A large survey of countries including the USA, China, Russia, France, and others indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color. Suppose a random sample of 86 college students were surveyed and 30 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05.1. State your null and alternate hypothesis. What is the level of significance? Will you use a left tail, right tail or two-tail test?2. What is the value of the test statistic. 3.lFind the P-value. Sketch the sampling distribution z = to show the area corresponding to the P-value. 4. Based on 1-3, will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α ? State your conclusion in the context of the application.
Answers
We have to perform an hypothesis test of a proportion.
The claim is that the sample has a different proportion than the population.
Then, the null and alternative hypothesis are:
[tex]\begin{gathered} H_0\colon\pi=0.24 \\ H_a\colon\pi\neq0.24 \end{gathered}[/tex]The significance level is 0.05.
The sample has a size n=86.
The sample proportion is p=0.349.
[tex]p=X/n=30/86=0.349[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt[]{\dfrac{0.24\cdot0.76}{86}} \\ \sigma_p=\sqrt{0.002121}=0.046 \end{gathered}[/tex]Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.349-0.24-0.5/86}{0.046}=\dfrac{0.103}{0.046}=2.241[/tex]This test is a two-tailed test*, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>2.241)=0.025[/tex]* We use a two-tailed test because we are looking for difference above or below the population proportion.
As the P-value (0.025) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the sample has a different proportion than the population.
Answer:
1) The null and alternative hypothesis are:
[tex]\begin{gathered} H_0\colon\pi=0.24 \\ H_a\colon\pi\neq0.24 \end{gathered}[/tex]2) The test statistic is z=2.241.
3) The P-value is 0.025. The value in the standard normal distribution is:
4) As the effect is significant (the P-value is less than the significance level), there is evidence to reject the null hypothesis.
The conclusion is that this sample has a proportion that is significantly different from that from the population.
Related Questions
If this represents the sides of a triangle, classify it by it being an acute triangle, obtuse triangle, right triangle, or not being a triangle.
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1. Determine if it is a rtiangle by using the triangle inequality: the sum of any two sides of a triangle is greater than or equal to the third side.
[tex]\begin{gathered} 13+14\ge16 \\ 27\ge16 \\ \\ 14+16\ge13 \\ 30\ge13 \\ \\ 13+16\ge14 \\ 29\ge14 \end{gathered}[/tex]It is a triangle
2. To classify a triangle knowing its sides you use the next: In a triangle ABC with longest side c
Acute:
[tex]c^2Right:[tex]c^2=a^2+b^2[/tex]Obtuse:
[tex]c^2>a^2+b^2[/tex]For the given triangle;
- Find the square of the longest side:
[tex]16^2=256[/tex]-Find the sum of the squares of the other sides:
[tex]13^2+14^2=169+196=365[/tex]As the sum of the squares of the to smallest sides (365) is greater than the square of the longest side (256) it is an acute triangle.Answer: Acute triangleWrite equation below matches the following statement?Five more than two times a number,n, is sixteen.
Answers
"Five more than two times n" indicates that you have to multiply n by 2 and add 5, the result of this operation is 16, so the expression is:
[tex]2n+5=16[/tex]Put a T for a true or a F for false .and don't worry this is just a practice :)and let me know if you can see the picture !!
Answers
1)
Working with inequalities, when you draw them in a number line or a coordinate system. The Open circle, or "blank dot" indicates that the number itself is not included in the definition, while the closed circle or "blak dot" indicates the value is included.
For example:
The inequality marked in the number line can be expressed symbolically as:
[tex]x<2[/tex]So the first statement is True.
2)
When an inequality includes a variable (letter) this one can be writen in terms of said variable following almost the same rules as when you calculate the value of a variable in an equation.
The greatest exception is that when you divide by a negative number, the direction of the inequality changes.
