Answer: 1. Multiplying Powers with same Base
For example: x² × x³, 2³ × 2⁵, (-3)² × (-3)⁴
In multiplication of exponents if the bases are same then we need to add the exponents.
Consider the following:
1. 2³ × 2² = (2 × 2 × 2) × (2 × 2) = 23+2
= 2⁵
2. 3⁴ × 3² = (3 × 3 × 3 × 3) × (3 × 3) = 34+2
= 3⁶
3. (-3)³ × (-3)⁴ = [(-3) × (-3) × (-3)] × [(-3) × (-3) × (-3) × (-3)]
= (-3)3+4
= (-3)⁷
4. m⁵ × m³ = (m × m × m × m × m) × (m × m × m)
= m5+3
= m⁸
From the above examples, we can generalize that during multiplication when the bases are same then the exponents are added.
aᵐ × aⁿ = am+n
In other words, if ‘a’ is a non-zero integer or a non-zero rational number and m and n are positive integers, then
aᵐ × aⁿ = am+n
Similarly, (ab
)ᵐ × (ab
)ⁿ = (ab
)m+n
(ab)m×(ab)n=(ab)m+n
Note:
(i) Exponents can be added only when the bases are same.
(ii) Exponents cannot be added if the bases are not same like
m⁵ × n⁷, 2³ × 3⁴
Step-by-step explanation:
Answer:
2^4
Step-by-step explanation:
doing this type of division is like subtracting the powers, 9-5=4, 2^4.
the opposite applies for multiplaction, it's like addition for the powers,
2^9*2^5=2^14.
What is the measure of JG
measure of arc JG = 160 degrees
Step-by-step explanation:Main Concept: Intersecting chords
Chords are line segments with ends points that are both on the edge of the circle. Intersecting chords are a pair of chords on the same circle that intersect.
In an extreme example, the chords may intersect at one of the end points, making the intersecting chords an inscribed angle.
Because Intersecting chords intersect, if the line segments are extended into lines, the lines form two pairs of vertical angles. Vertical angles are congruent. Given one vertical angle pair, they will contain two arcs (in the extreme case, the arc will have a measure of zero).
The measure of each of the vertical angles is the average of the two contained arcs.
This problem
For this problem, FG and HJ are chords of the same circle, and they intersect.
If we call the intersection P, angle GPJ is given with a measure of 100 degrees.
Angle GPJ and Angle FPJ form a vertical angle pair, so they are congruent, because vertical angles are congruent.
The measure of each of the vertical angles is the average of the two contained arcs.
The two arcs that this vertical angle pair contain are the arc JG and arc FH.
The measure of arc FH is given as 40 degrees.
Substitute these known quantities into the equation describing the relationship between one of the vertical angles and the contained arcs.
[tex]m \angle GPJ=\frac{1}{2}(m ~\text{arc}JG + m ~\text{arc}FH)[/tex]
[tex](100^o)=\frac{1}{2}(m ~\text{arc}JG + (40^o))[/tex]
Multiply both sides by 2...
[tex]200^o=m ~\text{arc}JG + 40^o[/tex]
Subtract 40 degrees from both sides...
[tex]160^o=m ~\text{arc}JG[/tex]
On the day their son peter was born, madeline and ben invested $1500 for his education at 6.7% interest, compounded quarterly. today it’s peters birthday. he is 19 years old and wants to go to college
Based on the information provided, Madeline and Ben invested $1500 for their son Peter's education on the day he was born at an interest rate of 6.7% compounded quarterly. Since Peter is now 19 years old and wants to go to college, we can calculate the current value of his education fund.
To do this, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
In this case, we have:
P = $1500
r = 6.7% = 0.067 (as a decimal)
n = 4 (since the interest is compounded quarterly)
t = 19 (since Peter is now 19 years old)
So, the current value of Peter's education fund is:
A = $1500(1 + 0.067/4)^(4*19)
A = $1500(1.01675)^76
A = $1500(2.4826)
A = $3,723.90
Therefore, the current value of Peter's education fund is $3,723.90. This should help Madeline and Ben determine how much more they need to save for Peter's college expenses.
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.
