Anna's monthly Salary in June was $3600 as she received a 20% rate and her monthly Salary in July was $2880 as she received a 20% pay cut from June.
It is given to us that: Ana's salary in May =3000$
in June she received 20% raise
the amount she received in June after 20% raise = 3000 x 20/100
= 30 x 20 = 600
we have to first find Ana's salary at the end of June month with 20% raise. and then her salary after the end of July month with the pay cut of 20%.
Ana's salary after June month when she got 20% raise in his salary after May:
= 3000 + (20% x 3000)
= 3000 + (20/100 x 3000)
= $3600
her new salary after June will be 3600$.
therefore, she received 3600 in June.
in July she received 20% pay cut.
To find Ana's monthly salary after the two changes in June and July.
Ana's salary after June month when she got 20% raise in his salary after May = $3600
now she got a pay cut of 20% on his new salary from July month,
= 3600 - (20% x 3600)
= 3600 + (20/100 x 3600)
= 3600 - 720
= $2880
so, her salary after that would be equal to $2880.
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I need the awnser for this it’s due in 14 minutes
An equation for the line of best fit is y = 5x.
The y-intercept of the line of best fit is equal to (0, 0).
The size of a store which Feline Delights could expect to sell 20 bags per day is 4,000 square footage.
Feline Delights could expect to sell 20 bags per day in an 11,000 square foot store.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (45 - 30)/(9 - 6)
Slope (m) = 15/3
Slope (m) = 5
At data point (6, 30), a linear equation in slope-intercept form for this line can be calculated as follows:
y - y₁ = m(x - x₁)
y - 30 = 5(x - 6)
y = 5x - 30 + 30
y = 5x
When y = 20, the store size is given by;
20 = 5x
x = 20/5 = 4
In thousands, we have:
x = 4,000 square footage.
When x = 11,000 square footage, the number of bags is given by;
y = 5x
y = 5(11)
y = 55 bags.
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Solve the equation 101 3/5 =k+33 4/5 for k .
Answer: k = 67 4/5
Step-by-step explanation:
101 3/5 =k+33 4/5
first isolate your variable by subtracting 33 4/5 from both sides
101 3/5 - 33 4/5 = k
now subtract
to subtract 4/5 from 3/5, you have to borrow 5/5 or 1 whole from 101 and add it to 3/5. 5/5 + 3/5 = 8/5. 101 - 1 = 100.
so now you have
100 8/5 - 33 4/5 = k
100 - 33 = 67
8/5 - 4/5 = 4/5
your answer is 67 4/5
Check your work.
67 4/5 + 33 4/5 = 100 8/5 simplified to 101 3/5, our starting number.
solution is true so problem solved!
an old refrigerator consumes 202 w of power. assuming that the refrigerator operates for 18 hours every day, what is the annual operating cost of the refrigerator if the cost of electricity is $0.09 per kwh? answer to two decimal places without a unit.
The Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.)
Given:Power consumed by the old refrigerator = 202 WAssuming the refrigerator operates for 18 hours every day.Cost of electricity is $0.09 per kWh.Solution:Power consumed by the old refrigerator in an hour = 202 WTime for which the refrigerator operates every day = 18 hours Energy consumed by the refrigerator in a day = Power consumed × Time = 202 W × 18 hours = 3636 Wh Energy consumed by the refrigerator in a year (365 days) = 3636 Wh × 365 days= 1324740 Wh = 1324.74 kWhCost of electricity is $0.09 per Therefore, Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.).
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What is the explicit form of the geometric sequence given below 27,-18,12,-8,16/3,…
The explicit form of the geometric sequence is an = 27 * (-2/3)^(n-1)
Calculating the explicit form of the geometric sequenceIn a geometric sequence, each term is obtained by multiplying the previous term by a fixed number called the common ratio, denoted by r.
So, if we know the first term and the common ratio, we can find any term in the sequence, including the nth term, using the formula:
an = a1 * r^(n-1)
where a1 is the first term and an is the nth term.
