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Related Questions
5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
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Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
Find the slope of the line that passes through (54, -61) and (8, -56).
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Answer:
The slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]Explanation:
We want to calculate the slope of the line that passes through the given point;
[tex](54,-61)\text{ and }(8,-56)[/tex]Recall that the slope formula can be written as;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the given points;
[tex]\begin{gathered} (x_1,y_1)=(54,-61) \\ (x_2,y_2)=(8,-56) \end{gathered}[/tex]We have;
[tex]\begin{gathered} m=\frac{-56-(-61)}{8-54}=\frac{5}{-46} \\ m=-\frac{5}{46} \end{gathered}[/tex]Therefore, the slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]
Right Triangle ABC is pictured below.Which equation gives the correct value for BC?Option 1: sin(32) = BC/8.2Option 2: cos(32) = BC/10.6Option 3: tan(58) = 8.2/BCOption 4: sin(58) = BC/10.6
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Given the image, we are asked which equation gives the correct value for BC?
Explanation
From the image;
[tex]\begin{gathered} A+B+C=180 \\ 32+B+90=180 \\ B=180-90-32 \\ B=58^0 \end{gathered}[/tex]Therefore,
[tex]tan58^0=\frac{opposite}{Adjacent}=\frac{8.2}{BC}[/tex]Answer: Option three
Geo help please The price of an item has been reduced by 5% the original price was $60 what is the price of the item now
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To answer this question, we can proceed as follows:
1. The original price of the item was $60.
2. If the price of this item has been reduced by 5%, we need to find the 5% of the original price as follows:
[tex]5\%=\frac{5}{100}\Rightarrow5\%(\$60)\Rightarrow\frac{5}{100}\cdot\$60=\frac{\$300}{100}=\$3[/tex]3. Therefore, the price of the item now is:
[tex]P_{\text{item}}=\$60-\$3=\$57[/tex]In summary, the price of the item now is $57.
[From the question, we have that the words "reduced by" imply a subtraction.]
Please help me i have been struggling for two days
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we have the equation
[tex]\log _5(x+1)-\log _2(x-2)=1[/tex]using a graphing tool
see the attached figure
The solution is x=2.90Kindly help with these questions.
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because the constant relationship between the x and y coordinates makes the point go through the origin and makes a straight line.
The answer of the second question is k
X is the x coordinate
Y is the y coordinate
so, K is the constant of proportionality.
In a third day of randomly selected subjects, the mean age of the 36 respondents is 40 years and the standard deviation of ages is 10 years. Use the sample results to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected. Repeat the previous problem assuming that the population standard deviation is known to be six years.
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a. Given that:
- The mean age of the 36 respondents is 40 years.
- The standard deviation of ages is 10 years.
You need to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected.
Then, you need to use this formula:
[tex]x\pm z\cdot\frac{\sigma}{\sqrt{n}}[/tex]Where "x" is the sample mean, "z" is the confidence level value, "n" is the sample size, and σ is the standard deviation.
In this case:
[tex]\begin{gathered} x=40 \\ \sigma=10 \\ n=36 \end{gathered}[/tex]Therefore, by substituting values into the formula:
[tex]40\pm\frac{10}{\sqrt{36}}[/tex]You get these two values:
[tex]40+\frac{10}{\sqrt{36}}\approx41.67\text{ }[/tex][tex]40-\frac{10}{\sqrt{36}}\approx38.33[/tex]b. If you assume that:
[tex]\sigma=6[/tex]You get the following values by substituting them into the formula:
[tex]40+\frac{6}{\sqrt{36}}=41[/tex][tex]40-\frac{6}{\sqrt{36}}=39[/tex]Hence, the answers are:
a.
[tex](38.33,41.67)[/tex]b.
[tex](39,41)[/tex]
I need help answering this question, if you can thank you very much.
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Answer: We have to factor out the polynomial which is:
[tex]x^2+6x-16[/tex]The factorization is as follows:
[tex]\begin{gathered} \text{ Method:} \\ \\ (x+a)(x+b)=x^2+(a+b)x+ab \\ \\ \\ ----------------------- \\ \text{ Solution:} \\ \\ x^2+6x-16 \\ \\ \text{ The unknowns }\rightarrow\begin{cases}ab={-16} \\ a+b={6}\end{cases} \\ \\ \\ \text{ The possible values are:} \\ \\ \\ a=8 \\ b=-2 \\ \\ \\ \text{ Because:} \\ \\ \\ (8)\times(-2)=-16 \\ (8)+(-2)=6 \\ \\ \\ \text{ Therefore the factored form is:} \\ \\ \\ (x+8)(x-2)=x^2+6x-16 \end{gathered}[/tex]write a linear equation to: slope=2 and goes through point (4, 11)
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When you have to write a linear equation and you have the slope (m) and a point (4, 11) you:
1. Use the standard form of a linear equation:
[tex]y=mx+b[/tex]You know the value of:
m= 2
y= 11
x= 4
You make a substitution:
[tex]11=(2)(4)+b[/tex]You can find then the value of b:
[tex]11=8+b[/tex][tex]b=11-8=3[/tex]Then you have now the data to form the final linear equation:
[tex]y=2x+3[/tex]What is the domain of the function graphed below?
