Bethany's error is that she used cosine instead of inverse cosine when finding B.
When solving for B, she used the equation 4.1^2 = 4.5^2 + 2.7^2 - 2(4.5)(2.7)cosB, which is a correct application of the law of cosines. She also correctly isolated the cost and found its value to be 0.1276. However, when she solved for B, instead of using the inverse cosine function, arccos(0.1276), she used the cosine function with the value 0.1276 which resulted in an angle of 82.7 degrees. The correct value of B as per the provided equation should have been arccos(0.1276) which is not equal to 82.7.
Complete question :
4.1^2 = 4.5^2 + 2.7^2 - 2(4.5)(2.7)cosB
4.1 = 4.5 + 2.7 - 24.3cosB
-3.1 = -24.3cosB
0.1276 = cosB
B = 82.7
Where is Bethany's error?
Bethany made one side of the equation equal to the square of the incorrect side when solving for B.
Bethany took the square root of each squared term before isolating cosB and solving for B.
Bethany used cosine instead of inverse cosine when finding B.
Bethany neglected to multiply the expression involving the cosine by 2.
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Triangle KLM was dilated according to the rule Do,0.75(x,y) what is true about the image K’L’M’?
When triangle KLM is dilated with a scale factor of 0.75 the image K'L'M' will have sides reduced by the factor 0.75
What is dilation?Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor.
The scale factor determines magnification or shrinking as follow
magnification scale factor is greater than 1shrinking the scale factor is less than 1The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
Hence for the triangle KLM, with a scale factor of 0.75, the sides will shrink by 0.75 = 3/4
Resulting to a smaller image K'L'M'
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Work out
a) 5 - 21/
b) 7/3 + 2/1/2
Answer:
a) 14/4 or 3.5
b.) 148/15 or 9.8667
Step-by-step explanation:
a) 5¾ - 2¼
=23/4 - 9/4
LCM = 4
=23/4 - 9/4
=23. - 9
4
=14/4 OR 3.5
b) 7⅔ + 2⅕
=23/3 + 11/5
LCM = 15
=23/3 + 11/5
115. + 33
15
=148/15 OR 9.8667
which graph best represents the following inequality y<_ -5/6 +2/3
The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ y ≤ - 5/6x + 2/3
Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.
Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.
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5. A ribbon is cut into two pieces. The length of the longer piece is 60 inches and the length of
the shorter piece is 12 inches.
A) How many times the length of the shorter piece is the longer piece?
B) What is the total length of the ribbon?
The number of times the length of the shorter piece is the longer piece is 5 and The total length could be 72 inches.
What is ratio ?
ratio can be defined as the given value divided by the total value.
Given ,
A ribbon is cut into two pieces. The length of the longer piece is 60 inches and the length of the shorter piece is 12 inches.
The number of times the length of the shorter piece is the longer piece is
let the number of times be x .
so,
x = 60/12
x = 5
The total length could be = 60+12 = 72
hence, The number of times the length of the shorter piece is the longer piece is 5 and The total length could be 72 inches.
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A bulletin board has a perimeter of 300 in. Write an equation that expresses the area A(w) of the bulletin board as a function of its width
the width of the bulletin board is -200 in.
Step-by-step explanation:
Let w = the width of the bulletin board
Since the perimeter of the bulletin board is 300 in, we can write the equation:
2w + 2(300 - w) = 300
Simplifying:
2w + 600 - 2w = 300
0 = 300 - 600
-600 = 300
Therefore, the width of the bulletin board is -200 in.
Now that we know the width of the bulletin board, we can express the area A(w) as a function of its width w:
A(w) = w * (-200)
A(w) = -200w
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Is inverse relationship direct?
An inverse relationship can not direct.
We know that an inverse proportion represents inverse or indirect relation between two quantities.
In inverse relationship, one value increases while the other value decreases, and vice versa.
But in case of direct relationship, if one quantity increases , the other quantity also increases, and if one quantity decreases , the other quantity also decreases.
When two quantities 'm' and 'n' are inversely proportional to each other, it means when the value of m increases while the value of quantity 'n' decreases, and vice versa.
Also, an inverse relationship always has a negative slope.
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Express the trig ratios as fractions in simplest terms.
The trigonometric functions sin R and Cos Q will have same Trigonometric ratios as Sin R=24/51 and Cos Q=24/51
What are trigonometric functions?
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions
Now
As Trigonometric ratios for Sin R=Perpendicular/Hypotenuse and Cos Q=Base/Hypotenuse
Hence,
Sin R=24/51 and Cos Q=24/51
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Find angle x giving your answer to one decimal place
The value of angle x in decimal place is 57.8°.