To find the common ratio, we can divide any term by the previous term:
r = -18/27 = -2/3
Now we can use the formula to find the nth term.
an = 27 * (-2/3)^(n-1)
Therefore, the explicit form of the geometric sequence is an = 27 * (-2/3)^(n-1)
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Cose measures her Frisbee and calculates that it has a circumference of 18.84 inches. What
s the Frisbee's radius?
Use 3.14 for . If necessary, round your answer to the nearest hundredth.
inches
As a result, the Frisbee's radius is 3 inches (rounded to the nearest hundredth) .
Set a radius?The distance from a circle's center to any point along its perimeter is known as the radius of a circle. It's typically indicated by "R" or "r" .
Describe circumference?The distance around a circle's periphery is its circumference. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.
C = 2πr, where C is the circumference and r is the radius, is the formula for calculating a circle's circumference.
This formula is rearranged to give us r = C /π 2 .
In this instance, we are aware that the Frisbee's circumference is 18.84 inches.
As a result, the radius can be determined using the formula r = C / 2π:
r = 18.84 / (2 * 3.14)
r = 18.84 / 6.28
r = 3
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5th grade math problem for my sister. Very confused on what it is asking. Assuming it’s 1/4
Answer:
5/8
Step-by-step explanation:
1/4*2 4/8
1/4*2 1/2
1/4*5/2
5/8
use the law of sines to find the missing side of the triangle
Using the law of sine, the missing side of the triangle is approximately 4.01 units.
The law of sines states that for any triangle ABC with sides a, b, and c opposite to angles A, B, and C respectively
a / sin(A) = b/sin(B) = c / sin(C)
Using this law, we can find the missing side b as follows:
b/sin(B) = c/sin(C)
Since angle B and angle C are complementary, we can find angle C as:
C = 180 - A - B = 180 - 58 - 48 = 74 degrees
Now we have
b/sin(48) = 5/sin(74)
Solving for b, we get
b = (5 x sin(48))/sin(74) ≈ 4.01 units
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The given question is incomplete, the complete question is;
use the law of sines to find the missing side of the triangle
Identify the proof to show that △WZY≅△YXW , where WZ⊥ZY , WX⊥XY , ∠ZYW≅∠XWY , WX≅ZY , and WZ≅XY
Answer: To show that △WZY ≅ △YXW, we need to show that they are congruent by proving that all corresponding sides and angles are equal.
Given:
WZ⊥ZY and WX⊥XY, which implies ∠WZY = ∠YXW = 90°
∠ZYW ≅ ∠XWY (given)
WX ≅ ZY and WZ ≅ XY (given)
To prove:
△WZY ≅ △YXW
Proof:
By the given information, ∠WZY = ∠YXW = 90°.
By the given information, ∠ZYW ≅ ∠XWY.
Therefore, ∠WZY + ∠ZYW ≅ ∠YXW + ∠XWY. Combining these angles gives us ∠WZY + ∠ZYW = ∠YXW + ∠XWY.
Since the sum of interior angles in a triangle is 180°, we have:
∠WZY + ∠ZYW + ∠YZW = 180° for △WZY
∠YXW + ∠XWY + ∠YWX = 180° for △YXW
Substituting in the angle congruence (∠ZYW ≅ ∠XWY), we have:
∠WZY + ∠XWY + ∠YZW = 180° for △WZY
∠YXW + ∠ZYW + ∠YWX = 180° for △YXW
By the given information, WX ≅ ZY and WZ ≅ XY.
Therefore, by the Side-Angle-Side (SAS) congruence postulate, △WZY ≅ △YXW.
Hence, we have proved that △WZY ≅ △YXW.
Step-by-step explanation:
The quotient of 20 divide 5 is subtracted from the difference of 16 and 6
Arithmetic operations helps us to determine the value of x for quotient of 20 divide 5 is subtracted from the difference of 16 and 6 is equals to the 6.
