Answer:
m2 =1/4
Step-by-step explanation:
m1 . m2 = 1
m1 is given 4 then
4.m2 =1
4.m2/4 =1/4
m2 = 1/4
Hello there!
The slopes of perpendicular lines are opposite reciprocals.
So, if one line has a slope of 4, then the slope of the line perpendicular to it is the opposite of 4 flopped over (-1/4)
And we're done! Hope it helps you!
If you have any questions, feel free to ask!
~An excited gal
[tex]MagicalNature[/tex] here to help
lim (cosec 2x - xcosec³x)
x approaches 0
The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.
We have,
To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.
The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).
Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.
Substituting these into the expression,
We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).
Now, let's evaluate the limit term by term:
lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).
lim(x approaches 0) (x (1/(sin(x))³))
= 0 (1/(sin(0))³)
= 0 x 1/0 (which is also undefined).
Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.
Therefore,
The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.
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How many 20kobo make up #20
Answer:
100
Step-by-step explanation:
#20 naira - 20 * 100
= 2000kobo
2000/20
100
QED✅✅
you can support by rating brainly it's very much appreciated ✅ ✅
4÷52,678
I forgot how to do division.
Answer:0.00007593302
Step-by-step explanation:
Work out the total surface area of the frustum. Give your answer to 3 s.f.
Answer:
S = π(12)(20) + π(12^2) - (π(3)(5) + π(3^2))
= π(240 + 144 - (15 + 9))
= 360π = about 1,130.97 cm^2
In the diagram at right, DE is a midsegment of triangle ABC. If the area of triangle ABC is 96 square units, what is the area of triangle ADE? Explain how you know.
The area of triangle ADE is,
⇒ A = 48 square units
We have to given that,
In the diagram , DE is a midsegment of triangle ABC.
And, The area of triangle ABC is 96 square units
Now, We know that,
Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.
Hence, the area of triangle ADE is half the area of triangle ABC,
That is,
A = 96 / 2
A = 48 square units
Thus, The area of triangle ADE is,
⇒ A = 48 square units
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You are using a magnifying glass that shows the image of an object that is six tin image of the termite seen through the magnifying glass. 9.5 mm The image length through the magnifying glass is millimeters.
When viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.
When using a magnifying glass, the image of an object appears larger. In this case, the termite is being viewed through a magnifying glass that magnifies the image by a factor of six. The actual length of the termite is not mentioned in the given information. However, it is stated that the length of the image seen through the magnifying glass is 9.5 mm.To determine the actual length of the termite, we can divide the length of the image by the magnification factor. Therefore, the actual length of the termite would be 9.5 mm divided by 6, which is approximately 1.58 mm.Therefore, when viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.For more questions on magnifying glass
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A basket had 15 mangoes. A monkey came and took
away two-fifths of the mangoes. How many mangoes
were left in the basket
Given: ΔABC
AB=BC
PΔABC=50
PΔABD=40
Find: BD
The length of BD of the given triangle is: 15
How to find the perimeter of a triangle?The perimeter of a triangle is simply defined as the length of the boundary of that triangle.
Now, we are given that:
AB = BC = a
Perimeter of triangle ABC = 50
Perimeter of triangle ABD = 40
Thus:
2a + 2b = 50
a + b = 25 ------(1)
Similarly:
a + b + h = 40
a + b = 40 - h -----(2)
Put 40 - h for a + b in eq 1 to get:
40 - h = 25
h = 40 - 25
h = 15
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Find the measurement of m
The measure of the inscribed angle G in the circle is 85 degree.
What is the measure of angle G?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
Since the circle equals 360 degrees, we can determine the intercepted arc DF.
Hence:
Arc DF = 360 - ( 70 + 120 )
Arc DF = 360 - 190
Arc DF = 170°
Now, plug the value into the above formula:
Inscribed angle = 1/2 × intercepted arc.
Inscribed angle G = 1/2 × 170°
Inscribed angle G = 85°
Therefore, angle G has a measure of 85 degree.
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When a new machine is functioning properly, only 3% of the items produced are defective.
