the difference and enter below. -4 + (-4)
[tex]-4-4[/tex]
[tex]-4+(-4)[/tex]
[tex]=\fbox{-8}[/tex]
[tex]-4+(-4)[/tex] on a number line:
which of the following statements are true regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable? select all that apply. multiple answers: multiple answers are accepted for this question select one or more answers and submit. for keyboard navigation...show more a f(x)
The true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable is 0 < F(x) < 1. and F(x) = 1 for at least one value of x, F(x) = 1 for all values of x > a, where a is a constant.
What is meant by probability density function?
In math, probability density function refers most commonly associated with absolutely continuous univariate distributions.
Here we need to find the true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable.
In order to find the correct statement, we must know the definition of the cumulative density function also.
The cumulative density function means the probability function that X will take a value less than or equal to x.
Based on the both definition option (A), (B) and (C) are true.
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factor this expression completely, then place the factors in the proper location on the grid. 5x 3 40y 6
The final Factorisation of the expression of 5x³ + 40y⁶ is 5 ((x + 2y²) (x² - 2xy² + 4y⁴)).
Describe factorization.When an algebraic equation is expressed as the sum of its factors, it has been factorized. There might be these variables, elements, or algebraic expressions.
A number is broken down for the factor into components that may be multiplied to produce the original number.
Briefing:According to the question,
We have to factorize the expression
5x³ + 40y⁶
Taking a Common factor 5 out ,
5 (x³ + 8y⁶)
When the expression between the parenthesis is factored, we get:
5 ((x + 2y²) (x² - 2xy² + 4y⁴))
Right now, we cannot add another element.
Hence , The factored expression is given by: 5 ((x + 2y²) (x² - 2xy² + 4y⁴))
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Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Adults Seniors
Sample Size 102 258 319 31
x :2.00 3.10 3.06 2.81
s :1.59 1.66 1.69 1.87
For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using α = 0.01.
Calculate the test statistic. (Round your answer to two decimal places.) F = ?
What can be said about the P-value for this test?
P-value > 0.100
0.050 < P-value < 0.100
0.010 < P-value < 0.050
0.001 < P-value < 0.010
P-value < 0.001
What can you conclude?
Reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
Reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
You may need to use the appropriate table in Appendix A to answer this question.
Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Adults Seniors
Sample Size 102 258 319 31
x :2.00 3.10 3.06 2.81
s :1.59 1.66 1.69 1.87
for this test
P-value > 0.100
0.050 < P-value < 0.100
0.010 < P-value < 0.050
0.001 < P-value < 0.010
P-value < 0.001
Hence , Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
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Find all fixed points of the linear transformation. Recall that the vector v is a fixed point of T when T(v) v. (Give your answer in terms of the parameter t.) A reflection in the x-axis.
{ _____ : t is rea}
The set of all T's fixed points is {(x,0): x € R} of the linear transformation of vector(v).
linear transformation:
It is a function from one vector space to another that respects the structure of each vector space, which is also known as a linear operator or map
Two important examples of linear transformations are zero and identity transformation. The zero transformation defined by T(→x)=→(0) for all →x is an example of a linear transformation.
Similarly, the identity transformation defined by T(→x)=→(x) is also linear.
Note that the representation matrix for the reflection in the y-axis:
[tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right][/tex]
Here the condition
T(x,y)=
[tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}x\\-y\\\end{array}\right] =\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]
can only happen when y=0 and x is arbitrary.
Thus the fixed points for all T are points with y=0 or all points on the x-axis
Thus, The set of all T's fixed points is {(x,0): x€R}
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If the center of the circle is Point A, what is the difference between the circumference of the circle and the perimeter of the triangle, to the nearest tenth of a unit?