So for the given inequality:
[tex]-10w>100[/tex]To determine one possible value of w you have to divide both sides of the expression by "-10" and when you do so, the direction of the inequality gets inverted from > to <
[tex]\begin{gathered} -10w>100 \\ w<\frac{100}{-10} \\ w<-10 \end{gathered}[/tex]So this statement is False.
3)
This statement is True, when the variable is "alone" the coefficient is 1. Since multiplying a number by one results in said number it is redundant to write it, but altough "invisible" one is the coefficient of any variable that is "alone" in any given expression.
4)
"At most" indicates that it is the maximum value possible for the determined inequality. So the inequality can be equal or less than the determined value.
For example, "The cell phone repair will cost at most $100" → You know that you will pay no more than $100 dollars for the repair, it can be less but not more.
Let "x" symbolize the repair cost, you can express this as:
[tex]x\leq100[/tex]So this statement is True
5)
"Minimum" indicates that is the lowest value of the inequality, it is the startpoint, from the determined value onwards.
If △STU is similar to △XYZ, the sides of △STU must be congruent to thecorresponding sides of △XYZ.A. TrueB. False
Answers
Similar triangles are triangles that have the same interior angles and the corresponding sides are proportional, that is, for triangles STU and XYZ we have the proportion:
[tex]\frac{ST}{XY}=\frac{TU}{YZ}=\frac{SU}{XZ}[/tex]The corresponding sides are congruent only if the proportion rate is 1, but that is not always true and it's not necessary.
Therefore the correct option is B: False
If the corresponding sides are congruent, the triangles are congruent.
PLS ANSWER, will mark brainliest
The total cost after tax to repair Deborah’s computer is represented by 0.08(50h)+50h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
Answers
Answer:
The expression of the total cost after tax, 0.08(50h) + 50h, has a tax part and a cost part.The tax part is 0.08(50h).The cost part is 50h.What is tax?Tax is the amount paid by the consumer to the government for the use of goods and services produced in/by the country.It is charged over the total cost for the particular good or service, at a pre-determined rate called the rate of tax.How to solve the question?In the question, we are informed that the total cost after tax to repair Deborah's computer is represented by 0.08 (50h) +50h, where h represents the number of hours it takes to repair Deborah's computer.We are asked what part of the expression represents the amount of tax Deborah has to pay.We know that the total cost = Tax + Fixed Cost,where tax = tax rate * fixed cost.Therefore, we write the total cost function like this:Total cost = Tax Rate(Fixed cost) + Fixed Cost.Comparing the given expression of the total cost, 0.08(50h) + 50h, with this expression, we can say that 0.08(50h) represents the tax part, where 0.08 is the tax rate and 50h is the fixed cost.Learn more about taxes atbrainly.com/question/5022774#SPJ2
Step-by-step explanation:
The area of the parallelogram is 273in squared what’s the height ?
Answers
The formula for determining the area of a parallelogram is expressed as
Area = base x height
Given that
base = 39
area = 273
Then,
273 = 39 x height
height = 273/39
height = 7 ft
Point D is in the interior of
Answers
The given problem can be exemplified in the following diagram:
The conditions are:
[tex]\begin{gathered} m\angle ABD=6x+5 \\ m\angle ABC=10x+7 \\ m\angle DBC=36 \end{gathered}[/tex]We also have the following relationship:
[tex]m\angle ABD+m\angle DBC=m\angle ABC[/tex]Substituting the values we get:
[tex]6x+5+36=10x+7[/tex]Solving the operations:
[tex]6x+41=10x+7[/tex]Now we solve for "x", first by subtracting 10x on both sides:
[tex]\begin{gathered} 6x-10x+41=10x-10x+7 \\ -4x+41=7 \end{gathered}[/tex]Now we subtract 41 on both sides:
[tex]\begin{gathered} -4x+41-41=7-41 \\ -4x=-34 \end{gathered}[/tex]Now we divide both sides by -4
[tex]x=-\frac{34}{-4}=\frac{17}{2}[/tex]Now we replace the value of "x" in the expression for angle ABD:
[tex]\angle ABD=6x+5[/tex]Replacing the value of "x":
[tex]\angle ABD=6(\frac{17}{2})+5[/tex]Solving the operations:
[tex]\angle ABD=3(17)+5=56[/tex]Therefore angle ABD is 56 degrees.
