We have been given that in ΔJKL, k = 22 cm, ∠L=23° and ∠J=26°. We are asked to find the length of j to the nearest tenth of a centimeter.
We will use law of sines to solve for side j.
[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], where, a, b and c are opposite sides to angles A, B and C respectively.
We need to find measure of angle K to apply law of sine to our given problem.
Using angle sum property, we will get:
[tex]\angle J+\angle K+\angle L=180^{\circ}[/tex]
[tex]26^{\circ}+\angle K+23^{\circ}=180^{\circ}[/tex]
[tex]\angle K+49^{\circ}=180^{\circ}[/tex]
[tex]\angle K+49^{\circ}-49^{\circ}=180^{\circ}-49^{\circ}[/tex]
[tex]\angle K=131^{\circ}[/tex]
[tex]\frac{j}{\text{sin}(J)}=\frac{k}{\text{sin}(K)}[/tex]
[tex]\frac{j}{\text{sin}(26^{\circ})}=\frac{22}{\text{sin}(131^{\circ})}[/tex]
[tex]\frac{j}{\text{sin}(26^{\circ})}\cdot \text{sin}(26^{\circ})=\frac{22}{\text{sin}(131^{\circ})}\cdot \text{sin}(26^{\circ})[/tex]
[tex]j=\frac{22}{0.754709580223}\cdot 0.438371146789[/tex]
[tex]j=\frac{9.644165229358}{0.754709580223}[/tex]
[tex]j=12.77864423889[/tex]
Upon rounding to nearest tenth, we will get:
[tex]j\approx 12.8[/tex]
Therefore, the length of j is approximately 12.8 cm.
Answer:
12.8
Step-by-step explanation:
delta math
100 pts
Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error? 4 (x minus one-fifth) = 2 and two-thirds. Step 1, 4 x minus four-fifths = 2 and two-thirds. Step 2, 4 x = StartFraction 8 over 3 EndFraction + four-fifths. Step 3, 4 x StartFraction 40 over 15 EndFraction + StartFraction 16 over 15 EndFraction. Step 4, 4 x = StartFraction 56 over 15 EndFraction times one-fourth. X = StartFraction 14 over 15 EndFraction. step 1 step 2 step 3 step 4
Answer:
Step 3
Reason:
I toke the test/review.
Answer:
the and should be step 3
Step-by-step explanation:
Two 10 pound forces act on the same object at the same time. Find the
magnitude of their resultant if 135° is between the two forces.
Final Answer:
The magnitude of the resultant force when two 10 pound forces act on the same object 135° apart is approximately 18.47 pounds.
Explanation:
To find the magnitude of the resultant force when two forces are acting at an angle to each other, we can use the law of cosines. In this scenario, we have two forces each of 10 pounds acting on an object with an angle of 135° between them. Let's denote the forces as F1 and F2, both of which have magnitudes of 10 pounds. The angle between them is θ = 135°.
The formula for the resultant force R when two forces act at an angle θ is:
[tex]\[ R = \sqrt{F1^2 + F2^2 + 2 \cdot F1 \cdot F2 \cdot \cos(θ)} \][/tex]
In our case:
[tex]\[ F1 = F2 = 10 \, \text{pounds} \][/tex]
[tex]\[ θ = 135° \][/tex]
Plugging these values into the formula, we get:
[tex]\[ R = \sqrt{10^2 + 10^2 + 2 \cdot 10 \cdot 10 \cdot \cos(135°)} \][/tex]
[tex]\[ R = \sqrt{100 + 100 + 200 \cdot \cos(135°)} \][/tex]
The cosine of 135° is -√2/2 (since 135° is in the second quadrant where the cosine is negative):
[tex]\[ R = \sqrt{200 - 200 \cdot \frac{-\sqrt{2}}{2}} \][/tex]
[tex]\[ R = \sqrt{200 + 100\sqrt{2}} \][/tex]
[tex]\[ R = \sqrt{200 + 100 \cdot 1.414} \] (Since √2 is approximately 1.414)[/tex]
[tex]\[ R = \sqrt{200 + 141.4} \][/tex]
[tex]\[ R = \sqrt{341.4} \][/tex]
[tex]\[ R \approx 18.47 \text{ pounds} \][/tex]
Therefore, the magnitude of the resultant force when two 10 pound forces act on the same object 135° apart is approximately 18.47 pounds.