In arithmetic, a quotient can be defined as the result of the division of a number by any divisor. It is the number of times the divisor is contained in the dividend a quantity produced by the division of two numbers. The quotient can be determined by dividing the dividend with the divisor. Formula, Quotient = Dividend ÷ Divisor. We have to determine value of x which equals to quotient of 20 divide 5 is subtracted from the difference of 16 and 6. First we have to determine quotient 20 divides 5. Using quotient formula, quotient= 20 ÷ 5 = 4. So, Quotient is 4. Now, the difference of 16 and 6 that is equals to 16 minus 6 = 16 - 6 = 10. Thus, x = 16 - 6 - ( 20÷ 5)
=> x = 10 - 4
=> x = 6
Hence, required value of x is 6.
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Complete question :
The quotient of 20 divide 5 is subtracted from the difference of 16 and 6 equals to x. what is x?
Answer:
x=6
Step-by-step explanation:
20 ÷ 5 = 4. So, Quotient is 4. Now, the difference of 16 and 6 that is equals to 16 minus 6 = 16 - 6 = 10. Thus, x = 16 - 6 - ( 20÷ 5)
=> x = 10 - 4
=> x = 6
Hence, required value of x is 6.
Supreme cookie dough has 25% chocolate chips. Magic cookie dough has 35% chocolate chips. Samantha mixes 4 cups of Supreme cookie dough with 4 cups of Magic cookie dough. Enter the percent of chocolate chips in the mixture.
The percent of chocolate chips in the mixture is a total of 30% as supreme cookie dough has 25% chocolate chips and Magic cookie dough has 35% chocolate chips.
Let one cup be equal to one gram,
therefore, one cup or gram of supreme cookie dough has 25% of chocolate cookie dough
25% of 4 cups = 25/100 x 400
= 100 gm of chocolate cookie dough
35% of chocolate cookie dough in one cup of Magic cookie dough
35% of 4 cups = 35/100 x 400
= 140 gm of chocolate cookie dough
therefore the dough Samantha has prepared has a total of 140 + 100 gm of chocolate cookie dough,
whereas total dough = 4 cups of magic cookie dough + 4 cups of supreme cookie dough = 8 cups
we assumed one cup will be 100 gm, therefore, 8 cups will be 800 gm
let the percentage of the chocolate cookie dough be x:
therefore, x/100 = 240/800
x = 240/800 x 100
x = 30
therefore, the percent of chocolate chips in the mixture is a total of 30%
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Insurance Plan Summary
Deductible
$5,000.00
Wellness Exams
No-deductible
100% covered
Premium (monthly)
Individual
Individual+Spouse
A. $400.00
C. $0
$45.00
$4:0.00
What is the monthly
payment an employee
with a family plan on
this health plan is
required to pay, even
if they do not visit a
doctor or hospital?
B. $5,000.00
D. $45.00
the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.
what is insurance ?
Insurance is a contract between an individual or an entity (the insured) and an insurance company (the insurer), in which the insurer agrees to compensate the insured for financial losses or damages that occur due to unexpected events, in exchange for the payment of premiums by the insured.
Based on the information provided, the employee with a family plan is on the "Individual+Spouse" premium plan, which has a monthly premium of $450.00. This means that regardless of whether or not the employee visits a doctor or hospital, they are required to pay this amount every month to maintain their insurance coverage.
Therefore, the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.
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HELP 34 PONITS
6. Fill in the blanks within the area model for (5d - 12)(3d + 1) and then put a
check next to the answer you'll get after simplifying (combining like terms).
The answer to the simplified expression is option D. 15d^2 - 31d - 12
What is expansion by grid method?Expansion is the process of multiplying a given set of terms in a bracket with other terms in another bracket. It can be done using the grid method of expansion.
Considering the given question to fill the blanks, we have;
3d + 1
5d 15d^2 5d
-12 -36d -12
Thus, adding the terms one to another gives;
15d^2 + 5d - 36d - 12
15d^2 -31d - 12
The correct answer after simplifying the expression is: 15d^2 -31d - 12. Thus option D.