3. a piece of paper is folded into thirds multiple times. the area, a, of the piece in square inches, after n folds, is a = 90•(1/3)n
a. what is the value of a when n=0? what does this mean in the situation?
b. how many folds are needed before the area is less than 1 square inch?
The paper initial area of the paper is 90 square inches and needs to be folded at least 5 times before its area becomes less than 1 square inch.
a. When n=0, the expression for the area of the paper after folding becomes:
a = 90•(1/3)⁰ = 90•1 = 90 square inches
This means that the initial area of the paper before any folding is 90 square inches.
b. To find out how many folds are needed before the area is less than 1 square inch, we can set the expression for the area of the paper after folding to be less than 1 and solve for n:
a = 90•(1/3)ⁿ < 1
(1/3)ⁿ < 1/90
Taking the logarithm of both sides with base 1/3, we get:
n > log(1/90)/log(1/3)
n > 4.8
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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() Jamison works as a server at a local restaurant. He made $42.80 in tips on
Thursday night. He made 2 1/4 times that amount in tips on Friday night. How much
in tips did he earn on Friday?
Therefore, Jamison made $96.30 in tips on Friday night.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.
Here,
Jamison made $42.80 in tips on Thursday night.
To find out how much he made in tips on Friday night, we need to multiply the Thursday amount by 2 1/4, which is the same as multiplying it by 9/4.
$42.80 x 9/4 = $96.30
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 Solve for the value of p
Answer:
p = 38
Step-by-step explanation:
We Know
The 104° angle + (2p) angle must be equal to 180°.
Solve for the value of p.
Let's solve
104° + 2p = 180°
2p = 76°
p = 38
The first steps in writing f(x) = 4x2 48x 10 in vertex form are shown. f(x) = 4(x2 12x) 10 (twelve-halves) squared = 36 what is the function written in vertex form? f(x) = 4(x 6)2 10 f(x) = 4(x 6)2 – 26 f(x) = 4(x 6)2 – 134 f(x) = 4(x 6)2 154
The function in vertex form is f(x) = 4(x - 6)² - 26.
How to write f(x) in vertex form?The function in vertex form is f(x) = 4(x - 6)² - 26.
To get to this form, the first step is to factor out the coefficient of x², which is 4:
f(x) = 4(x² - 12x) + 10
Next, complete the square by adding and subtracting (12/2)² = 36 inside the parenthesis:
f(x) = 4(x² - 12x + 36 - 36) + 10
Simplify the expression inside the parenthesis and combine like terms:
f(x) = 4((x - 6)² - 36) + 10
f(x) = 4(x - 6)² - 134
Therefore, the function in vertex form is f(x) = 4(x - 6)² - 26.
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Translate the following statement into a mathematical equation:
Five times a number, minus three, is twelve.
Its translation is 5×3-3=12
Let f(t) be the outside temperature (°F) 7 hours after 2 A.M. Explain the meaning of f(4) < f(11) .
The term f(4) < f(11) means that the temperature is lower at 4 A.M. than it is at 11 A.M., and this inequality can be used to make predictions about temperature changes over time.
The function f(t) represents the temperature at a specific time t. In this case, f(t) is the outside temperature (in degrees Fahrenheit) 7 hours after 2 A.M. So, we can think of f(4) as the temperature 4 hours after 2 A.M. and f(11) as the temperature 11 hours after 2 A.M.
Now, the inequality f(4) < f(11) means that the temperature 4 hours after 2 A.M. is less than the temperature 11 hours after 2 A.M. In other words, the temperature is lower at 4 A.M. than it is at 11 A.M. This might seem obvious, as we generally expect temperatures to rise as the day progresses and the sun comes up. However, this inequality is useful for making more specific predictions about temperature changes.
For example, if we know that f(4) < f(11), we can predict that the temperature will increase between 4 A.M. and 11 A.M. This might be important information if you're planning outdoor activities or need to dress appropriately for the day's weather.
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1. A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.
(a) Write an equation to represent this situation.
(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?
1 pt for correct answer to part (b), 4 pts for showing steps you took to get the correct answer and showing the formula with variable x that you used in part (a).