3|x + 1| - 9 = 0? Solution set?
Answers
x = (2, -4)
Explanation:Given:
[tex]\begin{gathered} 3|x+1|-9=0 \\ \\ 3|x+1|=9 \\ \\ |x+1|=3 \\ \\ x+1=3 \\ \Rightarrow x=2 \\ \\ OR \\ -(x+1)=3 \\ \\ -x-1=3 \\ \\ -x=3+1 \\ \\ -x=4 \\ \\ x=-4 \end{gathered}[/tex]x = (2, -4)
Determine whether the given ordered pair is a solution of the system.
y = 6
2x - 5y = 24
Is (2,-4) a solution of the system?
Answers
Answer:
[tex](2, -4)[/tex] is not a solution.
Step-by-step explanation:
The ordered pair [tex](2, -4)[/tex] cannot be a solution of the system since, given the first equation of [tex]y=6[/tex], the only possible value for [tex]y[/tex] is 6. In other words, the only possible value that makes [tex]y=6[/tex] true is 6.
Therefore, to figure [tex]x[/tex], we substitute 6 for [tex]y[/tex] in the second equation and solve:
[tex]2x-5y=24[/tex]
[tex]2x-5(6)=24[/tex]
[tex]2x-30=24[/tex]
[tex]2x=54[/tex]
[tex]x=27[/tex]
The ordered pair, then, that solves the system is [tex](27,6)[/tex].
Jim borrows $300 at 7% per annum compounded quarterly for 7 years. Determine the interest due on the loan.
Answers
Answer:
[tex]I=\text{ \$187.62}[/tex]Step-by-step explanation:
Compounded interest is represented as;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ P=\text{ principal } \\ r=\text{ interest rate} \\ n=\text{ times compounded per unit time} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, for a principal of $300 at 7% per annum compounded quarterly;
[tex]\begin{gathered} A=300\cdot(1+\frac{0.07}{4})^{4\cdot7} \\ A=487.62 \\ \text{Then, the interest due would be the subtraction of A-P} \\ I=487.62-300 \\ I=\text{ \$187.62} \end{gathered}[/tex]How many solutions exist for the equation cos 2θ − sin θ = 0 on the interval [0, 360°)?
Answers
We are given the following equation
[tex]\cos 2\theta-\sin \theta=0[/tex]Let us solve the above trigonometric equation.
Using the double angle identity,
[tex]\cos 2\theta=1-2\sin ^2\theta[/tex]So, the equation becomes
[tex]\begin{gathered} \cos 2\theta-\sin \theta=0 \\ 1-2\sin ^2\theta-\sin \theta=0 \end{gathered}[/tex]Now, let us solve the equation by substitution
Let sinθ = u
[tex]\begin{gathered} 1-2\sin ^2\theta-\sin \theta=0 \\ 1-2u^2-u=0 \\ -2u^2-u+1=0 \end{gathered}[/tex]Let us solve the above equation using the quadratic formula
[tex]u=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The coefficients are
a = -2
b = -1
c = 1
[tex]\begin{gathered} u=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(-2)(1)}}{2(-2)} \\ u=\frac{1\pm\sqrt[]{1+8}}{-4} \\ u=\frac{1\pm\sqrt[]{9}}{-4} \\ u=\frac{1\pm3}{-4} \\ u=\frac{1-3}{-4},\; \; u=\frac{1+3}{-4} \\ u=\frac{-2}{-4},\; \; u=\frac{4}{-4} \\ u=\frac{1}{2},\; \; u=-1 \end{gathered}[/tex]So, the two possible values are u = 1/2 and u = -1
Substitute them back into sinθ = u
[tex]\begin{gathered} \sin \theta=\frac{1}{2},\; \; \sin \theta=-1 \\ \theta=\sin ^{-1}(\frac{1}{2}),\; \; \theta=\sin ^{-1}(-1) \\ \theta=\frac{\pi}{6}\; and\; \frac{5\pi}{6},\; \; \theta=\frac{3\pi}{2}\; \\ \theta=30\degree\; and\; \; 150\degree,\; \; \theta=270\degree \end{gathered}[/tex]Therefore, the two solutions of the given equation are θ = 30°, θ = 150°, θ = 270° on the interval [0, 360°)
Answer:
I got it correct, by graphing on desmos
Step-by-step explanation:
Look at picture
You are interested in purchasing a $144,000 home. You plan to make a 25% downpayment and obtain an 8% mortgage for 20 years for the remaining amountthrough City Savings and Loan. Complete the form below to determine the totalclosing cost.
