Answers
The amount invested at 4% interest rate that is $3900 and
the amount invested at 3% interest rate is $4300.
Last year Sarah invested money in two accounts. The first account had an interest rate of 3% and the second account had an interest rate of 4%. If she invested $400 more in the first account than the second and her total interest income was $285,
the equations are:
s= f + 400 (1)
0.03s + 0.04f = 285 (2)
modifying (1) and (2) for simpler calculations
3s - 3f = 3 * 400 (3)
3s + 4f = 100 * 285 (4)
by solving eqns (3) and (4) we get
we get f=3900 and s=4300
Here, f is the amount invested at 4% interest rate that is $3900 and
s refers to the amount invested at 3% interest rate is $4300.
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Related Questions
For a 20-year endowment insurance on (65) with face amount 1,000:
benefits are payable at the moment of death, or at the end of 20 years if the
insured survives.
− Mortality follows the Illustrative Life Table with = 0.06.
− Deaths are uniformly distributed between integral ages.
− Gross premiums are payable at the beginning of each year for 20 years, and are
determined by the equivalence principle.
− Commissions and taxes are 35% of the gross premium in the first year, 5% in the
other years, and are paid at the beginning of each year.
− Other expenses are 1 in all years, paid at the beginning of the year.
Calculate the gross premium for the endowment insurance
Answers
The gross premium for the endowment insurance is 73.
How to solveTo calculate the gross premium for the endowment insurance, we can use the equivalence principle, which states that the present value of the premiums must equal the present value of the benefits.
We can break down the problem into two parts: the present value of the death benefit and the present value of the endowment benefit.
First, let's calculate the present value of the death benefit. The death benefit is payable at the moment of death, and the probability of dying at age x is given by qx, where qx is the probability of surviving to age x.
Since deaths are uniformly distributed between integral ages, we can assume that deaths occur at the midpoint of the age interval. Therefore, the probability of dying at age x can be approximated by
.
Let's denote the present value of the death benefit as DB. Using the equivalence principle, we can write:
DB = A*(1+0.35) - E0 - C1 - 0.05A(1+0.05)
- 0.05A(1+0.05)
- ... - 0.05A(1+0.05)
where A is the annual premium, E0 is the expense paid at the beginning of the first year, and C1 is the commission and tax paid at the beginning of the first year.
The factor (1+0.35) accounts for the commission and tax on the first year premium.
Using the formula for the present value of a perpetuity, we can simplify the above equation to:
DB =
= 116.22
where q65/2 is the probability of dying at age 65. We can obtain q65/2 from the Illustrative Life Table, which gives
q65/2 = 0.112488.
Therefore, the gross premium for the endowment insurance is 73.
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Please help. It's quite urgent : )
[tex] \frac{3}{8} + \frac{4}{5} - \frac{5}{16} - \frac{3}{10} [/tex]
Answers
The answer of given question is 9/16.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It typically consists of mathematical symbols, such as numbers, variables, operators, and equal signs. Equations are used to represent relationships between quantities and are commonly used in various fields of mathematics, science, and engineering to solve problems, make predictions, and describe phenomena.
Define fraction?A fraction is a mathematical representation of a part or parts of a whole. It consists of two numbers, separated by a horizontal or diagonal line, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole.
3/8+4/5-5/16-3/10
(30+64-25-24)/80
45/80
=9/16
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Use the graph to answer the question.
graph of polygon ABCD with vertices at 0 comma 0, 5 comma 2, 5 comma negative 5, 0 comma negative 3
Determine the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 90° counterclockwise.
A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0)
A′(0, 0), B′(−2, −5), C′(−5, 5), D′(−3, 0)
A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0)
A′(0, 0), B′(−5, −2), C′(−5, −5), D′(0, 3)
Answers
the Correct option of coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 90° counterclockwise is A
What is coordinate?A coordinate is a set of numbers that represents the position of a point in space. It is often used to describe the location of a point on a graph or a map
According to given informationTo determine the coordinates of polygon A′B′C′D′, we need to rotate each vertex of polygon ABCD 90° counterclockwise.
We can do this by using the following formulas for a 90° counterclockwise rotation of a point (x, y):
x' = -y
y' = x
Using these formulas, we can find the coordinates of each vertex of polygon A′B′C′D′ as follows:
A′(0, 0): Since (0, 0) is the origin, a 90° counterclockwise rotation will still result in (0, 0).
B′(-2, 5): To rotate the point (5, 2) 90° counterclockwise, we have x' = -y = -2 and y' = x = 5. So, B′ is (-2, 5).
C′(5, 5): To rotate the point (5, -5) 90° counterclockwise, we have x' = -y = 5 and y' = x = 5. So, C′ is (5, 5).
D′(3, 0): To rotate the point (0, -3) 90° counterclockwise, we have x' = -y = 0 and y' = x = 3. So, D′ is (3, 0).
Therefore, the coordinates of polygon A′B′C′D′ are A′(0, 0), B′(-2, 5), C′(5, 5), and D′(3, 0).
So, the answer is A) A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0).
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please help asap!!!!!!!