Note: correct answer to part (a) has only one variable, the variable x. Need to set up a ratio and cross multiply to solve for x.
X represents how many more consecutive tries she needs to make in a row
to raise her overall average up to 60%
2.
Simplify the expression 3x-12/x^2-15x+44. Show your work.
(NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors. )
3.
1. Write the expression as a simplified rational expression. Show your work.
14x+4
-----------
2 1
----- + -----
3x 2x+1
Thank you for any help
She requires 55 consecutive successful throws to get a success rate of 60%
The number of successful throws she made is 8 out of 50
Now to calculate the percentage we will use the formula
[tex]\frac{8}{50} X 100 = 16[/tex]
According to the problem, she needs to make her success percentage 60% and for that, we need to estimate the number of consecutive successful throws. Hence the new equation will be
[tex]\frac{8+x}{50+x} X 100 = 60[/tex]
[tex]or, \frac{8+x}{50+x} = 0.6[/tex]
This is the equation concerned.
Now,to solve this, we will take the denominator on the other side will give us
[tex]or, 8+x = 0.6(50+x)[/tex]
[tex]or, 8+x = 30+ 0.6x[/tex]
[tex]or, x - 0.6x = 30 -8[/tex]
[tex]or, 0.4x= 22[/tex]
or, x = 55
Hence we see that she requires 55 consecutive successful throws to get a success rate of 60%
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Complete Question
A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.
(a) Write an equation to represent this situation.
(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?
The loudest animal on earth is the blue whale. blue whales can emit sound with an intensity of 106.8 watts/meter2. the equation relates the sound level, , in decibels (db), of a noise with an intensity of i to the smallest sound intensity that can be heard by the human ear, (approximately watts/meter2).based on this information, which value is closest to the sound level, in decibels, of the vocalizations of a blue whale?
The sound level of the vocalizations of a blue whale is approximately 140.28 decibels.
How to find sound level?The question asks us to find the sound level in decibels (db) of the vocalizations of a blue whale, given its sound intensity of 106.8 watts/meter2.
The formula for sound level in decibels is:
L = 10log(i/I0)
Where L is the sound level in decibels, i is the sound intensity in watts/meter2, and I0 is the smallest sound intensity that can be heard by the human ear (approximately 1x10⁻¹² watts/meter2).
Plugging in the given values, we get:
L = 10log(106.8/1x10⁻¹² )
Simplifying this expression, we get:
L = 10log(1.068x10¹⁴)
L = 10(14.028)
L = 140.28
Therefore, the sound level of the vocalizations of a blue whale is approximately 140.28 decibels.
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PLEASE HELP ASAP!! The image is attached 30 points!!
Answer:
366 times
Step-by-step explanation:
The volume of this cone is 3.0144 cubic centimeters. What is the height of this cone? Use ≈ 3.14 and round your answer to the nearest hundredth.
Therefore, the height of the cone is approximately 4.23 centimeters.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object or region. It is the total amount of space enclosed by the boundaries of the object or region. Volume is usually measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). Knowing the volume of an object can be useful for many purposes, such as determining how much material is needed to fill a container or how much space is needed to store a certain quantity of objects.
Here,
The formula for the volume of a cone is given by:
V = (1/3)πr²h
where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cone is 3.0144 cubic centimeters, so we can plug this into the formula:
3.0144 = (1/3)πr²h
Next, we need to find the radius of the cone. Since we are not given the radius directly, we may need to use other information that is not given in the problem. If we assume that the cone is a right circular cone, then we can use the fact that the radius and height are proportional to find the radius:
r/h = 1/3
r = (1/3)h
We can substitute this expression for r into the volume formula:
3.0144 = (1/3)π((1/3)h)²h
Simplifying this equation:
3.0144 = (1/27)πh³
Multiplying both sides by 27/π:
h³ = 84.96
Taking the cube root of both sides:
h = 4.23 (rounded to the nearest hundredth)
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The linear density of a rod of length 9 m is given by p(a) - 3+2017 - measured in kilograms per meter, where is measured in meters from one end of the rod. Find the total mass of the rod. Total mass = kg
The total mass of the rod is 81622.5 kg. To find the total mass of the rod, you need to integrate the linear density function with respect to the length of the rod.