Ivanna is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random.
This game is this: Ivanna spins the spinner once. She wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner stops on the number 3, and $7 if the spinner stops on the number 4. She loses $8 if the spinner stops on 5 or 6.
Answer:
The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.
I guess that we want to find the expected value in one spin:
number 1: wins $1
number 2: wins $3
number 3: wins $5
number 4: wins $7
number 5: losses $8
number 6: loses $8
The expected value can be calculated as:
Ev = ∑xₙpₙ
where xₙ is the event and pₙ is the probability.
We know that the probability for all the events is 1/6, so we have:
Ev = ($1 + $3 + $5 + $7 - $8 - $8)*(1/6) = $0
So the expected value of this game is $0, wich implies that is a fair game.
The question is a probability problem in Mathematics. It requires calculating the expected value of a game based on the potential winnings and losses and their respective probabilities. On average, Ivanna will lose a dollar each time she plays.
Explanation:The subject matter of this question is a probability problem within Mathematics. One way to approach the problem would be to calculate the expected value of Ivanna's winnings from a single spin of the spinner. Each outcome (1, 2, 3, 4, 5, 6) has an equal chance of being chosen, which is 1/6, because there are 6 equally likely outcomes.
The formula for the expected value is the sum of all potential outcomes multiplied by their respective probabilities. Numerically, this would be (1*$1 + 1*$3 + 1*$5 + 1*$7 - 2*$8) / 6, which equals -$1.
Therefore, on average, Ivanna will lose a dollar each time she plays this game.
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find, to the nearest inch, the volume of a circular cone with a radius of 12 inches and a slant height of 20 inches. include step by step process. HELP PLEASE ASAP
We have been given that a cone has a radius of 12 inches and slant height of 20 inches. We are asked to find the volume of the cone.
We will use volume of cone formula to solve our given problem.
[tex]V=\frac{1}{3}\pi r^2\sqrt{l^2-r^2}[/tex], where
V = Volume of cone,
r = Radius,
l = Slant height.
Upon substituting our given values in volume formula, we will get:
[tex]V=\frac{1}{3}\pi\cdot 12^2\cdot \sqrt{20^2-12^2}[/tex]
[tex]V=\frac{1}{3}\pi\cdot 144\cdot \sqrt{400-144}[/tex]
[tex]V=48\pi\cdot\sqrt{256}[/tex]
[tex]V=48\pi\cdot16[/tex]
[tex]V=2412.743157[/tex]
[tex]V\approx 2412.74[/tex]
Therefore, the volume of the cone is approximately 2412.74 cubic inches.
7w+3 =24 so what does W =
Answer:
Step-by-step explanation:
hello :
7w+3-3 =24-3
7w=21
w=21/7 =3
Takiya recorded the heights of two sets of plants, one set planted in the shade and one set planted in full sun. Her data are shown in the plots below.
A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Shaded plants (inches). There are 0 dots above 1.5, 4 above 2, 3 above 2.5, 2 above 3, 0 above 3.5 and 4, and 1 above 4.5.
A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Full Sun plants (inches). There are 0 dots above 1.5, 1 above 2, 0 above 2.5, 2 above 3, 0 above 3.5, 4 above 4, and 3 above 4.5.
Which best explains the variability of the sets?
The shaded plants set has greater variability because more data is clustered around the median.
The sets are equally variable because the ranges of the data sets are equal.
The full sun plants set has greater variability because the IQR for full sun plants is greater.