A 20.6 units
B 28.2 units
C 80.7 units
D 95.5 units
The difference between the circumference of the circle and the perimeter of the triangle is 28.2 units. (Option B)
To find the length of each side of triangle, the distance is calculated between the vertices using the formula:
d = √((x2 – x1)^2 + (y2 – y1)^2)
Hence,
AB =√((-4 – 0)^2 + (9 – 0)^2) = 9.85 units
AC = √((9 – 0)^2 + (4 – 0)^2) = 9.85 units
BC = √((9 – (-4))^2 + (4 –9)^2) = 13.93 units
Hence, the perimeter of the triangle = 9.85 + 9.85 + 13.93 = 33.6 units
As AB and AC is the radius of the circle, the circumference of the circle is:
C = 2πr = 2π(9.85) = 61.8 units.
Hence, the difference between the circumference of the circle and the perimeter of the triangle = 61.8 – 33.6 = 28.2 units.
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Calculate the difference and enter below. -9 - (-10)
Answer:
1
Step-by-step explanation:
subtract the two numbers
Answer: 19
Step-by-step explanation: Imagine a number line -9 is on the left side and 10 is on the other. Now you have to clculate how many jumps or spaces it takes to reach 10. Which is 19, or 9 + 10.
I hope this helps.
Complete the proof of the identity by choosing the Rule that justifies each step. Sin^2x + 4cos^2x = 4 -3sin^2x To see a detailed description of a Rule in the Rule menu, select the corresponding question mark. Statement Rule sin^2 x + 4cos^2 x sin^2 x + 4 (1 -sin^2 x) Rule? sin^2 x + 4 -4sin^2 x Rule? 4 -3sin^2 x Rule? Reciprocal identities: sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u Quotient identities: tan u = sin u/cos u cot u = cos u/sin u Pythagorean identities: sin^2u + cos^2u = 1 tan^2u + 1 = sec^2 u cot^2 u + 1 = csc^2 u Odd/Even function identities: sin(-u) = -sin(u) cos(-u) = cos(u) tan(-u) = -tan(u) csc(-u) = -csc(u) sec(-u) = sec(u) cot(-u) = -cot(u)
Previous question
Hello, I need help with this problem. Please explain with work.
Thank you.
The Venn Diagram is shown at the end of the answer.
From the diagram, the percentages are given as follows:
Light rail or bus, but not carpool: 10%.Carpool and bus: 0%.Did not answer light rail, carpool or bus: 72%.Exactly one: 21%.Light rail, carpool, or bus: 28%.How to fill the Venn Diagram?The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.
2% of people answered all three, hence space V on the diagram has a value of 2%, which is the intersection of the three sets.
3% of people answered light rail and bus, hence space IV has a value of 1%, as light rail and bus also involve light rail, bus and carpool.
6% of people answered light rail and carpool, hence space II has a percentage of 4%, following the same logic above.
2% of people answered carpool and bus, hence space V has a percentage of 0%.
11% of people answered carpool, hence space III has a percentage of 5%, as this percentage is a combination of:
Carpool and bus.Carpool and rail.Carpool, bus and rail.Only carpool.From the total bus and light rail percentages, the percentages are given as follows:
VI = 7%.I = 9%.The percentage of people that use at least one of these mediums is given as follows:
9 + 7 + 5 + 1 + 2 + 4 = 28%.
The percentage of people who use none of these mediums is given as follows:
100 - 28 = 72%.
Then the missing percentages at the end of the problem, along with their spaces, are given as follows:
Light rail or bus, but not carpool: I + IV = 9 + 1 = 10%.Carpool and bus: VI = 0%.Exactly one: I + III + VII = 9 + 5 + 7 = 21%.More can be learned about Venn Diagrams at brainly.com/question/24713052
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Quick! Which expression is equivalent? I think either D or C but I’m a bit confused, please help!
The expression that is equivalent to 6⁻¹⁰/(6⁴)(6⁰) is (d) 1/6¹⁴
How to determine the expression that is equivalent?From the question, we have the following parameters that can be used in our computation:
6⁻¹⁰/(6⁴)(6⁰)
Express 6⁰ as 1
So, we have the following representation
6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴) * 1
Evaluate the products
6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴)
Apply the law of indices
So, we have
6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁰⁺⁴
Evaluate the differences
6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁴
Hence, the expression is (d) 1/6¹⁴
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Help me with these pairs thank u
Answer: R(7, 9), S(6, 7), T(2, 3), U(8, 5), V(5, 5)
The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine.