To find the total mass of the rod, we need to integrate the linear density function over the entire length of the rod.
Let's start by finding the linear density function at the end of the rod, which is a = 9:
p(9) = 3 + 2017 = 2020 kg/m
Now we can integrate the linear density function from a = 0 to a = 9 to find the total mass:
m = ∫₀⁹ p(a) da
m = ∫₀⁹ (3 + 2017a) da
m = [3a + 1008.5a²] from 0 to 9
m = (3(9) + 1008.5(9)²) - (3(0) + 1008.5(0)²)
m = 81622.5 kg
Therefore, the total mass of the rod is 81622.5 kg.
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Which function is a parabola?
F(x)=5-x^2
X - 2 -1 -0 0 3
G(x) 3 0 -1 0 3
1. F(x) only
2. G(x) only
3. Both f(x) and g(x)
4.neither
Answer:
1. F(x) only-----------------------
F(x) is in the format of a quadratic function:
y = ax² + bx + c, with a = - 1, b = 0, c = 5Hence it is a parabola.
The table represents a relation with two x-intercepts and two y-intercepts (points with the coordinate of 0).
We know that parabola can have maximum of one y-intercept, hence G(x) is not a parabola.
The matching answer choice is the first one.
Andre owns a condominium with a value of $155,000. He has a stock portfolio worth $8,100. He owes $3,300 on his car, which is valued at $9,100. He has $7,600 in student loans to repay. He has a credit card balance of $4,327. He also has $2,600 in a bank account. Construct a net worth statement to find Andre's net worth.
Using net worth statement, Andre's net worth is $159,573.
How to Construct a net worth statement to find Andre's net worth.Andre's net worth can be calculated by subtracting his total liabilities from his total assets.
Total assets = $155,000 (condominium) + $8,100 (stock portfolio) + $9,100 (car value) + $2,600 (bank account) = $174,800
Total liabilities = $3,300 (car loan) + $7,600 (student loans) + $4,327 (credit card balance) = $15,227
Net worth = Total assets - Total liabilities = $174,800 - $15,227 = $159,573
Therefore, Andre's net worth is $159,573.
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The height in meters of a projectile can be modeled by h = -4. 9t^2 + vt + s where t is the time (in seconds) the
object has been in the air, v is the initial velocity
(in meters per seconds) and s is the initial height (in meters). A
soccer ball is kicked upward from the ground and flies through the air with an initial vertical velocity of 4. 9
meters per second. Approximately, after how many seconds does it land?
The soccer ball will land approximately 1 seconds after it was kicked upward. This is found by setting the height equation to 0 and solving for t using the quadratic formula.
To solve for the time the soccer ball lands, we need to find the time when h = 0. We can use the given equation
h = -4.9t² + vt + s
where v = 4.9 m/s (since it's kicked upward) and s = 0 (since it starts at ground level).
Substituting those values, we get
0 = -4.9t² + 4.9t
Factoring out 4.9t, we get
0 = 4.9t(-t + 1)
So, either t = 0 or -t + 1 = 0
Since time cannot be negative, we discard the second solution and solve for t
-t + 1 = 0
t = 1
Therefore, the soccer ball lands after approximately 1 second.
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Need help on question b- the question is attached in the photo.
The height of the new player is given as follows:
210 cm.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
Considering the frequencies and the height of the new player of x, the sum of the observations is given as follows:
198 x 1 + 199 x 3 + 200 x 2 + 201 x 5 + 202 x 2 + x = 2604 + x.
The total number of players, considering the new player, is given as follows:
1 + 3 + 2 + 5 + 2 + 1 = 14.
The mean is of 201 cm, hence the height of the new player is obtained as follows:
(2604 + x)/14 = 201
2604 + x = 14 x 201
x = 14 x 201 - 2604
x = 210 cm.
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7. AFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph AFIG and AP'I'G' after a rotation of 90° clockwise about the origin.
Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).
Explain about the rotation rules:A rotation is a turn made about a specific axis. Both clockwise and anticlockwise rotations are possible. Whereas the image is really the rotating image, the pre-image is the original item.