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9) in a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean? a) none of them b) about 27 c) about 100 d) about 127
In a sample of 10,000 observations from a normal population, about 27 would be expected to lie beyond three standard deviations of the mean, therefore, the correct option is b.
For a normal distribution, about 99.7% of the data is expected to lie within three standard deviations of the mean. This is known as the empirical rule or the 68-95-99.7 rule.
Using this rule, we can estimate the number of observations beyond three standard deviations of the mean for a sample of 10,000. Since the distribution is normal, we know that the mean and standard deviation completely describe the distribution.
Assuming the sample is representative of the population, we can use the empirical rule to estimate the number of observations beyond three standard deviations of the mean. Since three standard deviations from the mean cover 99.7% of the data, the remaining 0.3% of the data would be expected to lie beyond three standard deviations.
Therefore, the correct answer is c. about 27, since 0.3% of 10,000 is approximately 27.
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Marcia deer foot purchased a $120000,5-year term life insurance policy when she was 55. Now she is 60, what is the percent increase in the premium
The percent increase in the premium for Marcia's life insurance policy is approximately 17.06%.
How to find percent increase in the premium?To calculate the percent increase in the premium for Marcia's life insurance policy, we can use the following formula:
[tex]$Percent increase = \frac{ (New premium - Initial premium)}{ Initial premium} \times 100[/tex]
First, we need to find the initial premium, which can be calculated using the formula for the present value of a term life insurance policy:
[tex]Initial premium = \frac{Face amount of the policy}{Present value factor}= \frac{120,000}{4.3295} = $27,730.25[/tex]
Assuming the same face amount and an interest rate of 5%, the new premium can be calculated as follows:
[tex]New premium= \frac{\text{Face amount of the policy}}{\text{Present value factor}} \ &= \frac{120,000}{3.6962} \ &= $32,466.72 \end{aligned}[/tex]
Now we can use the formula above to calculate the percent increase in the premium:
[tex]Percent increase= \frac{(\text{New premium} - \text{Initial premium})}{\text{Initial premium}} * 100 \ &= \frac{(32,466.72 - 27,730.25)}{27,730.25} * 100 \ &= 17.06% \end{aligned}[/tex]
Therefore, the percent increase in the premium for Marcia's life insurance policy is approximately 17.06%.
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at midnight the temperature was -8f. at noon, the temperature was 23f. which expression represents the increase in temperature?
A. -8 - 23
B. |-8| - 23
C. -8 - |23|
D. |-8 - 23|
Answer:
D
Step-by-step explanation:
23 - (-8)
23 + 8 = 31°
The temperature rose 31 degrees.
l-8 -23l = l-31l = 31 Absolute value is asking the distance from zero.
Helping in the name of Jesus.
Suppose it takes John 40 minutes to run 4 miles. How long would it take him to run 9 kilometers? Round your answer to the nearest minute
John can run 4 miles in 40 minutes, so running 9 kilometers would take him approximately 56 minutes.
We're given that John can run 4 miles in 40 minutes. To find out how long it would take him to run 9 kilometers, we need to first convert 4 miles to kilometers.
One mile is equal to 1.60934 kilometers, so 4 miles is equal to 6.43736 kilometers (rounded to five decimal places).
Next, we can use the formula for speed:
Speed = Distance / Time
To solve for John's speed, we divide the distance he covered (6.43736 kilometers) by the time it took him to cover that distance (40 minutes):
Speed = 6.43736 km / 40 min ≈ 0.160935 km/min
Now we can use this speed to determine how long it would take John to run 9 kilometers. We can use the same formula as before, but this time we'll be solving for time:
Time = Distance / Speed
Substituting in the values we know:
Time = 9 km / 0.160935 km/min ≈ 55.8627 min
Rounding this answer to the nearest minute, we get:
Time ≈ 56 min
Therefore, it would take John approximately 56 minutes to run 9 kilometers.