x<7
x_<7
-2_< X_<3
all real numbers
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The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function so option (A) is correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given graph of the function,
The value of the function at x = -1 is -2.
In another place, the graph is not breaking before x = 7.
So, at x > 7 the function is not defined.
The domain of the function will be (-∞ ,7).
Hence "The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function".
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The given question is incomplete, the complete question follows with the graph below;
Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA. 3x2−5x+1=0 Enter the exact answers.
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The given quadratic equation is,
[tex]3x^2-5x+1=0[/tex]let us use the formula,
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where,
[tex]\begin{gathered} a=3 \\ b=-5 \\ c=1 \end{gathered}[/tex]subistute the values in the formula,
[tex]\begin{gathered} =\frac{-(-5)\pm\sqrt[]{(-5)^2-4\times3\times1}}{2\times3} \\ =\frac{5\pm\sqrt[]{25-12}}{6} \\ =\frac{5\pm\sqrt[]{13}}{6} \\ x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6} \end{gathered}[/tex]The roots of the quadratic equation are ,
[tex]x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6}[/tex]roblems in Construction Mathematics me Frandy Ive the following problems. Show your work. Write your answers in the spaces provided. 1. A triangular frame has sides that measure 15-7, 20'-4 and 26-2". What is the total length of the three sides?
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A triangular frame has sides that measure 15-7, 20'-4 and 26-2". What is the total length of the three sides?
Remember that
1 ft =12 inches
Convert all the measure to inches
so
15' 7 "=15(12)+7=187 in
20' 4"=20(12)+4=244 in
26' 2"=26(12)+2=314 in
The number of cities in a region over time is represented by the function
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For this question, in order to find T(x), we need to multiply the two given functions.
[tex]T(x)=(C\cdot P)(x)[/tex][tex]T(x)=C(x)\cdot P(x)[/tex][tex]=(2.9)(1.05)^x\cdot(1.05)^{3x+5}[/tex][tex]=(2.9)(1.05)^{x+3x+5}[/tex][tex]T(x)=2.9(1.05)^{4x+5}[/tex]Therefore, the answer must be option A.
Find the area of the figure.A. 57 square yardsB. 66 square yardsC. 180 square yards D. 234 square yards
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We would section the figure into two shapes as shown below
We can see a trapezium and a rectangle. We would find the area of each figure and add them.
For the trapezium,
Area = 1/2 * (a + b)h
a nd b are the opposite sides of the trapezium while h represents the height.
Thus,
a = 20, b = 24 and h = 9es of the trapezium while h represents the height.
Thu sid
Segment EF is rotated 90° clockwise around the origin and then translated by (-6, y + 7).
The resulting segment E" F" has coordinates E" (-4, 5), F"(-1,-2).
What are the coordinates of the segment EF?
does anyone know this??
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Answer:
E = 2,2 F = 5,-9
Step-by-step explanation:
First, you have to add (6, -7) to both coordinates (that being (-4,5)(-1,-2)
This results in E = 2,-2 and F = -5,-9
Next, you need to rotate both coordinates 90 counterclockwise, resulting in: E being (2,-2) and F being (5,-9)
Hope this helped!
Domingo had 250 baseball cards, andJennifer had 82 baseball cards. At thefirst meeting of the Card Club and atevery meeting thereafter, Domingo sold12 cards to Jennifer. After which meetingdid the two have the same numberof cards?
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Data:
Domingo: D
Jennifer: J
Initial number of cards:
D=250
J=82
After each meeting(m):
D=250-12m
J=82+12m
After the first meeting: m=1
[tex]D=250-12(1)=238[/tex][tex]J=82+12(1)=94[/tex]You increase in 1 the m after each meeting and get the next table:
Then, they have the same number of cards after 7th meetingDifferentiate. f(x) = (x3 - 3)2/3 2x f'(x) 3 x 8 х f'(x) 3 | 23-8 2x2 f'(x) 3 S x2 f'(x) 3 8
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1) Let's calculate the derivative of f(x) = (x³-8) ^(2/3)
Let's start applying the power rule :
[tex]undefined[/tex]Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.