Assume that we will randomly select two parts produced on the machine and that we are
interested in the number of defective parts found.
a. Describe the conditions under which this situation would be a binomial experiment.
b. Draw a tree diagram similar to Figure 5.3 showing this problem as a two-trial experiment.
c. How many experimental outcomes result in exactly one defect being found?
d. Compute the probabilities associated with finding no defects, exactly one defect, and
two defects.
a. This situation would be a binomial experiment if the following conditions are met:
The trials are independent: The selection of one part does not affect the selection of the other.
Each trial has two possible outcomes: In this case, defective or non-defective.
The probability of success (finding a defective part) remains constant for each trial: In this case, the probability is 3% or 0.03.
The number of trials is fixed: We are selecting two parts, so the number of trials is predetermined.
b. Here is a tree diagram representing the two-trial experiment:
D ND
/ \ / \
D ND D ND
The branches represent the two trials, with D representing a defective part and ND representing a non-defective part.
c. To find the number of experimental outcomes resulting in exactly one defect, we can observe that there are two outcomes that meet this criterion: D-ND and ND-D. Both represent one defective part and one non-defective part.
d. The probabilities associated with finding no defects, exactly one defect, and two defects can be calculated as follows:
Probability of finding no defects: (1 - probability of finding a defective part) * (1 - probability of finding a defective part) = (1 - 0.03) * (1 - 0.03) = 0.97 * 0.97 = 0.9409.
Probability of finding exactly one defect: (probability of finding a defective part) * (probability of finding a non-defective part) + (probability of finding a non-defective part) * (probability of finding a defective part) = 0.03 * 0.97 + 0.97 * 0.03 = 0.0582.
Probability of finding two defects: (probability of finding a defective part) * (probability of finding a defective part) = 0.03 * 0.03 = 0.0009.
Therefore, the probabilities associated with finding no defects, exactly one defect, and two defects are approximately 0.9409, 0.0582, and 0.0009, respectively.
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NO LINKS!! URGENT HELP PLEASE!!!
Given the explicit formula for a geometric sequence find the first five terms and the 8th term.
36. a_n = -3^(n-1)
37. a_n = 2 * (1/2)^(n - 1)
Answer:
see explanation
Step-by-step explanation:
to find the first 5 terms substitute n = 1, 2, 3, 4, 5 into the explicit formula
36
a₁ = - [tex]3^{1-1}[/tex] = - [tex]3^{0}[/tex] = - 1 [ [tex]a^{0}[/tex] = 1 ]
a₂ = - [tex]3^{2-1}[/tex] = - [tex]3^{1}[/tex] = - 3
a₃ = - [tex]3^{3-1}[/tex] = - 3² = - 9
a₄ = - [tex]3^{4-1}[/tex] = - 3³ = - 27
a₅ = - [tex]3^{5-1}[/tex] = - [tex]3^{4}[/tex] = - 81
the first 5 terms are - 1, - 3, - 9, - 27, - 81
to find a₈ substitute n = 8 into the explicit formula
a₈ = - [tex]3^{8-1}[/tex] = - [tex]3^{7}[/tex] = - 2187
37
to find the first 5 terms substitute n = 1, 2, 3, 4, 5 into the explicit formula
a₁ = 2 × [tex](\frac{1}{2}) ^{1-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{0}[/tex] = 2 × 1 = 2
a₂ = 2 × [tex](\frac{1}{2}) ^{2-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{1}[/tex] = 2 × [tex]\frac{1}{2}[/tex] = 1
a₃ = 2 × [tex](\frac{1}{2}) ^{3-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{2}[/tex] = 2 × [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{2}[/tex]
a₄ = 2 × [tex](\frac{1}{2}) ^{4-1}[/tex] = 2 × ([tex]\frac{1}{2}[/tex] )³ = 2 × [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{4}[/tex]
a₅ = 2 × [tex](\frac{1}{2}) ^{5-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{4}[/tex] = 2 × [tex]\frac{1}{16}[/tex] = [tex]\frac{1}{8}[/tex]