Answers
Cost of the house = $144,000
25% down payment = 25 / 100 * $144,000 = $36,000
Amount of mortgage = $144,000 - $36,000 = $108,000.
The closing costs are detailed in the form, and two rows need to be filled in and get the total closing costs row.
The first missing row is the Loan origination fee that corresponds to 2% of the mortgage:
2% of $108,000 = 2 / 100 * $108,000 = $2,160
The last row corresponds to 3/16 of the total interest on the mortgage.
Calculate the final value of the mortgage:
[tex]\begin{gathered} FV=\$108,000\cdot(1+0.08)^{20} \\ FV=\$503,383.37 \end{gathered}[/tex]The total interest is:
I = $503,383.37 - $108,000
I = $395,383.37
3/16 * $395,383.37 = $74,134.38
Out of 50 students, 17 want pepperoni pizza, 19 want sausage pizza and the rest want a supreme pizza. What percent of the students want a supreme pizza?
Answers
First, lets find how many students want the supreme pizza. Let 'x' be the number of those students. Then, given the information, we have:
[tex]x+17+19=50[/tex]solving for 'x', we get:
[tex]\begin{gathered} x+17+19=50 \\ \Rightarrow x+36=50 \\ \Rightarrow x=50-36=14 \\ x=14 \end{gathered}[/tex]we have that x = 14 students want a supreme pizza.
Now, if we suppose that the 50 students are the 100%, then, using a rule of three, we get:
[tex]\begin{gathered} 50\rightarrow100\% \\ 14\rightarrow y\% \\ \Rightarrow y=\frac{14\cdot100}{50}=\frac{1400}{50}=28 \\ y=28\% \end{gathered}[/tex]therefore, 28% of the students want a supreme pizza
Don’t get part ii of this question ? I needed help with this, please help me as I am confused.
Answers
We are given the following function:
[tex]y=\frac{1-10x}{(2x-1)^5}[/tex]We are asked to differentiate with respect to "x". To do that we need to have into account that the function is rational and therefore, we need to use the quotient rule for derivatives, which is the following:
[tex]\frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{f^{\prime}(x)g(x)-f(x)g^{\prime}(x)}{g^2(x)}[/tex]Therefore, we need to determine the derivatives of f(x) and g(x). In this case, we have:
[tex]\begin{gathered} f(x)=1-10x \\ g(x)=(2x-1)^5 \end{gathered}[/tex]Now, we determine the derivative of f(x):
[tex]\frac{d}{dx}(f(x))=\frac{d}{dx}(1-10x)[/tex]First, we distribute the derivative:
[tex]\frac{d}{dx}(f(x))=\frac{d}{dx}(1)-\frac{d}{dx}(10x)[/tex]The first, derivative is the derivative of a constant and therefore is zero:
[tex]\frac{d}{dx}(f(x))=-\frac{d}{dx}(10x)[/tex]For the second derivative we use the following rule:
[tex]\frac{d}{dx}(ax)=a[/tex]Applying the rule we get:
[tex]\frac{d}{dx}(f(x))=-10[/tex]Therefore:
[tex]f^{\prime}(x)=-10[/tex]Now, we determine the derivative of g(x):
[tex]\frac{d}{dx}(g(x))=\frac{d}{dx}(2x-1)^5[/tex]Now, we determine the derivative using the following rule:
[tex]\frac{d}{dx}(g(x))^n=n(g(x))^{n-1}(g^{\prime}(x))[/tex]Applying the rule we get:
[tex]\frac{d}{dx}(g(x))=5(2x-1)^4(2)[/tex]Simplifying:
[tex]\frac{d}{dx}(g(x))=10(2x-1)^4[/tex]Therefore, we have:
[tex]g^{\prime}(x)=10(2x-1)^4[/tex]Now, we substitute the function in the quotient rule:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{(-10)(2x-1)^5-(1-10x)(10)(2x-1)^4}{((2x-1)^5)^2}[/tex]Now we simplify the denominator:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{(-10)(2x-1)^5-(1-10x)(10)(2x-1)^4}{(2x-1)^{10}}[/tex]Now, we take (2x - 1)^4 as a common factor on the numerator:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{(2x-1)^4((-10)(2x-1)^{}-(1-10x)(10))}{(2x-1)^{10}}[/tex]Now, we simplify the function:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{((-10)(2x-1)^{}-(1-10x)(10))}{(2x-1)^6}[/tex]Now, we apply the distributive property on the numerator:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{-20x+10^{}-10+100x}{(2x-1)^6}[/tex]Now, we cancel out the 10 and add like terms:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{80x}{(2x-1)^6}[/tex]Since we can't simplify any further this is the final answer.
0 2 4 6 8 10 12 14 16 What is the interquartile range of plot A
Answers
The given Data set can be arranged in the ascending order as,
0,2,4,6,8,10,12,14,16.
Given x = pi/3, what is the exact value of cos (pi+x)?
Answers
Using the unit circle above you can identify the cosine as the x-coordinate.
Then, the cosine of (4pi/3) is -1/2
$3.40 for a box of 20 trash bags. Find unit cost
Answers
Answer:
$0.17
Explanation:
To find the unit cost, we need to divide the total cost by the number of units, so
$3.40 divided by 20 is
$3.40/20 = $0.17
Therefore, the unit cost is $0.17
If you will conduct a research about the poor study habits of Grade 7 students, how will you present your research problem using mathematical function?
Answers
I would define what a poor study habit is, using a parameter like study time in hours or days.
Let a study time of at least 2 hours per day be good, and less than 2 hours per day be poor.
Let f(x) be the study habit of a particular grade, so we write:
Good study time as:
[tex]f(x)\ge2[/tex]Bad study time as:
[tex]f(x)<2[/tex]The last one can represent the study habits of Grade 7 students.
Evaluate each of the following. Illustrate with a point on the graph g(-2)=g(3)=g(0)=g(7)=
Answers
Solution
From the graph given we have this:
g(-2)= -3
g(3)= 4
g(0)= -3
g(7)= 0
writing exponential functions (4, 112/81), (-1, 21/2)
Answers
The given points are (4, 112/81) and (-1, 21/2).
To find an exponential function from the given points, we have to use the forms.
[tex]\begin{gathered} y_1=ab^{x_1} \\ y_2=ab^{x_2} \end{gathered}[/tex]Now, we replace each point in each equation.
[tex]\begin{gathered} \frac{112}{81}=ab^4 \\ \frac{21}{8}=ab^{-1} \end{gathered}[/tex]We solve this system of equations.
Let's isolate a in the second equation.
[tex]\begin{gathered} \frac{21}{8}=\frac{a}{b} \\ \frac{21b}{8}=a \end{gathered}[/tex]Then, we replace it in the first equation
[tex]\frac{112}{81}=(\frac{21b}{8})\cdot b^4[/tex]We solve for b.