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Given that:
• There are a total number of 22 students in the classroom.
,• 10 of them are transfer students.
,• 7 are nursing students.
,• 4 are AAS students.
,• 1 student is undecided.
,• Three students are chosen randomly.
Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:
[tex]P(A)[/tex]Where Event A is that one of the students is a nursing student.
Therefore, the probability that three of the chosen students are nursing students can be set up as:
[tex]\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}[/tex]Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:
[tex]P(A)=\frac{7}{22}[/tex]Therefore:
[tex]P=(\frac{7}{22})^3[/tex][tex]P=0.0322[/tex]Hence, the answer is:
[tex]P=0.0322[/tex]How much will it cost to buy a low fence to put all the way around the bed? The fencing material costs $0.59 per foot and can only be bought in whole numbers of feet.
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To find the cost we first need to know how many feet of fence we need. To do this we add all the lengths of the sides:
[tex]6+6+8.5=20.5[/tex]Now, since we can only buy whole numbers of feet we need to buy 21 feets of fence, then the total cost is:
[tex]21\cdot0.59=12.39[/tex]Therefore the cost will be $12.39
You want to purchase an automobile for 28,711. The dealer offers you 0% financing for 60 months or a 3,972 rebate. You obtain 5.7% financing for 60 months at the local bank. Which option should you choose
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Answer:
option 1
Step-by-step explanation:
the dealer one ok.......
In a test of the effectiveness of garlic for lowering cholesterol, 48 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 5.3 and a standard deviation of 19.6. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
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1) The 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment is 5.3 ± 5.6.
2) Regarding the effectiveness of garlic in reducing LDL cholesterol, the confidence interval suggests A. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
What is the confidence interval estimate?The confidence interval estimate shows us the mean estimate plus or minus the margin of error (or variation in the estimate).
On the other hand, the margin of error is the difference between the actual and projected results in a random sample.
The number of subjects treated with garlic, n = 48
The mean changes in LDL cholesterol level = 5.3
The standard deviation = 19.6
The 95% confidence interval gives a Z-score of 1.96
The margin of error = Z-score x standard deviation/√n
= 1.96 x 19.6/√48
= 1.96 x 19.6/6.9
= 1.96 x 2.84
= 5.6
Lower Limit = Mean - Margin of Error
= 5.3 - 5.6
= -0.3
Upper Limit = Mean + Margin of Error
= 5.3 + 5.6
= 10.9
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Question Completion with Answer Options:2. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
A.The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
B.The confidence interval limits do not contain0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
C.The confidence interval limits do not contain0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
D.The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
what is the slope of any line is perpendicular to the equation y=1/2x-7
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The slope = -2
Explanations:The given equation is:
[tex]y\text{ = }\frac{1}{2}x\text{ - 7}[/tex]This is of the form y = mx + c
where the slope, m = 1/2
The equation perpendicular to the equation y = mx + c is:
[tex]y-y_1=\frac{-1}{m}(x-x_1)[/tex][tex]\begin{gathered} \text{The slope = }\frac{-1}{m} \\ \text{The slope = }\frac{-1}{\frac{1}{2}}=\text{ -2} \end{gathered}[/tex]The slope = -2
The one-to-one function f is defined below.
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The inverse function of the relation is f-1(x) = 5x/(7x -6), while the domain and the range are x < 6/7 or x > 6/7 and f(x) < 5/7 or f(x) > 5/7, respectively
How to determine the inverse function?The definition of the function is given as
f(x) = 6x/7x - 5
Rewrite the function as
y = 6x/7x - 5
Next, we swap or switch the variables x and y
So, we have the following equation
x = 6y/7y - 5
Cross multiply in the above equation
This gives
x(7y - 5) = 6y
Open the brackets
7xy - 5x = 6y
Collect the like terms
7xy -6y = 5x
Factor out y
y(7x -6) = 5x
So, we have
y = 5x/(7x -6)
Express as inverse function
f-1(x) = 5x/(7x -6)
Using a graphing calculator, we have
Domain: x < 6/7 or x > 6/7
Range: f(x) < 5/7 or f(x) > 5/7
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if a certain number is added to the numerator and denominator of 9/13 the result is 9/11. find the number
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We have the following:
When they tell us a certain number, we will assume a value x.