the first 5 terms are 2 , 1 , [tex]\frac{1}{2}[/tex] , [tex]\frac{1}{4}[/tex] , [tex]\frac{1}{8}[/tex]
to find a₈ substitute n = 8 into the explicit formula
a₈ = 2 × [tex](\frac{1}{2}) ^{8-1}[/tex] = 2 × [tex](\frac{1}{2}) ^{7}[/tex] = 2 × [tex]\frac{1}{128}[/tex] = [tex]\frac{1}{64}[/tex]
Answer:
The explicit formula for a geometric sequence is:
a_n = a_1 * r^(n - 1)
where:
a_n is the nth term in the sequencea_1 is the first term in the sequencer is the common ratio between the terms in the sequenceIn equation 36,
we can see that the first term is -3 and the common ratio is -3. Therefore, we can write the explicit formula for this sequence as:
a_n = -3 * (-3)^(n - 1)
Using this formula, we can find the first five terms and the 8th term in the sequence:
a_1 = -3
a_2 = -3 * (-3) = 9
a_3 = -3 * (-3)^2 = -27
a_4 = -3 * (-3)^3 = 81
a_5 = -3 * (-3)^4 = -243
a_8 = -3 * (-3)^7 = 6561
In equation 37,
we can see that the first term is 2 and the common ratio is 1/2. Therefore, we can write the explicit formula for this sequence as:
a_n = 2 * (1/2)^(n - 1)
Using this formula, we can find the first five terms and the 8th term in the sequence:
a_1 = 2
a_2 = 2 * (1/2) = 1
a_3 = 2 * (1/2)^2 = 1/2= 0.5
a_4 = 2 * (1/2)^3 =1/4= 0.25
a_5 = 2 * (1/2)^4 = 1/8=0.125
a_8 = 2 * (1/2)^7 = 1/64=0.015625
Refer to the information below to answer Questions 1 to 4. 1. Billy's gross pay is K850.00 Billy is taxed 12% on his taxable income, and contributes 7% to Nusfund. His loan deduction is 5%. What is his net pay? (1 mark)
The Billy's net pay is K646
The given information are; Billy's gross pay is K850.00, he is taxed 12% on his taxable income, and contributes 7% to Nusfund. His loan deduction is 5%.
To find out his net pay, the following steps must be taken:Firstly, calculate Billy's tax amount, Nusfund contribution, and loan deduction by using their respective percentages and the gross pay.
tax amount= 12/100 × 850= K102 Refund contribution= 7/100 × 850= K59.50Loan deduction= 5/100 × 850= K42.50 Secondly, the sum of all the deductions made from the gross pay is calculated to obtain the total deductions.
Total deductions= K102 + K59.50 + K42.50= K204The final step is to subtract the total deductions from the gross pay to find Billy's net pay. Net pay= K850 − K204= K646.
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Which table matches the equation for y = 3/2x-3
Answer: I think it's H, if it isn't and you get a second try it should be N
Step-by-step explanation: Both H and N start with 0/-3 except F which means F is wrong. Maybe you should wait for a better answer...but it shouldn't be F
Mark’s cost does not vary directly with time spent talking because
Mark's cost does not vary directly with time spent talking, it indicates the presence of other factors, such as pricing structure, additional services, peak hours, bundled packages, or promotions, that influence the overall cost. These factors can lead to non-linear cost variations and a lack of direct proportionality between the cost and time spent talking.
If Mark's cost does not vary directly with the time spent talking, it means that there is not a simple proportional relationship between the two variables. In other words, doubling the time spent talking does not necessarily result in doubling the cost. This indicates that there are other factors influencing Mark's cost besides just the time spent talking.
There can be several reasons why Mark's cost does not vary directly with time spent talking:
Pricing structure: Mark's cost may be determined by a pricing structure that includes fixed fees or additional charges based on certain conditions. For example, there might be a base rate for a certain duration of talk time, and any additional time may be billed at a different rate.
