You have the derivative of a product:
first limit (7x+3)
second limit (4-3x)
The Rule for the derivative of a product is:
(first limit × derivative of second limit) + (second limit × derivative of first limit)
f(x) = (7x+3)(4-3x)
f'(x)=(7x+3)×-3 + (4-3x)×7 = -21x- 9 + 28-21x
f'(x) = -42x + 19
which is larger the number of meters in the Milky Way or the number of cells in all humans
Answer:
the number of meters in the milky way
Step-by-step explanation:
becuse the world is infinite
Describe the end behavior of the graph of the function f(x) equals minus 5 4X -2 for affinity type in the word infinity four minus infinity typing minus infinity -followed by the word infinity. Make sure that you type in the word infinity with a lowercase i
The end behavior of the graph of the function f(x) = -5(4x - 2) as x approaches infinity can be described as follows:
As x approaches infinity (or positive infinity), the value of 4x becomes infinitely large compared to the constant -2. Therefore, we can ignore the constant (-2) and simplify the function as f(x) = -5(4x) = -20x.
Since the coefficient of x is negative (-20), the graph of the function will decrease without bound as x approaches infinity. In other words, the function will approach negative infinity (or -∞) as x becomes infinitely large.
Similarly, as x approaches negative infinity, the value of 4x becomes infinitely large in the negative direction. Thus, we can simplify the function as f(x) = -5(4x) = -20x.
Since the coefficient of x is negative (-20), the graph of the function will also decrease without bound as x approaches negative infinity. Therefore, the function will approach negative infinity (or -∞) as x becomes infinitely negative.
Heather has a bag with 8 balls numbered 1 through 8. She is playing a game of chance.
This game is this: Heather chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected,$8 if the number 5 is selected, and $10 if the number 6 is selected. She loses $13 if 7 or 8 is selected.(a) Find the expected value of playing the game.
(b) What can Heather expect in the long run, after playing the game many times?
(She replaces the ball in the bag each time.)
Heather can expect to gain money.
Heather can expect to lose money.
Heather can expect to break even (neither gain nor lose money).
(a) The expected value of playing the game is 0.
(b) Heather can expect to break even in the long run.
To find the expected value of playing the game, we need to calculate the weighted average of the possible outcomes.
Expected value calculation:
The probability of selecting each ball is the same since Heather replaces the ball in the bag each time.
The probability of selecting any particular number is 1/8.
Expected value = (Probability of outcome 1 × Value of outcome 1) + (Probability of outcome 2 × Value of outcome 2) + ... + (Probability of outcome 8 × Value of outcome 8)
Expected value = (1/8 × 1) + (1/8 × 2) + (1/8 × 5) + (1/8 × 6) + (1/8 × 8) + (1/8 × 10) + (1/8 × (-13)) + (1/8 × (-13))
Expected value = (1/8) + (2/8) + (5/8) + (6/8) + (8/8) + (10/8) + (-13/8) + (-13/8)
Expected value = 26/8 - 26/8
Expected value = 0
Since the expected value of playing the game is 0 On average, she neither gains nor loses money over multiple plays of the game.
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Hi! I usually wouldn't ask for homework help but I have been stuck on this section for quite a few hours now and I'm really unsure as to how I should answer it. Thank you! :)
Answer:
1) 5/6
2) 19/30
3) They are mutually exclusive.
Step-by-step explanation:
Let's break the diagram down.
We have four types of smoothies:
Contains apple but not blueberry - 12
Contains blueberry but not apple - 7
Contains both blueberry and apple - 3
Doesn't contain either - 8
From here, we find that there are 30 smoothies in total.
In addition, we know that the number of smoothies containing an apple is 15, and the number of smoothies containing blueberry is 10.
Therefore,
[tex]P(\text{contains apple}) = \frac{\text{contains apple}}{\text{total}} = \frac{15}{30} = \frac12\\\\P(\text{contains blueberry}) = \frac{\text{contains blueberry}}{\text{total}} = \frac{10}{30} = \frac13\\\\\text{a) } P(\text{contains apple}) + P(\text{contains blueberry}) = \frac12 + \frac13 = \frac36 + \frac26 = \frac56[/tex]
Now, the probability of getting apple OR strawberry is given by adding the probabilities of getting one of the flavors but not the other.