Answers
As we have shown that both AE is congruent to CE and BE is congruent to DE.
Now, let's focus on the diagonals of the parallelogram, AC and BD. We are told that they intersect at point E.
To prove that AE is congruent to CE, we can use the fact that opposite sides of a parallelogram are congruent. Since AC is a diagonal of the parallelogram, it divides it into two congruent triangles, AEC and CED. This is because AE is parallel to CD (as they are opposite sides of the parallelogram), and EC is common to both triangles.
Therefore, by the Side-Angle-Side (SAS) congruence theorem, we can conclude that triangle AEC is congruent to triangle CED. In particular, this means that AE is congruent to CE.
Similarly, to prove that BE is congruent to DE, we can use the same reasoning. Since BD is a diagonal of the parallelogram, it divides it into two congruent triangles, AEB and DEC. This is because BE is parallel to AC (as they are opposite sides of the parallelogram), and ED is common to both triangles.
Therefore, by the SAS congruence theorem, we can conclude that triangle AEB is congruent to triangle DEC. In particular, this means that BE is congruent to DE.
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Cari owns a horse farm and a horse trailer that can transport up to 8,000 pounds of livestock and tack. She travels with 5 horses whose combined weight is 6,240 pounds. Let t represent the average weight of tack per horse. What inequalities could show the weight of each horse?
Answers
The inequalities that could show the weight of each horse are:
h ≤ 1248
t ≤ 352
To determine the inequalities that could show the weight of each horse, we can use the fact that the total weight of the horses and tack must be less than or equal to the capacity of the horse trailer. We can set up the following inequalities:
5h + 5t ≤ 8000
where h represents the average weight of each horse.
However, we don't know the value of t, so we need to express it in terms of h. We are given that the combined weight of the horses is 6,240 pounds, so we can write:
5h ≤ 6240
Solving for h, we get:
h ≤ 1248
This means that the weight of each horse must be less than or equal to 1,248 pounds.
Now we can substitute this upper bound for h into the first inequality to get:
5(1248) + 5t ≤ 8000
6240 + 5t ≤ 8000
5t ≤ 1760
t ≤ 352
This means that the average weight of tack per horse must be less than or equal to 352 pounds.
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There have been many cases where long-standing issues that divided societies have been resolved, such as the reunification of Germany and the end
of apartheid in South Africa. Both of these benefitted society as whole, but one of the short-term results was an increase in crime. Why is this the case?
O A. Both experienced racially motivated crime.
OB.
O C.
O D.
Both involved a sudden reorganization of society.
Both came after a massive reform in public education.
Both are the result of implementing social service programs.
Answers
The increase in crime was caused by D. Both are the result of implementing social service programs.
What led to the increase in crime ?Significant modifications made to a society's social and political structures can cause periods of instability and uncertainty, leading to a rise in crime rates. The daunting tasks of restructuring society that came with the abolishment of apartheid in South Africa and Germany's reunification represent examples of such changes.
When power structures, economic systems, and social norms abruptly shift, gaps in authority may arise, thereby presenting opportunities for criminal activity to escalate. Criminal elements can capitalize on these unexpected power vacuums.
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The heights of 18 year old men are approximately normally distributed with mean 68 inches in standard deviation 3 inches what is the probability that an 18-year-old man do that random is greater than 74 inches tall
Answers
The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.
We have,
We can use the standard normal distribution to solve this problem by standardizing the height value using the formula:
z = (x - μ) / σ
where:
x = the height value (in inches)
μ = the mean height (in inches)
σ = the standard deviation (in inches)
Substituting the given values, we get:
z = (74 - 68) / 3
z = 2.0
Using a standard normal table or calculator, we can find the probability that a random standard normal variable is greater than 2.0 to be approximately 0.0228.
Therefore,
The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.
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Help with this math please.
Answers
if 1cm = 110 m then, 4.5 cm = 495 m and 4cm = 440 m
so perimeter is equal to all the sides added up
495 + 440 + 495 + 440 which is equal to 1870
A ribbon is 29 centimeters long. How many millimeters long is the ribbon?
2.9 millimeters
2,900 millimeters
290 millimeters
58 millimeters
Answers
Answer: The 290 millimeters long is the ribbon.
Step-by-step explanation:
To convert centimeters to millimeters
1 cm =10 millimeters
therefore,
29cm= 290 millimeters
Therefore, the ribbon is 290 millimeters long.
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Compound Inequalities
The manufacturers of Cheerios only ship boxes that weigh more than 13.98 and less than 14.02 oz.
a. Represent the weights of boxes that will ship in three forms.
b. Represent the weights of boxes that will not ship in three forms.
*In Symbolic/Inequality and number line*
Answers
An compound inequality that describes the acceptable weights for a 20 oz box is 19.25 ≤ x ≤ 20.75.
We have,
The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To determine the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.
We are Given that, cereal manufacturer has a tolerance of 0.75 oz for a box of cereal that is supposed to weigh 20 oz.