What is the rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled? Place your answer in the box:
The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .
Given :
The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine .
From the table:
Take any two points ( 0 , 380 ) and ( 15 , 545 )
slope m = 545 - 380 / 15 - 0
= 165 / 15
= 33 / 3
= 11 / 1
= 11 feet
Hence the slope m is 11 feet .
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Two random samples of professional baseball players were selected and the number of home runs hit were recorded. One sample was obtained from the National League, and the other sample was obtained from the American League. Ata -0.10, is there a difference in the means? Use the critical value method with tables. National League American League 18 18 12 25 24 Download data Use μ 1 for the mean number of home runs from the National League. Assume the variables are normally distributed and the variances are unequal. Part 1 out of 5 State the hypotheses and identify the claim with the correct hypothesis. H0:#1 (select) | ▼ Ma (select) H2:A9 (select) μ2 (select) This hypothesis test is a (select) test
Hypotheses: H0: μ1 = μ2 and H1: μ1 ≠ μ2.This hypothesis test is a two-tailed test.
Calculate the pooled standard deviation of the two samples.
Let x1 and x2 be the sample means of the National League and American League, respectively. Let s1 and s2 be the sample standard deviations of the National League and American League, respectively. Let n1 and n2 be the sample sizes of the National League and American League, respectively.
Pooled standard deviation = √[( (n1 - 1)s1^2 + (n2 - 1)s2^2 ) / (n1 + n2 - 2)]
s1 = 6.9282
s2 = 6.3246
n1 = 2
n2 = 2
Pooled standard deviation = √[( (2 - 1)6.9282^2 + (2 - 1)6.3246^2 ) / (2 + 2 - 2)]
Pooled standard deviation = 6.6759
Calculate the degrees of freedom (df).
Degrees of freedom (df) = n1 + n2 - 2
df = 2 + 2 - 2
df = 2
Calculate the t-statistic.
Let μ1 and μ2 be the population means of the National League and American League, respectively.
t-statistic = (x1 - x2 - (μ1 - μ2)) / √(s^2 / n1 + s^2 / n2)
x1 = 18
x2 = 19
μ1 = μ2
s2 = 6.6759
n1 = 2
n2 = 2
t-statistic = (18 - 19 - (μ1 - μ2)) / √(6.6759^2 / 2 + 6.6759^2 / 2)
t-statistic = (-1) / (4.4518)
t-statistic = -0.2244
At a significance level of 0.10,
The critical value for a two.
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find a polynomial f(x) 3 of degree that has the following zeros. 0,-5,4
The polynomial f(x) of degree 3 is
f(x) = x³ + x² - 20x
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The zeroes of the polynomial are 0, -5, and 4.
This can be written as,
x = 0, x
x = -5, (x + 5)
x = 4, (x - 4)
x(x + 5)(x - 4)
(x² + 5x)(x - 4)
x³ - 4x² + 5x² - 20x
x³ + x² - 20x
Thus,
The polynomial is f(x) = x³ + x² - 20x
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TRUE/FALSE. analysis is defined as describing the data in the sample with the use of percentages or averages.
Comparison analysis is defined as describing the data in the sample with the use of percentages or averages. Hence, option A is the most suitable answer to this question.
Comparative analysis talks about the comparison of two or more data sets, or other objects. Comparing data becomes very easy when the data is consolidated with the help of average or mean, percentages, and rounding up of the decimals.
Comparison is a very important method to check the difference in the parameters of the two data sets. Not just comparing, summarization of this data is vital for understanding what that data actually means. Hence, we can say that comparison analysis is defined as describing the data in the sample with the use of percentages or averages.
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The complete question is -
Fill in the blanks -
________ analysis is defined as describing the data in the sample with the use of percentages or averages.
A) Comparison
B) Generalization
C) Relationship
D) Summarization
E) Confidence
using traditional methods it takes 90 hours to receive an advanced driving license. a new training technique using computer aided instruction (cai) has been proposed. a researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. after performing the test on 190 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance.