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ERROR ANALYSIS Describe and correct the error in identifying the vertex, axis of symmetry, and
intercepts of the graph.
X
V
-2
A AY
6
8
Vertex: (1,
2
·N
xV
-8)
x-intercept: (-1,0) and (3,0)
y-intercept: (0, – 6)
axis of symmetry: y = 1
Corrected analysis of errors : Vertex: (-2, -8), x-intercepts: (-1,0) and (6,0), y-intercept: (0,-8), Axis of symmetry: x = -2
What are the errors?
There are multiple errors in the given analysis which are given below.
1. The x-coordinate of the vertex is incorrectly given as 1 instead of -2.
2. The y-coordinate of the vertex is incorrectly given as 8 instead of -8.
3. The x-coordinate of the axis of symmetry is incorrectly given as 1 instead of -2.
4. The given x-intercepts are incorrect. The correct x-intercepts are (-1,0) and (6,0).
5. The given y-intercept is incorrect. The correct y-intercept is (0,-8).
Corrected analysis:
Vertex: (-2, -8)
x-intercepts: (-1,0) and (6,0)
y-intercept: (0,-8)
Axis of symmetry: x = -2
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Inez is taking a bicycling trip across the United States. Her destination is 3,280 miles away. If Inez travels 80 miles per day, how far does she have left to travel after 25 days of bicycling?
Answer: The distance left after 25 days is 1280 miles
Step-by-step explanation:
To calculate the distance, we use the formula:
[tex]s=\dfrac{d}{t}[/tex]
where,
s = speed of the bicycle = 80 miles/day
t = time taken = 25 days
d = distance travelled = ? miles
Putting values in above equation, we get:
[tex]\text{d}=(80 \ \text{miles}/\text{day} \times 25 \ \text{days})=2000 \ \text{miles}[/tex]
Total distance to the destination = 3280 miles
Distance traveled in 25 days = 2000 miles
Distance left after 25 days = [3280 - 2000] = 1280 miles
Hence, the distance left after 25 days is 1280 miles
how many minute will a car take to travel
The number of days in which Meena would be able to complete the work alone is 24 days.
How to determine the required number of days?In order to determine the number of days in which Meena would be able to complete the work alone, we would have to assign variables to the amount of time taken by Mala, Meena, and Vinay, and then translate the word problem into an algebraic equation as follows;
Let the variable y represent the number of days taken by Mala.Let the variable x represent the number of days taken by Meena.Let the variable z represent the number of days taken by Vinjay.Note: Combined work rate = 1/x + 1/y + 1/z
Based on the information provided, we have the following equations that models the work rate by each person;
1/(x + y) = 10 ⇒ 1/10 = x + y ........equation 1.
1/(y + z) = 12 ⇒ 1/12 = y + z ........equation 2.
1/(x + z) = 15 ⇒ 1/15 = x + z ........equation 3.
x + y + y + z + x + z = 1/10 + 1/12 + 1/15
2(x + y + z) = 15/60
2(x + y + z) = 1/4
x + y + z = 1/8
From equation 2, we have:
x + (y + z) = 1/8
x + 1/12 = 1/8
x = 1/8 - 1/12
x = 1/24
x = 24 days.
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Suppose another team of researchers in 2009 believed that the rate of encounters in which the
whale comes within 3,281 feet of the bow in the lower bay sub-region of Glacier Bay was higher
than 20%. This team observed a sample of 85 encounters between cruise ships and whales in the
lower bay: the whale came within 3.281 feet of the bow in 25 of these encounters.
What will the standard deviation be???
The standard deviation of the normally distributed variable is given as follows:
s = 0.0434.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The mean this problem is given as follows:
[tex]\mu = p = 0.2[/tex]
Considering a sample size of 85, the standard deviation is given as follows:
s = sqrt(0.2 x 0.8/85)
s = 0.0434.
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The point W(-2, 6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, W'?