[tex]\begin{gathered} \frac{112\cdot8}{81\cdot21}=b\cdot b^4 \\ \frac{896}{1701}=b^5 \\ b=\sqrt[5]{\frac{896}{1701}}=\frac{2\sqrt[5]{4}}{3} \\ b\approx0.88 \end{gathered}[/tex]Once we have the base of the exponential function, we look for the coefficient a.
[tex]a=\frac{21b}{8}=\frac{21}{8}(\frac{2\sqrt[5]{4}}{3})=\frac{7\sqrt[5]{4}}{4}[/tex]Therefore, the exponential function is[tex]y=\frac{7\sqrt[5]{4}}{4}\cdot(\frac{2\sqrt[5]{4}}{3})^x[/tex]The image below shows the graph of this function.
find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. x^2+10x+n
Answers
From the problem, we have :
[tex]x^2+10x+n[/tex]To make it a perfect square trinomial, we will use the formula :
[tex]n=(\frac{b}{2a})^2[/tex]and we can factor the trinomial as :
[tex](x+\frac{b}{2a})^2^{}[/tex]a = 1 and b = 10
so n will be :
[tex](\frac{b}{2a})^2=(\frac{10}{2\times1})^2=5^2=25[/tex]The value of n is n = 25
and the factor of the trinomial will be (x + 5)^2
Answer: the answer is (x + 5)^2
Step-by-step explanation:
8. Mel's mean on 10 tests for the semester was 89. She complained to the teacher that she should be given an A because she missed the cutoff of 90 by only a single point. Explain whether it is clear that she really missed an A by only a single point if each test was based on 100 points. Explain how many points she actually missed.
Answers
Answer
Check Explanation
Explanation
The mean of a group of numbers is the average of these numbers.
Mathematically, the mean is the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
So, when Mel's mean is 89 for 10 tests, this means
Mean = 89
N = Number of variables = 10
So, we can calculate the sum of all of Mel's scores
Mean = (Σx)/N
Cross multiply,
Σx = N [Mean]
Σx = 10 (89) = 890
For Mel to have an average score of 90 from 10 tests,
Mean = 90
N = Number of variables = 10
So, we can calculate the sum of all of Mel's scores
Mean = (Σx)/N
Cross multiply,
Σx = N [Mean]
Σx = 10 (90) = 900
So, we can see that Mel does not actually need 1 point to score an A (90), Mel needs 10 extra points gathered from the 10 tests, to get the extra average 1 point.
Hope this Helps!!!
Could I please get help on finishing this math problem.
Answers
The triangles ABC and DEF have identical angles and one correspondent side identical. Therefore, they are congruent (AAS congruency).
The triangles UVW and XYZ have identical angles but there is no confirmation if they have identical correspondent sides. Therefore, they are not necessarily congruent.
The triangles GHI and JKL are congruent since they have three identical sides (SSS congruency).
Write √32 in simplest radical form4√22√42√168√2
Answers
Answer:
4√2
Explanation:
To write √32 in its simplest radical form:
Express it as a product of two factors where one is a perfect square.
[tex]\sqrt[]{32}=\sqrt[]{16\times2}[/tex]Next, we can separate the product of radicals as follows:
[tex]\begin{gathered} =\sqrt[]{16}\times\sqrt[]{2} \\ =4\times\sqrt[]{2} \\ =4\sqrt[]{2} \end{gathered}[/tex]The simplest radical form is 4√2.
PLS HELP FOR BRAINLIEST
Answers
Answer:
the answer is
5 cupcakes and 8 muffins
5+8=13
2(5)+1.5(8)=22
Choose all of the expressions that are equivalent to 2 1/2 divided by 1 2/6A 5/2 times 6/8B 2/5 times 6/8C 1 2/6 divided by 2 1/2D 5/2 divided by 8/6
Answers
I need to know the sum of the two terms
Answers
Answer: 194 degrees
From the given figure, we can see a transversal forming between the pairs of parallel lines.