This number is added to the numerator and denominator of the fractional number 9/13 and gives us the result 9/11.
it is as follows
[tex]\frac{x+9}{x+13}=\frac{9}{11}[/tex]solving for x:
[tex]\begin{gathered} \frac{x+9}{x+13}=\frac{9}{11} \\ 11\cdot(x+9)=9\cdot(x+13) \\ 11x+99=9x+117 \\ 11x-9x=117-99 \\ 2x=18 \\ x=\frac{18}{2}=9 \end{gathered}[/tex]Therefore, the certain number is 9
Determine whether the graph represents a function.
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A, the relation is not a function
in order for something to be a function, x (the input) can't repeat itself more than once
Tyrone's car can travel about 30 miles for each gallon
of gas.
Using d for distance traveled in miles and g for
gallons of gas, write two different equations relating d
and g.
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The equation can be written as d=30g
What is an equation?
An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Equations are used to describe geometric shapes in Cartesian geometry. The goal has changed since the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions.
Tyrone's car can travel about 30 miles for each gallon
So, the equation can be written as d=30g, where d is distance travelled and g is gallons of gas used.
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Use percents to find price of each set of items.(1) You purchase one pair of jeans, 2 hoodies and 3 t-shirts. what is the Total cost with no Sale? You purchase the same items but now you receive a 40% off coupon, How much is your total including the discount?
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We can multiply the number of items by the price of each item to find the total cost:
[tex]\begin{gathered} C=C_{jeans}+C_{hoodies}+C_{shirts}=1\cdot25+2\cdot30+3\cdot8 \\ C=25+60+24 \\ C=109 \end{gathered}[/tex]The total cost is $109.
If we have a 40% discount, we have to substract it from the total cost.
The discount is equal to 40% of the total cost, so we can calculate the discount as:
[tex]D=\frac{40}{100}\cdot C=0.4\cdot109=43.60[/tex]Then, we will pay a total cost with discount of:
[tex]C^{\prime}=C-D=109-43.60=65.40[/tex]The total including the discount is $65.40.
NOTE: we could also have calculated it as 109*(1-0.4)=109*0.6=65.40.
Eliminate the y in the following system of equations. What is the result when you add the two equations? [tex]x + y = 8 \\ 5x - 3y = 24[/tex]A: 6x = 32B: 8x = 32 C: x = 0D: 8x = 48
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EXPLANATION
x + y = 8 ----------------------------------------(1)
5x - 3y = 24 ------------------------------------------(2)
If we are to eliminate y in the equations, we first need to multiply through equation (1) by 3.
3x + 3y = 24 ----------------------------------------(3)
Add equation (2) and equation (3).
If we add equation(1) and equation(3) together, -3y will cancel-out 3y.
(5x + 3x) = (24 + 24)
8x = 48
Therefore, the correct option is D. 8x = 48
7. 4×= 3yy=-4x + 39. y+2=0x+ 2 = 011.x-5y=45x + y = 4Determine if the graphs will show parallel or perpendicular lines, or neither.
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Given:
[tex]\begin{gathered} 4x=3y \\ y=-4x+3 \end{gathered}[/tex]Sol:.
If the both line are perpendicular then multipilcation of slope is -1 then:
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ \end{gathered}[/tex][tex]\begin{gathered} 3y=4x \\ y=\frac{4}{3}x \\ m_1=\frac{4}{3} \end{gathered}[/tex][tex]\begin{gathered} y=-4x+3 \\ m_2=-4 \end{gathered}[/tex][tex]\begin{gathered} =m_1m_2 \\ =\frac{4}{3}\times-4 \\ m_1m_2\ne-1 \\ \text{That mean its not perpendicular } \end{gathered}[/tex]For parallel line slope are same then its not a parallel line
So line neither perpendicular or parallel.
A ball is thrown from an initial height of 1 meter with an initial upward velocity of 7 m/s. The balls height h (in meters) after t seconds is given by the following. h=1+7t-5t^2Find all values of t for which the balls height is 2 meters.Round the answer(s) to the nearest hundredth
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Solution
To find the values of t for which the ball's height is 2 meters
we set h = 2
=> 2 = 1 + 7t - 5t^2
=>5t^2 - 7t + 1 = 0
Using the quadratic formula,
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \Rightarrow t=\frac{7\pm\sqrt{\left(-7\right)^2-4\left(5\right)\left(1\right)}}{2\cdot5} \\ \\ \Rightarrow t=1.24s\text{ or }0.16s \end{gathered}[/tex]Therefore, t = 1.23s or 0.16s