[tex]P(\text{apple, no blueberry}) = \frac{12}{30}\\\\P(\text{blueberry, no apple}) = \frac{7}{30}\\\\P(\text{apple or blueberry}) = \frac{12}{30} + \frac7{30} = \frac{19}{30}[/tex]
We can check if the events are mutually exclusive using the formula:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In our case, A means contains apple, and B means contains blueberry.
[tex]P(A \cup B)[/tex] resembles the case for exclusively apple or exclusively blueberry (AKA our answer for b).
[tex]P(A \cap B)[/tex] resembles the case for both apple and blueberry (AKA the intersection), which is equal to 3/30 = 1/10.
If the two sides are equal, the cases are not mutually exclusive.
[tex]\frac{19}{30} = \frac{15}{30} + \frac{10}{30} - \frac{3}{30}\\\\\frac{19}{30} \ne \frac{22}{30}[/tex]
Therefore, the events are mutually exclusive.
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 10 kg, the acceleration of the object is 4m/s^2 . If the same force acts upon another object whose mass is 8kg , what is this object's acceleration?
owing equations, determine whether y is a function of x . x+4y=8
Answer:
Step-by-step explanation:
To determine whether y is a function of x in the equation x+4y=8, we can solve for y in terms of x:
x + 4y = 8
4y = 8 - x
y = (8 - x)/4
Copy
Since every value of x corresponds to exactly one value of y, y is a function of x.
Find the inverse function Y = x² for x>0
Answer:
y= √x--------------
Given function:
y = x²In order to find its inverse, first swap x and y:
y = x² ⇒ x = y²Then solve for y:
y² = xy = √xThe inverse function is y= √x.
Determine: minimum, maximum, median, 1st quartile, and 3rd quartile
10,12,7,9,4,15,20,21
Minimum: _____
Maximum:_____
Median:_______
1st Quartile:____
3rd quartile:____
The minimum is the smallest value in the data set:
Minimum: 4
The maximum is the largest value in the data set:
Maximum: 21
The median is the middle value in the data set. Since there are an even number of values in this data set, we take the average of the two middle values:
Median: (10 + 12)/2 = 11
To find the quartiles, we first need to find the median of the lower half and upper half of the data set:
Lower half: 4, 7, 9, 10
Upper half: 12, 15, 20, 21
Median of lower half: (7 + 9)/2 = 8
Median of upper half: (15 + 20)/2 = 17.5
The first quartile (Q1) is the median of the lower half of the data set:
1st Quartile: 8
The third quartile (Q3) is the median of the upper half of the data set:
3rd Quartile: 17.5
Therefore: Minimum: 4 Maximum: 21 Median: 11 1st Quartile: 8 3rd Quartile: 17.5
I hope this helps! Let me know if you have any other questions.
you are riding your bike and notice the square sign above. You mentally draw a straight line from point A to C. Describe the angle relationship between DCA and BCA?
The angle relationship between DCA and BCA is that they are congruent.
What is an angle bisector?In Mathematics and Geometry, an angle bisector is a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
Generally speaking, the diagonals of a rhombus are angle bisectors. In this context, we can logically deduce that the two (2) angles that would result from the bisection of angle C by a straight line are congruent.
By applying the angle bisector theorem to the given square sign (rhombus ABCD) below, we would have the following congruent angles;
∠DCA ≅ ∠BCA
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Solve for x
:
Sophie recently ran a marathon. It took her 5.2 hours to run the 26.2 miles required to complete a marathon.
Find her average speed in miles per hour. Then convert her speed to feet per second. (Hint: 1 mile = 5,280 feet).
(Round your answers to two decimal places)
4x+c=7d
The average speed of Sophie in miles per hour is 5.04 miles per hour.
The speed in feet per second is 7.39 feet per second.
Given that,
Sophie recently ran a marathon.
It took her 5.2 hours to run the 26.2 miles required to complete a marathon.
Total distance ran = 26.2 miles
Total time taken = 5.2 hours
Speed = Total distance / Total time
= 26.2 / 5.2
= 5.04 miles per hour
Speed in feet per second = (5.04 × 5280 feet) / 3600 seconds
= 7.39 feet per second
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Multiply: −6ab3(a5b2−2a4b−10ab−7).