(2, -6)
When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate
So resulting point W' = (-(-2), -6) = (2, -6)
Answer:
(2, -6)
Step-by-step explanation:
When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate
So resulting point W' = (-(-2), -6) = (2, -6)
Select the correct answer. What is the domain of the exponential function shown in the graph? The graph of the exponential function f(x) = -2^(-x+1)-1 flipped over the x and y axis. It passes through points (0,-6) and (1,-3) with a horizontal asymptote at y = 1.
The domain of the given exponential function is also all real numbers. We can calculate it in the following manner.
The given exponential function is obtained by taking the negative of the original function f(x) = 2^(-x+1) and then subtracting 1 from it. Since the original function has a horizontal asymptote at y=0 and the given function has a horizontal asymptote at y=1, we need to flip the graph of the given function over the x-axis to obtain the graph of the original function.
The point (0, -6) on the given graph corresponds to the point (0, 5) on the graph of the original function, and the point (1, -3) on the given graph corresponds to the point (1, 2) on the graph of the original function.
The general form of an exponential function is f(x) = a^x, where "a" is a positive constant. In this case, we have f(x) = 2^(-x+1), so "a" is equal to 2^1 = 2.
Since "a" is positive, the domain of the function is all real numbers. Therefore, the domain of the given exponential function is also all real numbers.
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Kylie measured the length, x, of each of the insects she found underneath a
rock. She recorded the lengths in the table below.
Calculate an estimate of the mean length of the insects she found.
Give your answer in millimetres (mm).
Length (mm) Frequency
0≤x≤10 5
10 < x≤20 8
20≤x≤30 7
Answer: To estimate the mean length of the insects Kylie found, we can use the formula:
mean = (sum of (length * frequency)) / (sum of frequency)
We can calculate the sum of (length * frequency) by multiplying each length by its corresponding frequency and adding up the products. We can also calculate the sum of frequency by adding up all the frequencies. Using the table given, we have:
sum of (length * frequency) = (5 * 5) + (8 * 15) + (7 * 25) = 5 + 120 + 175 = 300
sum of frequency = 5 + 8 + 7 = 20
Substituting these values into the formula, we get:
mean = 300 / 20
= 15
Therefore, an estimate of the mean length of the insects Kylie found is 15 millimetres.
Step-by-step explanation:
For these equations of straight lines in the form y = mx + c, write down the value of m and c.
(i) y = 3x - 4
(ii) y = -3x + 7.
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(i)
y = 3x - 4
with slope m = 3 and y- intercept c = - 4
(ii)
y = - 3x + 7
with slope m = - 3 and y- intercept c = 7
Answer:
here we can see clearly,
y = mx+c is the formulay= 3x+4answer: m = 3 c = 4 y= -3x + 7 answer: m = -3 c = 7) The bag contains tiles labeled with the letters A, B,
and C. The box contains tiles labeled with the
numbers 1, 2, and 3. June draws one letter tile and
one number tile. Represent the sample space using
either a table or an organized list.
B
B
A
2
3
Here is an organized list representing the sample space of drawing one letter tile and one number tile: {(A, 1), (A, 2), (A, 3), (B, 1), (B, 2), (B, 3), (C, 1), (C, 2), (C, 3)}
What is a sample space?
In probability theory, sample space refers to the set of all possible outcomes of a random experiment.
For example, if we toss a coin, the sample space would consist of two possible outcomes, heads or tails. Similarly, if we roll a die, the sample space would consist of six possible outcomes, the numbers 1 through 6.
The sample space is an important concept because it allows us to define the probabilities of events. In order to calculate the probability of an event, we divide the number of outcomes that are favorable to the event by the total number of possible outcomes in the sample space.
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cholesterol levels among fourteen-year-old boys are roughly normal, with mean 170 and standard deviation 30 milligrams per deciliter (mg/dl). you choose an srs of 4 fourteen-year-old boys and average their cholesterol levels. if you do this many times, the standard deviation of all the average cholesterol levels you get will be close to
The standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.