Question;
1) The shaded plants set has greater variability because more data is clustered around the median.
2) The sets are equally variable because the ranges of the data sets are equal.
3) The full sun plants set has greater variability because the IQR for full sun plants is greater.
Answer:
The correct option is;
3) The full sun plants set has greater variability because the IQR for full sun plants is greater
Step-by-step explanation:
To answer the question, we present the dot plot as follows;
Heights of Shaded plants (inches)
0 4 3 2 0 0 1
0 1.5 2 2.5 3 3.5 4 4.5
We calculate the five numbers as follows;
Max = 4.5
Min = 2
1st quartile = (10+1)/4 th term = 2
2nd quartile (Median) = (10+1)/2 th term = 2.5
3rd quartile = 3×(10+1)/4 th term = 3
Interquatile range (IQR) = Q₃ - Q₁ = 3 - 2 = 1
Where:
Q₁ = 1st quartile
Q₃ = 3rd quartile
Heights of Full Sun plants
0 1 0 2 0 4 3
1.5 2 2.5 3 3.5 4 4.5
We calculate the five numbers as follows;
Max = 4.5
Min = 2
1st quartile = (10+1)/4 th term = 3
2nd quartile (Median) = (10+1)/2 th term = 4
3rd quartile = 3×(10+1)/4 th term = 4.5
Interquatile range (IQR) = Q₃ - Q₁ = 4.5 - 3 = 1.5
The interquartile range, IQR, is a measure of variability
Therefore, the full sun plants set has greater variability because the IQR for full sun plants is greater.
which trend is the plot
Answer:
positive trend
Step-by-step explanation:
the points are all positive
Answer: it shows no trend they’re all scattered and there is no straight line
Step-by-step explanation:
If a car travels at an average speed of x miles per hour, how far would the car travel in 120 minutes?
Answer:
2x
Step-by-step explanation:
if x equals the amount of miles per hour, then 2x would equal the amount of miles in 2 hours
Ali picked three numbers out of a hat. Use the information in the box to work out what numbers he picked. The lowest number was 11;the range was 13; the median was 17. Write All numbers in the boxes from lowest to highest
Final answer:
To find the numbers Ali picked, we identify the lowest number (11), calculate the highest number using the range (11 + 13 = 24), and confirm that the median (17) fits between these two numbers. Thus, the numbers are 11, 17, and 24.
Explanation:
Ali picked three numbers, and we have been provided with three pieces of information about these numbers: the lowest number was 11, the range was 13, and the median was 17. We can use this information to determine the three numbers Ali picked.
Step 1: Identify the Lowest Number
We know the lowest number is 11. This is our starting point.
Step 2: Determine the Range
The range of a set of numbers is the difference between the highest and the lowest numbers. Since the range is 13, we add this to the lowest number to find the highest number: 11 + 13 = 24. So, the highest number Ali picked is 24.
Step 3: Find the Median
The median is the middle number in a set of numbers that has been arranged in order. We are told the median is 17, which fits perfectly between our lowest and highest numbers, confirming that our calculations are correct.
Therefore, the numbers Ali picked, in order from lowest to highest, are: 11, 17, and 24.
The graph shows the function g(x) for a restricted domain.
On a coordinate plane, a function starts at (negative 4, 0) and then curves through the y-axis at (0, 1.5) and then goes through point (4, 2).
Which is the function g(x) for a restricted domain?
g(x) = Negative RootIndex 3 StartRoot x minus 4 EndRoot; x greater-than-or-equal-to –4
g(x) = Negative RootIndex 3 StartRoot x 4 EndRoot + 4; x greater-than-or-equal-to 0
g(x) = Negative RootIndex 3 StartRoot x + 4 EndRoot; x greater-than-or-equal-to –4
g(x) = Negative RootIndex 3 StartRoot x EndRoot minus 4; x greater-than-or-equal-to 0
Answer:
Option 3
g(x) = Negative RootIndex 3 StartRoot x + 4 EndRoot; x greater-than-or-equal-to –4
Step-by-step explanation:
Since the graph starts at x = -4 and towards the right, domain is x 》-4
g(x) = -(x + 4)^⅓
Because,
0 = -(-4 + 4)^⅓
0 = 0
The function g(x) for the restricted domain is g(x) = -∛(x-4); x ≥ -4.