Additional services: Mark's cost might include additional services or features that are not solely dependent on talk time. For instance, there could be charges for international calling, call forwarding, or other value-added services.
Peak hours or special rates: Mark's cost might be affected by peak hours or special rates. Some service providers offer different pricing during certain times of the day or specific days of the week. This could result in non-linear cost variations with respect to time spent talking.
Bundled packages: Mark's cost might be part of a bundled package that includes other services like internet or television. In such cases, the overall cost may be influenced by factors other than talk time.
Promotions or discounts: Mark's cost may be subject to promotional offers or discounts that are not directly related to the time spent talking.
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Joel Friedlander es un corredor de la Bolsa de
Valores de Nueva York y tiene curiosidad acerca del tiempo que transcurre entre la colocación de una
orden de venta y su ejecución. Joel hizo un muestreo de 45 órdenes y encontró que el tiempo medio
para la ejecución fue 24.3 minutos, con una desviación estándar de 3.2 minutos. Ayude a Joel con la
construcción de un intervalo de confianza del 95% para el tiempo medio para la ejecución de una
orden
We are 95% confident that the true mean time for the execution of an order is between 23.36 and 25.24 minutes.
How to explain the confidence intervalconfidence interval = mean ± 1.96 * standard deviation / ✓(sample size)
In this case, the mean is 24.3 minutes, the standard deviation is 3.2 minutes, and the sample size is 45. Plugging these values into the formula, we get the following confidence interval:
confidence interval = 24.3 ± 1.96 * 3.2 / ✓(45)
= 24.3 ± 0.94
= (23.36, 25.24)
This means that we are 95% confident that the true mean time for the execution of an order is between 23.36 and 25.24 minutes.
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Joel Friedlander is a stockbroker from New York Securities and you are curious about the time that elapses between the placement of a
sales order and its execution. Joel sampled 45 orders and found that the mean time for execution it was 24.3 minutes, with a standard deviation of 3.2 minutes. Help Joel with the construction of a 95% confidence interval for the mean time for the execution of an order
You just completed your math course and you want to calculate your overall grade. You
know that tests are weighted 15%, quizzes 10%. projects 35%, participation 35%, and the
final exam 5%. What is your overall grade if you scored the following in each category?
Your overall grade, if the percentage scored in the categories are given, is 86. 35.
How to find the overall grade ?To calculate your overall grade, you'll need to multiply each individual grade by its respective weight and then add all these products together.
Tests:
= 85 % * 15%
= 12. 75
Quizzes:
= 90% * 10%
= 9. 0
Projects:
= 92% * 35%
= 32 .2
Participation:
= 80% * 35%
= 28. 0
Final Exam:
= 88% * 5%
= 4. 4
The overall grade is:
= 12.75 + 9.0 + 32.2 + 28.0 + 4.4
= 86. 35
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The scores are :
Tests: 85%
Quizzes: 90%
Projects: 92%
Participation: 80%
Final Exam: 88%
QUESTION 9 1 POINT
Ron will be finishing his payments on his 8-year, $35,000 student loan and wants to know the amount of interest that he
paid over the course of the loan. The student loan has a 3.8% fixed interest rate that is compounded monthly. Calculate the
total amount of interest Ron paid, rounding to the nearest cent.
Provide your answer below:
FEEDBACK
The total amount of interest Ron paid over the course of the loan is approximately $12,220.63.
To calculate the total amount of interest paid on Ron's student loan, we need to use the formula for compound interest. The formula for compound interest is:
A = P(1 + r/n)^(nt) - P
Where:
A is the total amount including principal and interest.
P is the principal amount (loan amount).
r is the annual interest rate (as a decimal).
n is the number of times the interest is compounded per year.
t is the number of years.
In this case, Ron's loan amount is $35,000, the annual interest rate is 3.8% (or 0.038 as a decimal), the loan term is 8 years, and the interest is compounded monthly (n = 12).