The conclusion is that there is insufficient proof that the new training method increases training time at the 0.02 level of significance.
What is meant by Hypothesis test?Hypothesis test: Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H₀
The average amount of time required to obtain an advanced driving license using conventional techniques is μ=90 hours.
According to the researcher, the new method can result in a longer training period.
A researcher tests the hypothesis with 190 pupils.
At the significance threshold of α=0.02, the researcher fails to reject the null hypothesis.
To put to the test
H₀:The average amount of time required for the new method to obtain an advanced driving license is 90 hours, or μ=90
Hₐ: The new method often requires more than 90 hours, or μ>90, to obtain an advanced driving license.
Failure to reject the null hypothesis indicates that there was insufficient data in our sample to draw a conclusion on the existence of the effect. The absence of data, however, does not demonstrate that the effect is unreal.
The new method takes fewer than 90 hours on average to get an advanced driving license as a result.
Therefore, the researcher's assumption that the new method would increase training time was unfounded.
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the following data on price () and the overall score for stereo headphones that were tested by consumer reports were as follows. the estimated regression equation for these data is . brand price score bose 180 77 scullcandy 150 72 koss 85 62 phillips/o'neill 80 58 denon 80 40 jvc 35 26
The estimated regression equation for these data is Ŷ = 23.194 + 0.318x for every i=1,...,6.
What is meant by regression equation?
In math, the linear regression analysis output delivers some important information, which helps the researcher to predict the estimation, accuracy, and efficiency of the model.
Here we have the data on price and the overall score for stereo headphones that were tested by consumer reports were as follows.
And we need to find the estimated regression equation for these data.
Here let us consider x be the price in dollars of the stereo headphones of brand ii (the independent variable). and let y be the overall score of the stereo headphones of brand ii (the dependent variable).
Here first, we will compute the value of SSE.
The formula is given by
= > SSE = 1∑n (yi − y)²
Therefore, we will show the table of values of xi, Ŷ, Ŷ, (yi−Ŷ) and (yi−Ŷ)².
Now, we have to calculate the value of yi^, plug in the value of xi in the equation
=> Ŷ = 23.194 + 0.318x for every i=1,...,6.
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Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:
rev: 12_26_2015_QC_CS-36924
t distribution with df = 81.
t distribution with df = 82.
t distribution with df = 41.
t distribution with df = 80.
The appropriate distribution to use is t distribution with df = 80.
Variance
The variance of a random variable is the expected squared deviation from its population mean or sample mean. Variance is a measure of dispersion, which means it measures how far apart a set of numbers is from their average value.Distribution
A probability distribution is a mathematical function that calculates the chances of various possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and event probabilities (subsets of the sample space).Given that:
n1 = 37
n2 = 45
The variances of the populations are not know so we can use t distribution
Degree of freedom = n1 + n2 - 2
= 37 + 45 - 2
= 80
Therefore, t distribution with df = 80
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Find the measure of each angle.
Can you figure out what the answer is here
The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20
What is logical reasoning?Logical or deductive reasoning involves using a given set of facts or data to deduce other facts by reasoning logically. It involves drawing specific conclusions based on premises.
Figuring out the triangle first is easiest because since 3 triangles make 30, then each triangle must be 10.
Now, we have our second equation become 10 + C + C = 20, and we get C=5 after solving for the value of the circle.
Our third equation will be 5 + S + S = 13, which becomes 5+2S=13, 2S=8, and then S=4, so the value of a square is 4
Our fourth equation will be 10 + 5*(1/2)(4) = ?, and we see that half of 4 is 2, so we have 10 + 5(2) = 10 + 10 = 20 as our answer.
Hence, The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20
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Find the 13th term in the following
arithmetic sequence :
2, 5, 8, 11, .
The 13th term of the given Arithmetic sequence is 38.
Arithmetic sequence:A list of integers with a distinct pattern is known as an arithmetic sequence. It is an arithmetic sequence if you can subtract any number in the sequence from the one before it and get a value that is either constant or always the same. Here the constant value is called a common difference.