From the pre-image point, calculate the image. The listed pre-image point is (x , y). Change the x and y coordinates, then multiply this same previous y coordinate by -1 to get a 90 degree anticlockwise rotation. Use the guidelines mentioned below to calculate each rotation.
Clockwise :
90 degree rotation: (x , y) ----> (y , -x)180 degree rotation: (x , y) ----> (-x , -y)270 degree rotation: (x , y) ----> (-y , x)Given :
F(2, 4), I(5, 4) and G(3, 2)
After 90 degree rotation: (x , y) ----> (y , -x)
F'(4,-2), I'(4,-5) and G'(2,-3).
Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).
Graphs for the both triangles are obtained.
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Correct question:
ΔFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph ΔFIG and ΔF'I'G' after a rotation of 90° clockwise about the origin.
11. A town that uses 68 million BTUs of energy each month is using how many kilowatt-hours of
energy? (1 kWh-3400 BTUS)
Answer:
[tex]20,000 \text{ kWh}[/tex]
Step-by-step explanation:
We can convert 68 million British Thermal Units (BTUs) to kilowatt-hours (kWh) using the given conversion ratio:
[tex]\dfrac{1 \text{ kWh}}{3400 \text{ BTUs}}[/tex]
Multiplying by the ratio:
[tex]68,000,000 \text{ BTUs} \cdot \dfrac{1 \text{ kWh}}{3,400 \text{ BTUs}}[/tex]
↓ canceling the BTU units
[tex]68,000,000\cdot \dfrac{1 \text{ kWh}}{3,400}[/tex]
↓ executing multiplication
[tex]\dfrac{68,000,000}{3,400} \text{ kWh}[/tex]
↓ rewriting as a decimal
[tex]\boxed{20,000 \text{ kWh}}[/tex]
Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 3. 4. Scores on an aptitude test are normally distributed with a mean of 110 and a standard deviation of 6. 8. Boris scored a 55 on the knowledge test and 106 on the aptitude test. Callie scored 67 on the knowledge test and 119 on the aptitude test. (a) Which test did Boris perform better on? Use z-scores to support your answer. (b) Which test did Callie perform better on? Use z-scores to support your answer. (c) Boris also took a logic test. His z-score on that test was -0. 43. Does this change the answer to which test Boris performed better on? Explain your answer using z-scores
(a) Boris performed better on the aptitude test, since its z-score was higher.
(b) Callie performed better on the knowledge test.
(c) The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.
(a) To determine which test Boris performed better on, we need to compare his z-scores for the knowledge test and the aptitude test.
For the knowledge test, his z-score is calculated as:
z = (55 - 60) / 3 = -1.67
For the aptitude test, his z-score is:
z = (106 - 110) / 6.8 = -0.59
Since the z-score for the aptitude test is higher than the z-score for the knowledge test, Boris performed better on the aptitude test.
(b) To determine which test Callie performed better on, we need to compare her z-scores for the knowledge test and the aptitude test.
For the knowledge test, her z-score is:
z = (67 - 60) / 3 = 2.33
For the aptitude test, her z-score is:
z = (119 - 110) / 6.8 = 1.32
Since the z-score for the knowledge test is higher than the z-score for the aptitude test, Callie performed better on the knowledge test.
(c) Boris' z-score on the logic test (-0.43) is unrelated to his performance on the knowledge and aptitude tests, so it does not change the answer to which test he performed better on. The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.
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Triangle ΔABC has side lengths of a = 15, b equals 15 times radical 3 comma and c = 30 inches.