Answer:
--6a^6b^5+12a^5b^4+60a^2b^4+42ab^3
Step-by-step explanation:
Find the value of x and y in simplified radical form.
x and y have the values 7 and 7√2, respectively.
The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.
We can use this information to determine the values of x and y because the base is specified as being 7.
Let's give the perpendicular side the value of x, and the hypotenuse the value of y.
The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.
Consequently, x = 7.
We can determine that x:y:2x using the ratio of 1:1:2.
When we enter the value of x, we may calculate y:
7:y:√2(7)
Simplifying even more
7:y:7√2
Given that the hypotenuse (y) equals 72, we can write:
y = 7√2
Thus, x and y have the values 7 and 7√2, respectively.
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What is the value of y?
A right triangle has a vertical leg labeled square root of 2 with its opposite angle labeled 45 degrees. A second right triangle has a leg that is the hypotenuse of the first right triangle. At the top of the leg is a 60 degree angle with opposite side labeled y and at the bottom of the leg is the right angle.
Enter your answer, as an exact value, in the box.
y =
The value of y is 2 * √3.
In the second right triangle, we have a 60-degree angle and a leg opposite to that angle labeled y. The hypotenuse of the first right triangle is equal to the leg of the second right triangle.
Let's denote the hypotenuse of the first right triangle as h. From the first right triangle, we know that the vertical leg is equal to the square root of 2.
Using trigonometric ratios, we can relate the sides of a right triangle as follows:
sin(angle) = opposite/hypotenuse
In the first right triangle, the angle is 45 degrees, and the opposite side is the square root of 2. Therefore, we have:
sin(45 degrees) = √2 / h
By rearranging the equation, we can solve for h:
h = √2 / sin(45 degrees)
Using the value of sin(45 degrees) = 1/√2, we can simplify the equation:
h = √2 / (1/√2) = √2 * √2 = 2
Now, we can find the value of y in the second right triangle. Since the hypotenuse of the first right triangle is equal to the leg of the second right triangle, we have:
y = 2 * √3
Therefore, the value of y is 2 * √3.
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In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys and girls in the class.
Answer:
BOYS = 30.
GIRLS = 12.
Step-by-step explanation:
Boys: B
Girls: G
B = (2/5)G
B + G = 42.
(2/5)G + G = 42
2G + 5G = 210
7G = 210
G = 210/7
G = 30.
B = (2/5)G
B = (2/5)(30)
B = 60/5
B = 12.
Answer:
[tex]\Huge \boxed{\bold{\text{12 Boys}}}[/tex]
[tex]\Huge \boxed{\bold{\text{30 Girls}}}[/tex]
Step-by-step explanation:
Let the number of girls be [tex]g[/tex] and the number of boys be [tex]b[/tex].
According to the problem: [tex]b = \frac{2}{5} \times g[/tex]
We also know that the total number of students is 42, so [tex]b + g = 42[/tex].
Now, we have two equations with two variables:
[tex]b = \frac{2}{5} \times g[/tex] [tex]b + g = 42[/tex]We can solve these equations to find the values of [tex]b[/tex] and [tex]g[/tex].
Step 1: Solve for [tex]\bold{b}[/tex] in terms of [tex]\bold{g}[/tex]
From the first equation, we have[tex]b = \frac{2}{5} \times g[/tex]
Step 2: Substitute the expression for [tex]\bold{b}[/tex] into the second equation
Replace [tex]b[/tex] in the second equation with the expression we found in step 1.
[tex]\frac{2}{5} \times g + g = 42[/tex]
Step 3: Solve for [tex]\bold{g}[/tex]
Now, we have an equation with only one variable, [tex]g[/tex]:
[tex]\frac{2}{5} \times g + g = 42[/tex]
To solve for [tex]g[/tex], first find a common denominator for the fractions:
[tex]\frac{2}{5} \times g + \frac{5}{5} \times g = 42[/tex]
Combine the fractions:
[tex]\frac{7}{5} \times g = 42[/tex]
Now, multiply both sides of the equation by [tex]\frac{5}{7}[/tex] to isolate [tex]g[/tex]:
[tex]g = 42 \times \frac{5}{7}[/tex][tex]g = 30[/tex]Step 4: Find the value of [tex]\bold{b}[/tex]
Now that we have the value of [tex]g[/tex], we can find the value of [tex]b[/tex] using the first equation:
[tex]b = \frac{2}{5} \times g[/tex][tex]b = \frac{2}{5} \times 30[/tex][tex]b = 12[/tex]So, there are 12 boys and 30 girls in the class.