Plugging in these values into the formula:
A = $35,000(1 + 0.038/12)^(12*8) - $35,000
Calculating the exponent:
A = $35,000(1 + 0.00316667)^(96) - $35,000
Using a calculator to evaluate the expression within parentheses:
A = $35,000(1.00316667)^(96) - $35,000
Calculating the exponent:
A = $35,000(1.34898777) - $35,000
Subtracting the principal amount:
A = $47,220.63 - $35,000
A = $12,220.63
Therefore, the total amount of interest Ron paid over the course of the loan is approximately $12,220.63.
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solve for x showing all steps 12^x+1=79
Answer:
To solve the equation 12^(x + 1) = 79 for x, we need to isolate the exponent.
Step 1: Subtract 1 from both sides of the equation:
12^(x + 1) - 1 = 79 - 1
12^(x + 1) - 1 = 78
Step 2: Rewrite 12^(x + 1) as (12^x)(12^1) using the exponent property:
(12^x)(12) - 1 = 78
Step 3: Simplify the left side of the equation:
12(12^x) - 1 = 78
Step 4: Add 1 to both sides of the equation:
12(12^x) = 78 + 1
12(12^x) = 79
Step 5: Divide both sides of the equation by 12:
(12(12^x))/12 = 79/12
12^x = 79/12
Step 6: Take the logarithm (base 12) of both sides of the equation:
log12(12^x) = log12(79/12)
x = log12(79/12)
Therefore, the solution for x is x = log12(79/12)
Hope this helps!
The point P (x, y) is moving along the curve y = x² -10/3 x^3/2+ 5x in such a way that the rate of change of y is constant.
Find the values of x at the points at which the rate of change of x is equal to half the rate of change of y.
Answer:
To find the points where the rate of change of x is half the rate of change of y, we need to solve the equations:
dy/dx = k
dy/dt = k
where k is a constant representing the rate of change.
Step-by-step explanation:
Jules Girard bought 1 gallon of paint at a 33% markdown. Its regular price is $39.99.
Markdowns are usually applied before any additional discounts or promotions. In this case, the markdown reduced the regular price by 33%, resulting in the final price of $26.80.
Jules Girard bought 1 gallon of paint at a 33% markdown from its regular price of $39.99. To calculate the final price after the markdown, we can apply the percentage decrease to the regular price.
The markdown of 33% means that the price is reduced by 33% of the regular price. To calculate the amount of the markdown, we can multiply the regular price by the percentage decrease:
Markdown amount = 33% of $39.99 = 0.33 * $39.99
Next, we can subtract the markdown amount from the regular price to find the final price:
Final price = Regular price - Markdown amount = $39.99 - (0.33 * $39.99)
Calculating the expression within parentheses:
Final price = $39.99 - $13.19
Final price = $26.80
Therefore, Jules Girard bought 1 gallon of paint at a 33% markdown, resulting in a final price of $26.80.
Markdowns are usually applied before any additional discounts or promotions. In this case, the markdown reduced the regular price by 33%, resulting in the final price of $26.80.
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Given: Quadrilateral DEFG is inscribed in circle P.
Prove: m∠D+m∠F=180∘
It is given that quadrilateral DEFG is inscribed in circle P. Because a circle measures 360°, mEFG + mGDE =360∘. By the Response area, 12mEF + 12mGDE =180∘. By the inscribed angles theorem, Response area = 12mGDE and Response area = 12mEFG This means m∠D+m∠F=180∘ by the
The solution to the gaps in the angle proof are:
Multiplication Property of equality
m∠D = ¹/₂ * [arc EFG] and m∠F = ¹/₂ * [arc GDE]
substitution property
How to prove the missing angles?The inscribed angle Theorem states that the inscribed angle measures half of the arc of which it is composed.
Thus, we can say that:
m∠D = ¹/₂ * [arc EFG]
and
m∠F = ¹/₂ * [arc GDE]
Therefore:
arc EFG + arc GDE = 360°-------> full circle
Applying multiplication property of equality, we have:
¹/₂ * arc EFG + ¹/₂ * arc GDE = 180°
Applying substitution property of equality, we have:
m∠D = ¹/₂ * [arc EFG]
m∠F = ¹/₂ * [arc GDE]
¹/₂ * arc EFG + ¹/₂ * arc GDE = 180° ----> m∠D + m∠F = 180°
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The function B is defined any positive whole number N as being the product BN=(N-1)(N-2)(N-3) what is the sum of B1,B2,B3 and B4?