Part A: Determine the measure of angle B period (5 points)
Part B: Show how to use the unit circle to find tan B. (2 points)
Part C: Calculate the area of ΔABC. (3 points)
a) Where the information about triangle ABC is given above, the measure of angle B is 60°
How is this so ?Using the Cos Rules,
(15√3)² = 30² + 15² - 2(15 x 30) cos B
⇒ 657 = 1125 - 900 cosB
⇒ 2 Cos B = 1 Cos B = 1/2
So
B = Cos ⁻¹(1/2)
Hence,
B = 60°
B) Given the above,
Now, we can use the tangent function to find tan B:
tan B = sin B / cos B
= sin (π/3) / cos (π /3)
= (√3 / 2) / 0.5
tan B = √3
C ) the area of the rriangle is given as
s = (a + b + c) /2
Substituting
s = (15 + 15√ 3 + 30)/2
s = 30 + 15√3
Area = √ [ (30 + 15√3)(15√3) (15)(30 - 15 - 15√3))
Simplifying we can say
Area = √(30 + 15√3 )( 15√3)(15)(15 - 5√3 )]
= √[3(10 + 5√3)(15)(3√3 - 1)]
= √[2250 - 1125√3]
Hence,
Area ≈ 17.36in
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Complete the table by finding the balance a when p dollars is invested at rater for t years and compounded n times per year. (round your answer to the nearest cent.)
p = $3000, r = 4%, t = 20 years
1 2 4 12 365 continuous
The balance when $3000 is invested at 4% rate for 20 years and compounded annually, semi-annually, quarterly, monthly, daily, and continuously are $6,372.76, $6,454.81, $6,506.71, $6,535.94, $6,546.49, and $6,549.18 respectively.
How to calculate compound interest?Compounding Frequency Balance after 20 Years
Annually $6,372.76
Semi-annually $6,454.81
Quarterly $6,506.71
Monthly $6,535.94
Daily $6,546.49
Continuous $6,549.18
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the balance after t years, P is the principal (amount invested), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
For p = $3000, r = 4%, t = 20 years, and the different compounding frequencies, we get:
Annually: A = $3000(1 + 0.04/1)^(1*20) = $6,372.76
Semi-annually: A = $3000(1 + 0.04/2)^(2*20) = $6,454.81
Quarterly: A = $3000(1 + 0.04/4)^(4*20) = $6,506.71
Monthly: A = $3000(1 + 0.04/12)^(12*20) = $6,535.94
Daily: A = $3000(1 + 0.04/365)^(365*20) = $6,546.49
Continuous: A = $3000e^(0.0420) = $6,549.18 (where e is the constant 2.71828...)
Therefore, the balance a when $3000 is invested at 4% rate for 20 years and compounded n times per year (where n is the different frequencies given) are as mentioned above.
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What is the equation of the parabola?y = −one eighthx2 + 5 y = one eighthx2 + 5 y = one eighthx2 − 5 y = −one eighthx2 − 5
The equations represent four different parabolas with different shapes and orientations, but all of them have the same axis of symmetry, which is the y-axis (because there is no x term).
What is equation of parabola?The collection of all points in a plane that are equally spaced from a fixed line and another fixed point in the plane that is not on the line is known as a parabola. The focus of the parabola is the fixed point (F) and the fixed point (D) is known as the directrix.
The equation of a parabola in standard form is:
y = a x² + b x + c
where "a" is the coefficient of the quadratic term (x^2), "b" is the coefficient of the linear term (x), and "c" is the constant term.
Looking at the given equations:
y = -1/8 x² + 5, has a negative coefficient for the quadratic term (a = -1/8) and a positive constant term (c = 5).y = 1/8 x² + 5, has a positive coefficient for the quadratic term (a = 1/8) and a positive constant term (c = 5).y = 1/8 x² - 5, has a positive coefficient for the quadratic term (a = 1/8) and a negative constant term (c = -5).y = -1/8 x² - 5, has a negative coefficient for the quadratic term (a = -1/8) and a negative constant term (c = -5).So, the equations represent four different parabolas with different shapes and orientations, but all of them have the same axis of symmetry, which is the y-axis (because there is no x term).
To graph each parabola, you can use the vertex form of the equation:
y = a (x - h)² + k
where (h, k) is the vertex of the parabola.
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In ΔUVW, the measure of ∠W=90°, UV = 4. 7 feet, and WU = 2. 2 feet. Find the measure of ∠U to the nearest degree
The measure of angle U in triangle UVW is approximately 28 degrees. This is found by using the inverse tangent function to solve for angle U given the lengths of two sides and the fact that angle W is a right angle.