----------------------------------------------------------------------------------------------------------
5.2. The entrance fee for adults was R50 each and that for children was R20. If the school raised
R31 400 in total, write an equation in x to determine how many adults and how many children
attended the performance. Then solve the equation and write down the number of adults and
(4)
children attended the performance.
Answer:
Let's assume the number of adults attending the performance is represented by 'x', and the number of children attending is represented by 'y'.
According to the given information, the entrance fee for adults is R50 each, and for children is R20 each.
The total amount raised by the school is R31,400. We can write an equation based on the total amount raised:
50x + 20y = 31,400
This equation represents the total value of the entrance fees paid by adults and children.
To solve this equation, we need another equation to relate the variables 'x' and 'y'.
Since we don't have any other information about the number of adults or children, we cannot determine their relationship based on the given information. Therefore, we cannot find a unique solution for 'x' and 'y' unless there is additional information provided.
If there is additional information or if you have any specific values for 'x' or 'y', I can assist you in solving the equation and finding the number of adults and children attending the performance.
Step-by-step explanation:
The graph shows the number of weeks of practice () and the number of
shote missed in a free throw drill (). The equation of the trend line that best
fits the data is y- +6. Predict the number of missed shots after 8
weeks of practice.
A.3
B.2
C.4
D.5
Answer:
B. 2
Step-by-step explanation:
You want the predicted number of missed shots after 8 weeks if the trend line equation is ...
y = -1/2x +6
PredictionUsing x=8 in the given equation, we find the prediction to be ...
y = -1/2(8) +6 = -4 +6 = 2
The number of missed shots is predicted to be 2.
__
Additional comment
We can see that the trend line (red) goes through the point (8, 2). That tells you the prediction is 2 missed shots at 8 weeks of practice.
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Byror has 2 part-time jobs. His first job pays $70 per week before a 10%
deduction for taxes. Byron's other job pays $60 per week, but there is only a 5%
deduction for taxes. What is the total amount Byron takes home each week after
the deductions for taxes?
Answer:
$120
Step-by-step explanation:
Job1:
To find the tax, multiply the payment per week ($70) by 0.1.
Tax = payment * tax rate
= 70 * 10%
[tex]\sf = 70 * \dfrac{10}{100}\\\\ = \$7[/tex]
Now, to find his earning after deduction of tax, subtract 7 from 70.
Amount after deduction of tax = 70 - 7
= $ 63
Job2:
Tax = 60 * 5%
= 60 * 0.05
= $3
Amount after deduction = 60 - 3
= $ 57
Total amount Byron takes home = 63 + 57
= $120
solve the following system of equations (3x-5Y = -22) (4x +2y = 14)
The solution of the System of equation are,
⇒ x = 1
⇒ y = 5
We have to given that;
System of equation are,
⇒ 3x - 5y = - 22
⇒ 4x + 2y = 14
Now, We can simplify as;
From (ii);
2x + y = 7
y = 7 - 2x
Put above value in (i);
3x - 5 (7 - 2x) = - 22
3x - 35 + 10x = - 22
13x = - 22 + 35
13x = 13
x = 1
From (i);
⇒ 3x - 5y = - 22
⇒ 3 - 5y = - 22
⇒ 3 + 22 = 5y
⇒ 25 = 5y
⇒ y = 5
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Which expression is equivalent to 3(–2x – 1)?
*
Answer:
–6x – 3
Step-by-step explanation:
To find the expression that is equivalent to 3(–2x – 1), we need to distribute the 3 to each term inside the parentheses.
When we distribute 3 to –2x, we get:
3 * –2x = –6x
When we distribute 3 to –1, we get:
3 * –1 = –3
Therefore, the expression equivalent to 3(–2x – 1) is:
–6x – 3.
Answer:
-6x - 3
Step-by-step explanation:
Distribute 3 through the parenthesis:
[tex]\sf{3(-2x-1)}[/tex]
[tex]\sf{3*(-2x)+3*(-1)}[/tex]
[tex]\sf{-6x-3}[/tex]
Hence, the expression that is equivalent to 3(-2x - 1) is -6x - 3.