The calculated sum of B1,B2,B3 and B4 is 6
How to determine the sum of B1,B2,B3 and B4?From the question, we have the following parameters that can be used in our computation:
BN=(N-1)(N-2)(N-3)
Express properly
So, we have
B(N) = (N-1)(N-2)(N-3)
using the above as a guide, we have the following equations
B(1) = (1-1)(1-2)(1-3) = 0
B(2) = (2-1)(2-2)(2-3) = 0
B(3) = (3-1)(3-2)(3-3) = 0
B(4) = (4-1)(4-2)(4-3) = 6
When the above functions are added, we have
Sum = 0 + 0 + 0 + 6
Evaluate the sum
Sum = 6
Hence, the sum of B1,B2,B3 and B4 is 6
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Which of the following lists the range and IQR for this data?
The range is 12, and the IQR is 5.
The range is 12, and the IQR is 10.
The range is 5, and the IQR is 12.
The range is 5, and the IQR is 10.
Answer: D
Step-by-step explanation:
Indica cuáles de las funciones son afines y=-5 y=1-5x^2 y=-2x^2 y=3x+0,5
Based on the given functions, y = -5 and y = 3x + 0.5 are said to be affine functions. Hence option A and D are correct.
What is the function?An affine function is seen as a function that can be shown as y = mx + b, where m and b are constants.
So looking at the functions given:
y = -5
This function is one that has a constant function with a slope of 0. It can be shown as y = 0x - 5, thus is affine.y = 1 - 5x²
This function is seen as a quadratic function with a squared term. so it is not an affine.y = -2x²
This is the same with the upper function as it is a quadratic function with a squared term, so it is not an affine.y = 3x + 0.5
This function is a linear function with a slope of 3 as well as a y-intercept of 0.5. It can be shown as y = 3x + 0.5, thus, this function is affine.Learn more about functions from
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ASAP!!! Please help me solve
Answer: j(x) = (x-1)(x+2)
The x-1 part is because of the root x = 1
The root x = -2 leads to the factor x+2
[tex]24\ \textgreater \ 6x-3[/tex]
Answer:
x < 4.5
Step-by-step explanation:
To solve the inequality 24 > 6x - 3, we can follow these steps:
Start by adding 3 to both sides of the inequality to isolate the term with the variable:
24 + 3 > 6x - 3 + 3
This simplifies to:
27 > 6x
Divide both sides of the inequality by 6 to solve for x:
27/6 > 6x/6
Simplifying further:
4.5 > x
Therefore, the solution to the inequality 24 > 6x - 3 is x < 4.5.
Hope this helps!
The solution to the inequality is :
↬ [tex]\bf{x < \dfrac{9}{2}}[/tex]
Solution:
Let's solve [tex]\bf24\:\textgreater\:6x-3}[/tex].
First, add 3 to each side:
[tex]\sf{24+3\:\textgreater \:6x}[/tex]
[tex]\sf{27 > 6x}[/tex]
Divide each side by 6
[tex]\sf{27/6 > x}[/tex]
[tex]\sf{x < 27/6}[/tex]
[tex]\sf{x < 9/2}[/tex]
Hence, x < 9/2Match each drawing on the left with its geometric notation on the right. Some of the answer choices on the right may not be used.
Answer:
Please attach a photo to this so I can better answer your question
7. Find the trig function
Find sin 0 if cos 0= 15/17
Sin 0 is approximately 0.4709.