To find the measure of ∠U in ΔUVW, we can use trigonometry. We know that sin(∠U) = opposite/hypotenuse, which is equal to UW/VW. Therefore, we can plug in the given values and solve for sin(∠U)
sin(∠U) = UW/VW = 2.2/4.7 = 0.4681
Next, we can use the inverse sine function (sin⁻¹) to find the measure of ∠U
∠U = sin⁻¹(0.4681) = 28.34 degrees (rounded to the nearest degree)
Therefore, the measure of ∠U in ΔUVW is approximately 28 degrees.
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Which equations have the same value of x as 3/5 (30 x minus 15) = 72? Select three options.
A. 18 x - 15 = 72
B. 50 x -25 = 72
C. 18 x - 9 = 72
D. 3 (6 x - 3) = 72
E. x = 4.5
The equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.
Choosing the equations that are equivalentTo solve for x in 3/5 (30 x - 15) = 72, we can first simplify the left side by distributing the 3/5:
3/5 (30 x - 15) = 18 x - 9
Now we can solve for x by setting the right side equal to 72:
18 x - 9 = 72
Adding 9 to both sides:
18 x = 81
Dividing by 18:
x = 4.5
So we know that option E is one of the correct answers.
To check which of the other options have the same value of x, we can substitute x = 4.5 into each equation and see if it simplifies to 72:
A. 18 x - 15 = 72
18(4.5) - 15 = 72
81 - 15 = 72 (not equivalent)
B. 50 x - 25 = 72
50(4.5) - 25 = 200 - 25 = 175 (not equivalent)
C. 18 x - 9 = 72
18(4.5) - 9 = 72 (equivalent)
D. 3 (6 x - 3) = 72
3(6(4.5) - 3) = 3(24) = 72 (equivalent)
Therefore, the equations that have the same value of x as 3/5 (30 x - 15) = 72 are C, D, and E.
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6. ifmxkl=(8x - 6)° and the measure of major arc jml = (25x - 13), solve for the actual
measure of major arc jml. assume that lines which appear tangent are tangent.
k
ј,
l
m
a. 196°
b. 287°
c. 262°
d. 154°
The actual measure of major arc JML is approximately 289.33°, which is closest to 287°.
We know that minor arc KL is supplementary to major arc JML. So,
m∠KL = 180° - m∠JML
Substituting the given values, we get:
8x - 6 = 180 - (25x - 13)
Solving for x, we get:
33x = 193
x = 193/33
Substituting this value of x in the expression for m∠JML, we get:
m∠JML = 25(193/33) - 13
m∠JML = 1468/3
m∠JML ≈ 489.33°
However, since lines KL and JM appear tangent, we know that minor arc KL and major arc JML share the same endpoint and thus are part of the same circle. So, the actual measure of major arc JML is:
m(arc JML) = 360° - m(arc KL)
We can find m(arc KL) by subtracting m∠KLM from 180°:
m(arc KL) = 180° - m∠KLM
m(arc KL) = 180° - (8(193/33) - 6)
m(arc KL) ≈ 70.67°
Substituting in the formula for m(arc JML), we get:
m(arc JML) = 360° - 70.67°
m(arc JML) ≈ 289.33°
Therefore, the actual measure of major arc JML is approximately 289.33°, which is closest to option (b) 287°.
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Kristin made a scatter plot to represent the relationship between the temperature and the number of bottles of water sold at her concession stand at a soccer tournament. Which is a description of the location of the point Kristin will add to represent the 13 bottles of water that were sold when the temperature was 39 degrees Fahrenheit? Select one:
O Top left of the scatter plot
OBottom right of the scatter plot
O Top right of the scatter plot
OBottom left of the scatter plotâ
The location of the point Kristin will add to represent the 13 bottles of water sold at 39 degrees Fahrenheit is the bottom left of the scatter plot.
A scatter plot represents the relationship between two variables. In this case, the temperature (independent variable) is plotted along the x-axis, while the number of bottles of water sold (dependent variable) is plotted along the y-axis. As the temperature increases, it is expected that more bottles of water would be sold.
The bottom left area of the scatter plot is where lower values of both temperature and the number of bottles sold would be found. Since 39 degrees Fahrenheit is relatively low and 13 bottles of water is a lower quantity, the point representing this data will be in the bottom left quadrant of the scatter plot.