The standard deviation of the average cholesterol levels will be given by the standard error of the mean, which is calculated as
standard error of the mean = standard deviation / sqrt(sample size)
In this case, the sample size is 4, so we have
standard error of the mean = 30 / sqrt(4) = 15
Therefore, if we take many samples of 4 fourteen-year-old boys and average their cholesterol levels, the standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.
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I paid 99 euros for three shirts and two ties. What is the price of each item if a shirt costs €13 more than a tie?
A tie costs 12 euros and a shirt costs 25 euros.
Let's start by assigning variables to the unknown values. Let x be the price of a tie, and let y be the price of a shirt. We know that y = x + 13, since a shirt costs 13 euros more than a tie.
We also know that we bought three shirts and two ties, and paid a total of 99 euros. Using this information, we can set up an equation
3y + 2x = 99
Here we have to use to substitution method, substituting y = x + 13, we get
3(x + 13) + 2x = 99
Simplifying this equation, we get
5x + 39 = 99
Subtracting 39 from both sides, we get
5x = 60
Dividing both sides by 5, we get
x = 12 euros
Now that we know the price of a tie, we can use y = x + 13 to find the price of a shirt
y = x + 13
y = 12 + 13
y = 25 euros
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OFFERING 100 POINTS AND BRAINILEST!! show work please
Answer:
sorry for my pen!......
Huw wants to open a savings account.
Here are the details of savings accounts advertised by two local Welsh banks.
Banc Padarn
Nominal interest rate of 1.98%
per annum
Interest paid monthly
Banc Teilo
AER 1-99%
Which of these two banks should Huw choose in order to gain the most interest per
annum?
As a result, Bank Padarn's AER is 2.0186%. This shows that Bank Padarn gives a greater interest rate when compared to the AER provided by Banc Teilo (1.9%).
What's the interest rate right now?A benchmark 30-year fixed mortgage's current average interest rate is 6.91% as of today, Tuesdays, March 21, 2023, a decrease of 3 basis points from seven days ago. If you're looking to refinance your mortgage, the current average 30-year fixed interest rate of 6.93%, which has been constant over the past week.
We must convert a nominal rate provided by Bank Padarn to the an AER in order to contrast the two rates.
AER is calculated as (1 + r/n)n - 1 where r is just the nominal rate of return & n is the annual frequency of interest payments.
r = 1.98% and n = 12 for Banc Padarn (since interest is paid monthly). The algorithm yields the following results when we enter these values: AER Equals (1 + 0.0198/12)12 - 1 ≈ 0.020186 = 2.0186%
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PLEASE HELP DUE RIGHT NOW
Question 1(Multiple Choice Worth 5 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x −4 −1 0 1 2
y −4 2 −4 0 2
x 1 1 1 1 1
y −3 −2 −1 0 1
x −6 −1 0 2 3
y −7 negative sixteen thirds −5 negative thirteen thirds −4
x −2 −1 0 2 4
y −4 negative two thirds −1 two thirds 1
The second table is the one which represents a linear function.
What is a linear function?In mathematics, the terms "linear function" refer to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.
⇒ The first table does not represent a linear function because for two different values of x, there is same value for y.
⇒ The second table represents the linear function as it forms a straight line on the graph.
⇒ The third table does not represent a linear function because it does not have a constant slope.
⇒ The last table does not represent a linear function because it does not have a constant slope.
Hence, the second table represents a linear function.
As x is constant as 1, then all the y inputs will be in a straight vertical line
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Question: Which of the following tables represents a linear function?
A. x | −4 −1 0 1 2
y | −4 2 −4 0 2
B. x | 1 1 1 1 1
y | −3 −2 −1 0 1
C. x | −6 −1 0 2 3
y | −7 [tex]\frac{-16}{3}[/tex] −5 [tex]\frac{-13}{3}[/tex] −4
D. x | −2 −1 0 2 4
y | −4 [tex]\frac{-2}{3}[/tex] −1 [tex]\frac{2}{3}[/tex] 1