What is decimal place?A decimal number's digits are assigned a place value according to a chart that displays decimal place values. A digit in a number's place value is, as far as we are aware, its numerical value. The correct placement of each digit in a decimal number is therefore determined using decimal place value charts, just like with other place value diagrams. In this chart, the place values of the digits before and after the decimal point are shown.
Draw the altitude of the triangle
We know that
sinθ = Opposite / Hypotenuse
sin 38° = y/11
y = 11 sin 38°
y = 6.77
sin(x) = y/8
sin(x) = 6.77/8
sin(x) = 0.84625
sin(x) = 57.8°
Thus, the value of angle x in decimal place is 57.8°.
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Need help for number 14
Answer:
6x^2 - 5x - 4
Step-by-step explanation:
Here you go. A pic.
a photo contest awards five different prizes to its top five winners. how many ways can the prizes be awarded among the 2- entries received if no one gets more than one prize?
The number of different ways the prizes can be awarded among the 2 entries received is 2 if no one gets more than one prize.
The question states that there are five different prizes and the top five winners will get them, but no one can get more than one prize. Since there are only two entries received, the number of ways the prizes can be awarded is determined by the number of ways to select two winners from the two entries received
This is a combination problem where we have to select 2 items (winners) out of 2 items (entries) without regard to the order.
The number of ways to select k items out of n items without regard to the order is given by the binomial coefficient (n choose k), which is calculated as:
nCk = n! / (k!(n-k)!)
where n is the total number of items, k is the number of items selected and ! denotes factorial.
So in this problem, we have to calculate the number of ways to select 2 winners out of 2 entries, the binomial coefficient is:
2C2 = 2! / (2!(2-2)!) = 2*1/1 = 2
Therefore, the number of different ways the prizes can be awarded among the 2 entries received is 2 if no one gets more than one prize.
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What is the rule for parallel and perpendicular lines?
In case of parallel lines, the of the lines are always equal.
And the product of slopes of perpendicular lines is -1.
We know that the parallel lines are the lines in a plane that are always the same distance apart.
Also, the parallel lines never intersect.
The slopes of parallel lines are always equal.
The y-intercept of parallel lines is different.
Whereas, the perpendicular lines are the lines that intersect at a right angle (90 degrees angle).
The product of slopes of perpendicular lines is -1.
All perpendicular lines are always intersecting lines, but all intersecting lines need not be perpendicular.
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the triangle of numbers used to find the pattern for any power of binomials is called ___ triangle.
Answer:
Pascal's
Step-by-step explanation:
Sarah opens a new checking account. She deposits $211 to start initially. If sarah is able to deposit her allowance for 16 weeks straight, she will have $355. How much does Sarah receive for an allowance every week?
So, Sarah receives $9 as her allowance every week.
Sarah wants to deposit her allowance for 16 weeks straight, so she will have a total of $355 in her account.
We know that she had $211 initially in her account and after 16 weeks, she will have $355.
So the amount she will have to deposit every week as her allowance is:
$355 - $211 = $144
We can divide the total amount of allowance by the number of weeks to find out how much she receives per week:
$144 / 16 = $9
Therefore, Sarah receives $9 as her allowance every week.
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If y varies directly as x and y = 5 when x = 0.4, find x when y = 37.5.
The value of x when y = 37.5 if y varies directly as x and y = 5 when x = 0.4 is 3
How to calculate direct variation?y = k × x
Where,
k = constant of proportionality
If y = 5 when x = 0.4
y = k × x
5 = k × 0.4
5 = 0.4k
divide both sides by 0.4
k = 5/0.4
k = 12.5
If y = 37.5, find x
y = k × x
37.5 = 12.5 × x
37.5 = 12.5x
divide both sides by 12.5
x = 37.5 / 12.5
x = 3
Therefore, the value of x when y = 37.5 is 3
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The value of x from y is x = 3
How to determine the value of x from yFrom the question, we have the following parameters that can be used in our computation:
y varies directly as x and y = 5 when x = 0.4,
The equation of direct variation is
k = y/x
So, we have
k = 5/0.4
Evaluate
k = 12.5
So, we have
y/x = 12.5
When y = 37.5. we have
37.5/x = 12.5
Solve for x
x = 3
Hence, the solution is x 3
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give an arithmetic sequence of 20,16,12find it’s common difference and the 25th term
Answer: Common difference = -4, and 25th term = -56
Step-by-step explanation:
The common difference, d, is 20 - 16 or 16 - 12, which is -4.
Using the formula [tex]a_{n}=a_{1}+(n-1)d[/tex], [tex]a_{25}=20+(20-1)*-4[/tex]
= 20 + 19 * -4,
= 20 - 76
= -56
What is derivative of e7?