Which of the following statements is true?
The measure of arc XYL + measure of arc VUL + measure of arc VIX = 360°. Therefore, the correct answer is option D.
The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference.
From the given circle, measure of arc XYL + measure of arc VUL + measure of arc VIX = 360° (Complete angle)
Therefore, the correct answer is option D.
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From 1980 to 2008, the number of federally insured banks could be approximated by B(t)=-328.2t+13716 where t is the year and t=0 corresponds to 1980.
How many federally insured banks were there in 1985?
Find the slope of the graph of B.
Interpret this slope as a rate of change. Choose the correct answer below.
The number of banks increased by 13716 banks per year
The number of banks decreased by 12075 banks per year
The number of banks increased by 328.2 banks per year
The number of banks increased by 12075 banks per year
The number of banks decreased by 328.2 banks per year
The number of banks decreased by 13716 banks per year
Find the y-intercept of the graph of B.
The y-intercept is
Interpret the y-intercept. Choose the correct answer below.
The y-intercept is the number of banks in 1985
The y-intercept is the maximum number of banks allowed in the country
The y-intercept is the minimum number of banks allowed in the country
The y-intercept is the number of banks in 2008
The y-intercept is the number of banks in 1980
Answer:
To find the number of federally insured banks in 1985, we need to substitute t = 1985 into the equation B(t) = -328.2t + 13716:
B(1985) = -328.2 * 1985 + 13716
B(1985) = -648537 + 13716
B(1985) = 7122
So, there were approximately 7122 federally insured banks in 1985.
The slope of the graph of B represents the rate of change. From the equation B(t) = -328.2t + 13716, we can see that the slope is -328.2. Therefore, the interpretation of the slope as a rate of change is: "The number of banks decreased by 328.2 banks per year."
The y-intercept of the graph of B represents the value of B when t = 0, which corresponds to the year 1980. From the equation B(t) = -328.2t + 13716, the y-intercept is 13716. Therefore, the interpretation of the y-intercept is: "The y-intercept is the number of banks in 1980."
Evaluate the following.
Click on "Not a real number" if applicable.
Finding the nth roots of perfect nth powers with signs.
The nth roots of perfect nth powers evaluates to:
[tex]\sqrt[5]{-32}[/tex] = -2
[tex]-\sqrt[4]{256}[/tex] = -4
How to Find the nth roots of perfect nth powers with signs?
Perfect nth Power is an integer which is obtained from multiplying a single integer by itself n times.
The nth root of a Perfect nth Power is an integer which when multiplied by itself n times it will produce the original value under the radical.
To find the nth roots of perfect nth powers with signs, you can use the following steps:
1. Write the perfect nth power as a product of nth roots.
2. Find the nth root of each factor.
3. Combine the nth roots to get the final answer.
[tex]\sqrt[5]{-32}[/tex] = [tex]\sqrt[5]{-2^{5} }[/tex]
= -2
-[tex]\sqrt[4]{256}[/tex] = -[tex]\sqrt[4]{4^{4} }[/tex]
= -4
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7. De una caja que contiene 8 canicas verdes, 5 amarillas y 3 blancas se extrae una al azar. Determina la
probabilidad de que sea:
a) Verde
b) Amarilla c) Blanca
d) No amarilla e) Verde o blanca
answer:
a) 8
_ or 50%
16
b) 8 or 50%
_
16
c) 11 or 68.75%
_
16
A manufacturer has 576 square inches of material available to construct the 6 faces of a carton, which will be in the shape of a rectangular prism. To maximize the volume, the carton will have dimensions such that the length and width are each twice the height.
To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).
What is the dimension required to maximize the volume of the box?Assuming the height of the rectangular prism is h inches.
According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.
The total surface area of the rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the values, we have:
576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)
576 = 8h² + 4h² + 4h²
576 = 16h² + 4h²
576 = 20²
h² = 576/20
h² = 28.8
h = √28.8
h = 5.37
The height of the prism is approximately 5.37 inches.
The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.