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Complete question:
Kristin made a scatter plot to represent the relationship between the temperature and the number of bottles of water sold at her concession stand at a soccer tournament. Which is a description of the location of the point Kristin will add to represent the 13 bottles of water that were sold when the temperature was 39 degrees Fahrenheit? Select one:
O Top left of the scatter plot
O Bottom right of the scatter plot
O Top right of the scatter plot
O Bottom left of the scatter plotâ
The restaurant decides to add another choice for the entrée and another choice for a side on the children’s menu the additional entrée choice is grilled cheese and the additional side choice is mixed vegetables what is the probability that a child with cheese pizza or spaghetti with mixed vegetables for his or her meal?
The sample space for a child choosing one entrée and one side is A) BA, BF, CA, CF, PA, PF, SA, SF.So, the correct answer is A). Probability of a child choosing pizza or spaghetti with mixed vegetables is 2/15 or 0.1333 (rounded to four decimal places) or approximately 13.33%.
The sample space represents choose of one entrée and one side for his or her meal is BA, BF, CA, CF, PA, PF, SA, SF. So, the correct option is A).
After the addition of grilled cheese as an entrée choice and mixed vegetables as a side choice, there are now five entrée choices (B, C, P, S, G) and three side choices (A, F, MV). The total number of possible meal combinations is 5*3 = 15.
The number of meal combinations where the child chooses pizza or spaghetti with mixed vegetables is 2 (pizza with mixed vegetables and spaghetti with mixed vegetables). Therefore, the probability of choosing spaghetti or pizza with mixed vegetables for her or his meal is
P(pizza or spaghetti with mixed vegetables) = 2/15 = 0.1333 (rounded to four decimal places) or approximately 13.33%.
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--The given question is incomplete, the complete question is given
"At a restaurant, a children's meal gives a choice of four entrées: burger (B), chicken (C), pizza (P), or spaghetti (S), and two sides: apple (A) or fries (F).
Part A
Which sample space represents all the ways a child could choose one entrée and one side for his or her meal?
A) BA, BF, CA, CF, PA, PF, SA, SF
B) BA, CA, PA, SA
C) BF, CF, PF, SF
D) B, C, P, S, A, F
Part B
The restaurant decides to add another choice for the entrée and another choice for the side on the children's menu. The additional entrée choice is grilled cheese and the additional side choice is mixed vegetables. What is the probability that a child will choose pizza or spaghetti with mixed vegetables for his or her meal?"--
Part 3
sales tax is 8%
basketballs are 20% off
you have two customers john and david. john has $250 and
david has $150. john is coaching a baseball team and wants
to buy 10 baseball bats for his team. david wants to buy 3
pairs of running shoes for his kids. will each person be able
to buy the items that they want? explain.
baseball bats are 5% off
running shoes are 15% off
i
tax
with
discount
total
cost
john
david
John will be able to buy the 10 baseball bats for his team with some money left over is -$6.50 and David will be able to buy the 3 pairs of running shoes for his kids with some money left over is $12.30.
Based on the given information, we can calculate the total cost for each customer after factoring in the sales tax and discounts.
For John:
The cost of 10 baseball bats without any discounts or tax would be 10 * $25 = $250.
Since baseball bats are 5% off, John will get a discount of 0.05 * $250 = $12.50.
So, the cost of 10 baseball bats after discount is $250 - $12.50 = $237.50.
Adding 8% sales tax to this amount, the total cost for John will be $237.50 + (0.08 * $237.50) = $256.50.
For David:
The cost of 3 pairs of running shoes without any discounts or tax would be 3 * $50 = $150.
Since running shoes are 15% off, David will get a discount of 0.15 * $150 = $22.50.
So, the cost of 3 pairs of running shoes after discount is $150 - $22.50 = $127.50.
Adding 8% sales tax to this amount, the total cost for David will be $127.50 + (0.08 * $127.50) = $137.70.
Therefore, John will be able to buy the 10 baseball bats for his team with some money left over ($250 - $256.50 = -$6.50) and David will be able to buy the 3 pairs of running shoes for his kids with some money left over ($150 - $137.70 = $12.30).
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