Explanation:The function g(x) for the restricted domain can be determined by analyzing the given information. The function starts at (-4, 0) and curves through the y-axis at (0, 1.5) before passing through point (4, 2). Based on this, the correct function is g(x) = -∛(x-4); x ≥ -4.
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#1 Find the slope given the points (3,-20) and (5,8) *
Hey there :)
To find the slope with two points we will need to use the equation [tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
[tex]x^1[/tex] [tex]x^2[/tex] [tex]y^1[/tex] [tex]y^2[/tex]
( 3 , -20 ) ( 5 , 8 )
Here is what the equation should look like when replaced with the numbers (it will be a fraction) :
[tex]\frac{8 - (-20)}{5 - 3}[/tex]
We know that two negatives cancel out and make a positive, so the numerator would actually be 8 + 20.
Solve the fraction and we get [tex]\frac{28}{2}[/tex]
28 divided by 2 is 14. The slope is 14.
please help what is y=-3x+12y=−3x+12
I NEED HELP ASAP PLEASE! About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?
47.5%
68%
95%
99.7%
Answer:
c: 95%
Step-by-step explanation:
got it right on ed
Using the Empirical Rule, it is found that about 95% of the data lies within 2 standard deviations of the mean in a normal distribution.
What is the Empirical Rule?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Hence, 95% is the answer for this question.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
44 cm
Find the surface area of the triangular prism. The base of the
prism is an isosceles triangle.
25 cm
24 cm
14 cm
can you help me?
Answer:
Step-by-step explanation:
120 and 56
Which dimensions cannot create a triangle?
a
three angles measuring 90 degrees, 10 degrees, and 80 degrees
b
three angles measuring 30 degrees, 55 degrees, and 100 degrees
c
three sides measuring 7 cm, 9 cm, and 11 cm
d
three sides measuring 10 m, 16 m, and 10 m
Answer:
B
Step-by-step explanation:
it adds up to 185
if a scientist is able to use 4 kilograms of fertilizer for 5 weeks how much fertilizer did they use each week
Answer:
0.8 kilograms of fertilizer
Step-by-step explanation:
Looking at the data given to us in a fraction form, we can imagine:
4 kilograms / 5 weeks
To find out how many kilograms of fertilizer was used each week, we're going to divide that fraction out, so we're going to do 4 divided by 5. Dividing this will give you:
0.8 kilograms
Therefore your answer is that they use .8 kilograms of fertilizer each week.
Answer:
6
Step-by-step explanation:
Evaluate ab + 5c - d. If a =3, b=2, c=7, and d=4Immersive Reader
(1 Point)
Answer:
46
Step-by-step explanation:
a:3, b:2 , c: 7 and d:4
ab + 5c - d
(3*5) + 5(7) - 4
(15 + 35) -4
50- 4 :46
Answer:
37.
Step-by-step explanation:
ab + 5c - d
= 3*2 + 5*7 - 4
= 6 + 35 - 4
= 37.
Kendall went shopping and purchased 7 shirts, 3 pairs of pants, 2 jackets. How many different outfits are possible?
Answer:
42
Step-by-step explanation:
7 x 3 x 2 = 42
A group of 72 people travel to the beach for a clean-up day.Some of the people bring their own supplies .Write an equation for the number of people for whom supplies will be provided p,if b people bring their own supplies?