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aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
x = 8 and y = -4
Step-by-step explanation:
3x + 4y = 8 (call this equation '1')
x - y = 12 (call this '2')
multiply '2' by 3:
3x - 3y = 36 (call this '3')
subtract '1' from '3':
(3x - 3y = 36) - (3x + 4y = 8)
0x + -7y = 28
-7y = 28
y = -4.
sub that back into '1':
3x + 4y = 8
3x + 4(-4) = 8
3x - 16 = 8
3x = 8 + 16 = 24
x = 8.
sub both y =-4 and x =8 into '2' to check if everything adds up:
x - y = 12
8 - -4 = 8 + 4 = 12
so x = 8 and y = -4
find the surface area of the prism
Answer: 132 cm cubed
Step-by-step explanation:
0.5*3*4*2=12
10*5=50
4*10=40
3*10=30
30+40+50+12=132 cm cubed
classify the polynomial
The classification of the given polynomial is cubic polynomial, the correct option is C.
We are given that;
The equation=3x^3-x^2-x+4
Now,
Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
Degree of 3x^3=3
Degree of x^2=2
Degree of x=1
The heighest degree of the polynomial is three of 3x^3.
Therefore, by the polynomial the answer will be cubic polynomial.
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pls solve and explain
Answer:
[tex]\theta = 60; \theta \approx 83; \theta \approx 277; \theta = 300[/tex]
Note that the approximate value you should calculate properly with the inverse cosine function of your calculator to the number of digits you want.
Step-by-step explanation:
you already have a cosine. You might as well change that sine in a cosine too:
[tex]8(1-cos^2\theta) +6cos\theta-9=0\\8cos^2\theta -6cos\theta+1 =0[/tex]
(note that in the second line I also switched every sign by multiplying by -1 just to have a positive lead coefficient - just a pet peeve of mine. Now replace [tex]x=cos\theta[/tex] and let's solve
[tex]8x^2-6x+1=0\\\frac\Delta4 = 9-8 = 1\\x=\frac {3\pm1}8[/tex]
At this point we're back to the replacement. We have two options
[tex]cos\theta = \frac48 = \frac 12 \implies \theta = 60\°; \theta = 300\°\\cos\theta =\frac 18 \implies \theta \approx 83\°; \theta \approx 277\°[/tex]
Solve the system with elimination
2x + 5y = 13
-4x - 3y = 9
Answer:
x = -6 and y =5
Step-by-step explanation:
2x + 5y = 13 (call this equation '1')
-4x - 3y = 9 (call this '2')
multiply '1' by 2
4x + 10y = 26 (call this '3')
eliminate by adding '2' and '3':
(-4 + 4)x + (-3 + 10)y = 9 + 26
7y = 35
y = 5
sub that into '1':
2x + 5(5) = 13
2x + 25 = 13
2x = 13 - 25 = -12
x = -6
sub both x = -6 and y =5 into '2' to make sure everything adds up:
-4(-6) - 3(5) = 24 - 15 = 9
so x = -6 and y = 5
2.2.3 State one reason why a student would choose to study in a province different from their home province
Answer:
Step-by-step explanation:
There are several reasons why a student would choose to study in a province different from their home province. Some of the reasons include:
To gain a new perspective and experience different cultures.
To take unique classes that are not available in their home province.
To learn history through immersive experiences.
To improve their ability to adapt.
To gain independence.
To gain international experience and a global network.
To immerse themselves in another language.
To compare freshmen’s knowledge of mathematics in two departments of a university, a certain professor in Mathematics got a sample of Education and Nursing students and gave a special examination. A sample of 25 Education students has a mean score of 88.50 with standard deviation of 7.5. A sample of 29 Nursing students have a mean score of 90.25 with a standard deviation of 8.2. Is there a significant difference between the two sample means? Use α = .01 level of significance.
There is no significant difference between the mean scores of Education and Nursing students in mathematics.
Is there a significant difference between the mean scores?Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.
Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.
We will use significance level (α) of 0.01.
Given:
Sample mean for Education students (x₁) = 88.50
Sample mean for Nursing students (x₂) = 90.25
Standard deviation for the Education student sample (s₁) = 7.5
Standard deviation for the Nursing student sample (s₂) = 8.2
Sample size for Education students (n₁) = 25
Sample size for Nursing students (n₂) = 29
The t-test statistic for two independent samples is:
t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))
t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))
t ≈ -0.8187
In this case, df = 24.
The critical value for α = 0.01 and df = 24 is approximately ±2.797.
Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.
Therefore, we fail to reject the null hypothesis.
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