The formula for the nth term of the Arithmetic sequence is given by
a[tex]_{n}[/tex] = a+(n-1)dHere we have
Arithmetic sequence: 2, 5, 8, 11,....
Where first term a = 2
And common difference d = term2 - term 1 = 5 - 2 = 3
As we know nth term of AP = a + (n-1)d
=> 13th term of AP = a + (13-1)d = a + 12d
From the give data, a = 2 and d = 3
=> 13th term = a + 12d
= 2 + 12(3)
= 2 + 36
= 38
Therefore,
The 13th term of the given Arithmetic sequence is 38
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Sue borrows $3500 and will be charged 0.8% simple interest per year. How much will she owe in 5 years?
Answer:
$14000
Step-by-step explanation:
= (3500 x 0.8 x 5) / 100
= $14000
I hope my answer helps you.
A triangular ramp has a diagonal incline with a length of 153 inches. The ramp’s incline makes an angle of X/4 from the floor. How high off the ground is the top of the ramp’s incline? Round your answer to the nearest hundredth inch.
High off the ground the top of the ramp’s incline is 108.19 inch
Trigonometric ratios are what?
Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.
Given that :
hypotenuse = 153 inch
and angle is pi/4
Let h be the height
so sin pi/4 = h/153
h = 153 . sqrt 2/2
h = 108.19
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convert the following equation into slope intercept form. 2x - 4y = 8
Answer:
hey
4y = 2x – 8
Step-by-step explanation:
2x – 4y = 8
–4y = –2x + 8
multiply both sides by (–)
–(–4y) = –(–2x + 8)
4y = 2x – 8
i hope u rate it as brainliest
HELP PLEASEEEEEEEEEEEEEE
Answer:
A) [tex]g(x) = (x - 2 )^{2}[/tex]
Explanation:
Since the equation g(x) is similar to f(x), but translated horizontally, then we can conclude that there is a change in the x value.
Since, the equation g(x) is slide to the right by 2 factor, then there will be a change in x value by -2 factor.
For equation B, the graph will move to the left of f(x) by two factor.
For equation C, the graph will move up of f(x) by two factor.
For equation D, the graph will move down of f(x) by two factor.
Matteo bought a car that cost $12500. He put $4000 down and financed the rest at 3.8%/a compounded monthly. He wants to pay off his car in 19 months. a. How money does he need to pay each month? how much will he end up paying for his car
Answer:
a. $461.67
b. $12771.73
Step-by-step explanation:
You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.
AmortizationThe formula for the monthly payment is ...
A = P(r/12)/(1 -(1 +r/12)^-n)
where P is the amount borrowed at interest rate r compounded monthly for n months.
Here, the down payment of $4000 reduces the loan amount to ...
$12500 -4000 = 8500
a. Monthly paymentSo, the monthly payment is ...
A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67
Matteo needs to pay $461.67 each month.
b. Total paidThe total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:
total = $4000 +19×461.67 = $12771.73
Matteo will end up paying $12771.73 for his car.
Solve the system of equations using elimination. 2x + 3y = −15 3x + y = 2 (0, 5) (1, −1) (3, −7) (4, −10)
The solution to the system of equations is x = 3 and y = -7. The correct option is C. (3, -7).
The system of equations is given as follows:
2x + 3y = −15 ....(1)
3x + y = 2 ....(2)
Multiply Equation 2 by 3:
9x + 3y = 6 ....(3)
Now, we can subtract Equation 1 from Equation 3 to eliminate y:
(9x + 3y) - (2x + 3y) = 6 - (-15)
9x + 3y - 2x - 3y = 6 + 15
7x = 21
x = 21/7
x = 3
Substituting the value of x into Equation 2 to solve for y:
3(3) + y = 2
9 + y = 2
y = 2 - 9
y = -7
Therefore, the solution to the system of equations is x = 3 and y = -7.
Learn more about the elimination method here:
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Complete question:
Solve the system of equations using elimination.
2x + 3y = −15
3x + y = 2
A. (0, 5)
B. (1, −1)
C. (3, −7)
D. (4, −10)