The derivative of e7 is 7e7. The derivative of e^x is e^x, so the derivative of e7 is e7 times the derivative of x, which is 1, so the derivative of e7 is 7e7
The derivative of e^x is e^x, so the derivative of e7 is e7 times the derivative of x, which is 1, so the derivative of e7 is 7e7
The derivative of a function is a measure of how the output of the function changes with respect to a change in the input. In this case, we are looking for the derivative of the function e^7. The derivative of e^x is e^x, so the derivative of e7 is e7 multiplied by the derivative of x, which is 1. Therefore, the derivative of e7 is 7e7. This means that for every one-unit increase in the input value, the output of the function is increased by 7e7. This is useful for understanding how the output of a function changes in relation to a change in the input value. Knowing the derivative of a function can help us to better understand its behavior and make predictions about its future values.
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Over 4 days, Krista deposited $45 into her
bank account, transferred $30 to a friend,
deposited $59, and withdrew $18. What was
the mean change per day to Krista's account
during that week?
If Over 4 days, Krista deposited $45 into her bank account, transferred $30 to a friend, the mean change per day to Krista's account during that week is $14.
How to find the Mean change per day?First step is to find the total money in the account
Total money in the account = $45 - $30 + $59 - $18
Total money in the account = $56
Now let find the mean change per day
Mean change per day = Total money in the account /Total number of days
Mean change per day = $56 /4 days
Mean change per day = $14
Therefore the Mean change per day is $14.
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What is the slope of the line − 3x 5y 2x 3y?
Answer:
45y2
Step-by-step explanation:
let g be a group in which every element other than the identity has order two. show that g is abelian. show that if g is also nite, then the order of g is a power of 2. (consider a minimal generating set for g.) can such a group be innite?
The order of g is a power of 2, Hence G is abelian.
Everything is in order, with the exception of identification.
2, then a2=e
where a∈G
(including identity this time). So, a−1=a
for all a∈G
Hence ab=(ab)−1=b−1a−1=ba
for all a b∈G
For every x∈G
we have x2=e
where e
represents the identity in.
Then x−1=x
Now, let a,b
be two arbitrary elements in G
We have ab=(ab)−1=b−1a−1=ba
Hence G is abelian.
(First equality is true because ab
is also an element of G
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To begin a bacteria study, a petri dish had 2600 bacteria cells. Each hour since, the number of cells has increased by 15%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
The exponential function showing relationship between y and t will be y=2600(23/20)^t.
What are exponential functions?
An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Now,
Initial bacteria cells=2600 (p)
rate of increment = 15% (r)
Number of hours = t
y=Number of bacteria cells at any time
To find the relationship between y and t
we use the formula Quantity = Initial quantity*(1+r/100)^t
-- (A=p*(1+r/100)^t )
therefore,
y=2600(1+15/100)^t
y=2600(23/20)^t
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PLEASE HELP ASAP!!!!!!!!!!!
Answer:
1.) x = 7
3.) m = 1 and m = 5
5.) [tex]x=\frac{3}{7}\\[/tex]
7.) n = 4 , [tex]n=-\frac{3}{2}[/tex]
Extra credit) [tex]t=-\frac{1}{9}[/tex]
Step-by-step explanation:
Question 1
Multiply both sides by 5
simplify: x - 1 = 6
Add 1 to both sides
Question 3
Multiply by the Least common multiple (5 = 6m - m^2)
solve 5 = 6m - m^2!
Question 5
Cross multiply
move x to the left side
Divide both sides by 7
Simplify
Question 7
Cross Multiply
Solve
Extra Credit
Multiply by Least Common Denominator
move 2 to the right and t to the left side.
Divide both sides by 18
Simplify
mary, trey, and lamar sent a total of 100 text messages over their cell phones during the weekend. lamar sent 3 times as many messages as mary. mary sent 10 more messages than trey. how many messages did they each send?
Out of 100 messages, Trey sent 12 messages, Mary sent 15 messages and Lamar sent 75 messages.
Let the number of messages sent by Trey be x. So, the number of messages sent by Mary will be (x+10). The number of messages by Lamar will be 3×(x+10). Their sum of is 100, so representing the information in equation form.
x + x + 10 + 3(x + 10) = 100
Performing multiplication on Left Hand Side of the equation
x + x + 10 + 3x + 30 = 100
Performing addition
5x + 40 = 100
Rewriting the equation
5x = 100 - 40
Performing subtraction
5x = 60
x = 60/5
Performing division
x = 12
Messages sent by Trey = 12
Messages sent by Mary = 12 + 3
Messages sent by Mary = 15
Messages sent by Lamar = 3(15 + 10)
Messages sent by Lamar = 3×25
Messages sent by Lamar = 75
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Multiply.
(4a+5) (7a+3)
Simplify your answer.