Answer:
p=72-b
Step-by-step explanation:
From the statement, you can say that the number of people whom supplies will be provided would be equal to the number of people that travel to the beach minus the amount of people that bring their own supplies:
p=72-b, where:
p= number of people for whom supplies will be provided
b= number of people that bring their own supplies
Jimmy has $100 and would like to buy lottery tickets. Each ticket is $5 dollars. Jimmy finds that the equation for his situation would be y = 5x +100.
True or False?
Answer: False wouldn't it be -100 dollars if hes buying something. Correct me if im wrong.
Will give brainliest! please answer correctly!
Answer:
A and C
Step-by-step explanation:
w+c must be up to (<=) 41. corn must be less than (<) 28.
Can someone please help me with 10,11,and 12 I WILL MARK BRAINLIEST!!!
Answer:
10 is acute
11 is a right
12 obtuse
Step-by-step explanation:
What is the theoretical probability of the spinner landing on Elisondra’s section?
Answer:
1/4
Step-by-step explanation:
Just did this.
If Casey places $890 in a savings account,
how much interest will he earn in 12 years at a
5% simple interest rate?
Answer:
$534
Step-by-step explanation:
Simple Interest formula: I = Prt
I = $890 * (0.05)* 12
I = $534
Answer:
Step-by-step explanation:
534
I need help with everything.
Step-by-step explanation:
5. 102 = 6( 1 + 4p)
102 = 6 + 24p
102 - 6 = 24p
96 = 24p
96/ 24 = p
4 = p
2x3 to the second power plus 5 to the second power
Answer: 43
Multiply
3×3=9
New Problem: (2)(9)+5²
Multiply
2×9=18
New Problem: 18+5²
Multiply
5×5=25
New Problem: 18+25
Add
18+25=43
Answer:
it would be 43 :)
Step-by-step explanation:
first you have to do 3 squared which is 9 then you multiply it by 2. Then square 5 which is 25 and add 25 +18+ 43
at a restaurant you order a meal that costs 63.90 you leave a 20% tip. the sales tax is 5% what is the total cost of the meal
Which diagram represents the postulate that states exactly one line exists between any two points?
cOf
Answer: c on edg
Step-by-step explanation: I have no idea, i guess that’s just what it is, I’m no math genius.
Lines and points are both undefined terms in geometry.
The diagram that represents the postulate is line (c)
The given postulate states that:
Exactly one line exists between any two points.
This means that:
The line must pass through the two points.
From the given options (see attachment)'
Only option (c) is true
Because the line passes through points A and B.
Hence, the diagram that supports the postulate is line (c).
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X^2-x-20 how do I write that in factored form
Answer:
(x+4)(x-5)
Step-by-step explanation:
You need to find two numbers that multiply to be -20 but add up to be -1.
Answer:
( x - 5 ) ( x + 4 )
Step-by-step explanation:
When solving quadratic equations it's important to remember that they have 2 solution. We need to work out the factors, sum and the products to successfully factorise the quadratic and solve it. So,
x² - x - 20 = 0
Sum = -1
Product = -20
So we need two numbers that sum to -1 and multiply together to make -20
Factors = -5 and 4
x² - 5x + 4x - 20
Factor x² - 5x and 4x -20 separately
x² - 5x = x ( x - 5 )
4x - 20 = 4 ( x - 5 ) So
x ( x - 5 ) + 4 ( x - 5 )
We can see a common factor of ( x - 5 ) and the other bracket would be ( x + 4)
( x - 5 ) ( x + 4 )
A group of friends were working on a student film that had a budget of $500. They used $25 of their budget on props. What percentage of their total budget did they spend on props?
The students spent 5% of their $500 budget on props, calculated by dividing $25 by $500 and then multiplying by 100.
To determine the percentage of the total budget that was spent on props for the student film, we need to use the formula for calculating percentages. The formula is
(amount spent / total budget)
* 100 = percentage spent.
Applying this formula to the given values:
(25 / 500) * 100 = 5%.Therefore, the students spent 5% of their total budget on props.