To find sin 0 given that cos 0 = 15/17, we can use the Pythagorean identity:
[tex]sin^2 0 + cos^2 0 = 1[/tex]
Rearranging the equation, we have:
[tex]sin^2 0 = 1 - cos^2 0[/tex]
Since we know that cos 0 = 15/17, we can substitute this value into the equation:
[tex]sin^2 0 = 1 - (15/17)^2[/tex]
Calculating this, we find:
[tex]sin^2 0 = 1 - (225/289)\\sin^2 0 = (289/289) - (225/289)\\sin^2 0 = 64/289[/tex]
Taking the square root of both sides, we get:
sin 0 = √(64/289)
Now, we need to determine the sign of sin 0. Since cos 0 is positive (15/17), sin 0 will also be positive in the first and second quadrants.
sin 0 = √(64/289)
sin 0 ≈ √0.2213
sin 0 ≈ 0.4709 (rounded to four decimal places)
Therefore, sin 0 is approximately 0.4709.
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WHAT IS THE CORRELATION R FOR THE DATA SET
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The correlation coefficient (r) is -0.96.
Given the data:
x: 0, 1, 2, 2, 3, 4, 5, 5, 6
y: 12, 9.5, 9, 8.5, 8.5, 6, 5, 5, 3.5
Step 1: Calculate the mean (average) of x and y.
Mean of x = (0 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 6) / 9 = 3
Mean of y = (12 + 9.5 + 9 + 8.5 + 8.5 + 6 + 5 + 5 + 3.5) / 9 = 7
Step 2: Calculate the deviations from the mean for x and y.
Deviation of x (dx) = x - X
Deviation of y (dy) = y - Y
x: -3, -2, -1, -1, 0, 1, 2, 2, 3
y: 5, 2.5, 2, 1.5, 1.5, -1, -2, -2, -3.5
Step 3: Calculate the product of the deviations of x and y.
(dx * dy): -15, -5, -2, -1.5, 0, -1, -4, -4, -10.5
Step 4: Calculate the sum of the products of the deviations (Σ(dx * dy)).
Σ(dx * dy) = -15 - 5 - 2 - 1.5 + 0 - 1 - 4 - 4 - 10.5 = -43
Step 5: Calculate the standard deviations of x (σx) and y (σy).
Standard deviation of x (σx) = √(Σ(dx²) / (n-1))
Standard deviation of y (σy) = √(Σ(dy²) / (n-1))
Calculating dx²:
dx^2: 9, 4, 1, 1, 0, 1, 4, 4, 9
Σ(dx²) = 33
Calculating dy²:
dy²: 25, 6.25, 4, 2.25, 2.25, 1, 4, 4, 12.25
Σ(dy²) = 61
Calculating the standard deviations:
σx = √(33 / (9-1)) = √(33 / 8) ≈ 1.84
σy = √(61 / (9-1)) = √(61 / 8) ≈ 2.70
Step 6: Calculate the correlation coefficient (r).
r = Σ(dx dy) / (√(Σ(dx²) Σ(dy²)))
r = -43 / (√(33 61))
r ≈ -43 / (√(2013))
r ≈ -43 / 44.87
r ≈ -0.96
Therefore, the correlation coefficient (r) is approximately -0.96.
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The zeros of this polynomial:
p(x)=(2x^2-9x+7)(x-2)
Step-by-step explanation:
To find the zeros of the polynomial p(x) = (2x^2 - 9x + 7)(x - 2), we set p(x) equal to zero and solve for x:
(2x^2 - 9x + 7)(x - 2) = 0
This equation will be satisfied if either of the factors on the left side equals zero. So we set each factor equal to zero and solve for x separately.
Setting 2x^2 - 9x + 7 = 0:
Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 2, b = -9, and c = 7.
Plugging these values into the quadratic formula, we have:
x = (-(-9) ± √((-9)^2 - 4 * 2 * 7)) / (2 * 2)
x = (9 ± √(81 - 56)) / 4
x = (9 ± √25) / 4
x = (9 ± 5) / 4
So we have two solutions:
x1 = (9 + 5) / 4 = 14 / 4 = 3.5
x2 = (9 - 5) / 4 = 4 / 4 = 1
Setting x - 2 = 0:
x = 2
Therefore, the zeros of the polynomial p(x) = (2x^2 - 9x + 7)(x - 2) are x = 3.5, 1, and 2.