0
Answer:
[tex]28a {}^{2} + 47a + 15[/tex]
Step-by-step explanation:
Multiply what's inside the brackets with the outside brackets:
[tex](4a + 5)(7a + 3) = [/tex]
[tex](4a \times 7a) + (4a \times 3) + (5 \times 7a) + (5 \times 3) = [/tex]
[tex]28a {}^{2} + 12a + 35a + 15 = [/tex]
[tex]28a {}^{2} + 47a + 15[/tex]
Round the number 25849 to the nearest hundred.
Answer: 25800
Step-by-step explanation: If you want to round to the nearest hundred, then you look at the tens digit. Since the tens digit is 4, you round it down and then you get 25800.
SOMEONE, PLEASE HELP ME!!! I NEED AN ANSWER ASAP!
Answer:
Price per topping
Step-by-step explanation:
Because the price changes per number of toppings, the graph shows the price per number of toppings.
Adequate Preparation for Retirement. In 2018, RAND Corporation researchers found that 71% of all individuals ages 66 to 69 are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement.
a. Develop appropriate hypotheses such that rejection of H0 will support the con-clusion that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66–69 age group who did not complete high school than it is for the population of the 66–69 year old.
b. In a random sample of 300 people from the 66–69 age group who did not complete high school, 165 were not prepared financially for retirement. What is the p-value for your hypothesis test?
c. At a = .01, what is your conclusion
a. The null hypothesis (H0) is that the proportion of those who are adequately prepared financially for retirement is the same for people in the 66-69 age group who did not complete high school as it is for the population of the 66-69-year-old (71%).
The alternative hypothesis (Ha) is that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of the 66-69-year-old.
b. To calculate the p-value for this hypothesis test, we can use a one-sample proportion test. The sample proportion (p-hat) is 165/300 = 0.55. Using a z-test, with a z-score of -2.35 and a standard deviation of 0.058, the p-value is 0.011.
c. At a significance level of 0.01, the p-value of 0.011 is less than the significance level, so we reject the null hypothesis. We can conclude that there is evidence that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of the 66-69-year-old.
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How do you tell if a pair of equations are parallel perpendicular or neither?
Two non-vertical lines in the same plane are said to be parallel if they have the same slope. No two parallel lines will ever cross. A set of non-vertical lines within the same plane are considered to be perpendicular if they meet at a right angle.
Perpendicular lines and parallel lines both meet at 90 degrees, although parallel lines never do. Lines are perpendicular if the slope of one line is equal to the reciprocal of the second line's negative slope.
Lines that have the same slope are therefore said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are just intersecting lines.
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TRY MORE
Read and understand the following situations. Solve for the answer.
1. Mrs. Ramirez donated P 5 000. 00 for typhoon Ulysses victims. If 50% of
her donation was sent to Catanduanes while another 50% to Cagayan
how much did the victims from Catanduanes and Cagayan receive?
2. Mang Juan harvested calamansi in his backyard and put them in a
small basket. 2/5 of the calamansi were ripe and the rest were still
unripe. He used all the ripe calamansi and 25% of the unripe calamansi
for juice. What percentage was used for the juice
1. The victims from Catanduanes and Cagayan receive P 2,500.00.
Mrs. Ramirez donated P 5,000.00 and 50% of it was sent to Catanduanes while another 50% was sent to Cagayan.
So, the victims from Catanduanes received P 5,000.00 x 50/100 = P 2,500.00 and the victims from Cagayan received P 5,000.00 x 50/100 = P 2,500.00.
2. The percentage of the calamansi used for juice is 60%
Mang Juan harvested calamansi and put them in a small basket. 2/5 of the calamansi were ripe, and the rest were unripe. He used all the ripe calamansi and 25% of the unripe calamansi for juice.
So, the number of ripe calamansi used for juice is 2/5 x the total number of calamansi, and the number of unripe calamansi used for juice is 25/100 x (1-2/5) x the total number of calamansi.
The total percentage of the calamansi used for juice is (2/5 + 25/100 x (1-2/5)) x 100%.
So, The percentage of the calamansi used for juice = (2/5 + 1/5) x 100 = (3/5) x 100 = 60%
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Please help me solve this.....
lado Chus machigne Randi ko ban
Step-by-step explanation:
lado Chus bosadike louder you mother father mc mf
the point at which the angle bisectors intersect in a triangle___
The angle bisectors of a triangle bisect at a common point that is equidistant from the all the sides of the triangle, this point of coincidence is called the incenter of the triangle.
Incenter all the time lies inside the triangle, the circle drained with incenter as the center is inscribed in the triangle and it is called incircle.
The use of Angle bisectors in real life are in architecture, for making quilts and in produce cakes.
It is also used in playing several games as well like football, rugby, billiards.
we use the point of concurrency for angle sever of a triangle theorem.
From that theorem, R is equidistant from the three sides of triangle ABC, so XR= YR = ZR
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