Let us focus on the lines n, a, and e. Here, we can see a pair of parallel lines a and e, cut by a transversal n.
We are given a measurement for angle 4, which is 97. Then we are asked to find the sum of angle 2 and angle 4.
One theorem with respect to transversals that we must be familiar with is the Alternate Interior Angles Theorem which states that:
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
With this, we can see from the figure that angle 2 and angle 4 are actually alternate interior angles.
Since they are alternate interior angles, and they are congruent, this would mean that angle 2 also measures 97.
[tex]m\angle4=97;m\angle2=97[/tex]With this, we can now add the two measurements, and that would give us:
[tex]97+97=194[/tex]The sum of angle 2 and angle 4 is 194 degrees.
What is the slope of the line that passes through the points (9, 5) and (21,-5)?
Answers
The equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
How does the slope intercept form made?The slope-intercept form of an a line is a method of writing the equation of a line so that the slope as well as y-intercept are easily identifiable.The the line's slope represents its steepness, and also the y-intercept is the point at which the line intersects a y-axis.For the given question;
The line passes through points are-
(x1, y1) =(9, 5) and
(x2, y2) = (21,-5)
Slope = m = (y2 - y1)/(x2 - x1)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Equation of the line is found using slope intercept form.
y - y1 = m (x - x1)
y - 5 = (-5/6)(x - 9)
y = (-5/6)x - 25/2
Thus, the equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
To know more about the slope intercept form, here
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#13, can you please try to give a detailed run-through on how to identify the variables, and do the problem step by step, I have trouble learning math.
Answers
Given the general expression of a quadratic function,
[tex]f(x)=ax^2+bx_{}+c[/tex]The given function is,
[tex]f(x)=(x-3)(x+8)[/tex]Expanding the right-hand side of the equation
[tex](x-3)(x+8)[/tex]Apply FOIL method:
[tex]\begin{gathered} \mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd \\ \end{gathered}[/tex]Therefore,
[tex]\mleft(x-3\mright)\mleft(x+8\mright)=x\times x+x\times8-3\times x-3\times\: 8=x^2+8x-3x-24[/tex]Simplify
[tex]x^2+8x-3x-24=x^2+5x-24[/tex]Therefore, the function in standard form is
[tex]f(x)=x^2+5x-24[/tex]Now, comparing the general quadratic function and the function given.
[tex]\begin{gathered} ax^2=x^2 \\ \frac{ax^2}{x^2}=\frac{x^2}{x^2} \\ \therefore a=1 \end{gathered}[/tex][tex]\begin{gathered} bx=5x \\ \frac{bx}{x}=\frac{5x}{x} \\ \therefore b=5 \end{gathered}[/tex][tex]c=-24[/tex]Hence, the answers are
[tex]\begin{gathered} a=1 \\ b=5 \\ c=-24 \end{gathered}[/tex]In the diagram of △△ADC below, EB∥∥DC, AE=2, AB=10, and BC=45. What is the length of AD?
Answers
Answer:
11 units
Explanation:
Given that lines EB and DC are parallel, we use the proportional division theorem:
[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex]Substitute the given values:
[tex]\begin{gathered} \frac{2}{ED}=\frac{10}{45} \\ \text{Cross multiply} \\ ED\times10=2\times45 \\ \text{Divide both sides by 10} \\ \frac{ED\times10}{10}=\frac{2\times45}{10} \\ ED=9 \end{gathered}[/tex]Next, find the length of AD:
[tex]\begin{gathered} AD=AE+ED \\ =2+9 \\ =11\text{ units} \end{gathered}[/tex]The length of AD is 11 units.
Alternate Method
[tex]ED=AD-2[/tex]So, we have that:
[tex]\frac{AE}{ED}=\frac{AB}{BC}\implies\frac{AE}{AD-2}=\frac{AB}{BC}[/tex]Substitute the given values:
[tex]\frac{2}{AD-2}=\frac{10}{45}[/tex]Cross multiply:
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