Let the weight of cereal box be; w
Now, the inequality is
20-0.75 ≤ x ≤ 20+0.75
Add 20 on both sides of an inequality, we get
19.25 ≤ x ≤ 20.75
Here, 19.25 ≤ x ≤ 20.75
Therefore, an absolute value inequality to find the range of acceptable weights is 19.25 ≤ x ≤ 20.75.
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Which answer Choice contains only equations? A. 2 + H = 14 and K - 25 =2 B. C-14C-14 and d+134 C. 10=3+s and 22-y D. 15+x and 55= r-1
Answers
Answer:
The answer choice that contains only equations is:
A. 2 + H = 14 and K - 25 = 2
Explanation:
A. Both expressions are equations because they have an equal sign and a variable.
B. C-14C-14 is not an equation because it doesn't have an equal sign.
C. Both expressions are equations, but 22-y is not a complete equation (missing an equal sign).
D. Both expressions are equations, but 55= r-1 is not a complete equation (missing an equal sign).
Step-by-step explanation:
What is the missing side length??
Answers
The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
By Pythagoras rule we can evaluate for b as follows:
x = √(7.5² - 2.5²)
x = √50
x = x = 7.0711
f = √[(√78)² - 7²]
f = √(78 - 49)
f = √29
f = 5.3852
d = 2 × √(11² × 8²)
d = 2 × √53
d = 15.0996
Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and only need #1
Answers
The end behavior is if x becomes very large the value of f(x) also becomes very large, The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.
To describe the end behavior of f(x), we need to consider the limit of f(x) as x approaches positive infinity and negative infinity. We can write this as:
lim f(x) as x → ±∞ = ±∞
This means that as x becomes very large (either positive or negative), the value of f(x) also becomes very large (either positive or negative).
b. If we change the base of the exponential function from 5/7 to 7, the graph of f(x) will change in the following ways:
The function will grow faster, because 7 is greater than 5/7.
The function will start at a higher value, because f(0) = 4(7)^0 = 4.
The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.
c. If we add a constant to the exponential function, the graph of f(x) will be shifted vertically by the amount of the constant. In this case, the graph of f(x) will be shifted downwards by 2 units, because we are subtracting 2 from the function.
The equation of the new function is:
f(x) = 4(5/7)ˣ - 2
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sketch the graphs y=|x|, y=|x|+2, y=|x|-1
Answers
The graph of y=|x| is a v-shaped graph that starts at the origin and continues infinitely in both the positive and negative x-directions. The graph of y=|x|+2 is the same v-shaped graph, but it has been shifted up two units so that it no longer intersects the x-axis. Finally, the graph of y=|x|-1 is a v-shaped graph that has been shifted down one unit so that it intersects the x-axis at (1,0) and (-1,0). All three graphs are symmetric with respect to the y-axis.
A.
B.
11. Caden fills the box with 1-inch x 1-inch x-Inch cubes. How many cubes does he use to
fill the box without empty space?
NIP
?
23.625
63
94.5
C.
D. 189
NIT
HIN
in.
42/in.
1/in.
3 in.
weight in uneor each month
Answers
Caden needs to use 126 cubes to fill the box without empty space.
How many cubes does he use to fill the boxThe volume of the box is:
42 in. x 1 in. x 3 in. = 126 cubic inches
The volume of each small cube is:
1 in. x 1 in. x 1 in. = 1 cubic inch
To fill the box, the number of cubes needed is the volume of the box divided by the volume of each cube:
126 cubic inches ÷ 1 cubic inch per cube = 126 cubes
Therefore, Caden needs to use 126 cubes to fill the box without empty space.
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Rewrite each equation without using absolute value for the given conditions. y=|x-5|+|x+5| if x>5
Answers
Answer:
y = 2x
Step-by-step explanation:
If x > 5, then x - 5 is positive and x + 5 is also positive. So we can rewrite the equation as follows:
y = (x - 5) + (x + 5)
Simplifying the equation, we get:
y = 2x + 0
Therefore, the equation without using absolute value for the given conditions is y = 2x.
Hope this helps!
Using the image below, state what additional information is required to prove the triangles are congruent with ASA Postulate.
Answers
The additional information is required to prove the triangles are congruent with ASA Postulate is [tex]\bar{RS} \cong \bar{CS}[/tex] (option d)
In order to prove that two triangles are congruent using the ASA postulate, we need to know that they have two pairs of congruent angles and a congruent side that is in between those angles. The image below shows two triangles, but we do not have enough information to prove that they are congruent with the ASA postulate.
To use the ASA postulate, we need to have a congruent side in between the two congruent angles. In this case, we do not know if side RS is congruent to side CS. Therefore, we cannot use the ASA postulate to prove that these triangles are congruent.
In summary, to prove that two triangles are congruent using the ASA postulate, we need to have two pairs of congruent angles and a congruent side in between those angles. Without this information, we cannot use the ASA postulate to prove congruency.
Hence the correct option is (d)
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The initial temperature of a liquid in a beaker is 19°C. The beaker is heated and its temperature increased by 71°C after half an hour. Then, the beaker is left and the temperature decreased by 2°C every minute for half an hour. What is the final temperature of the liquid after one hour?
Answers
Answer:
Step-by-step explanation:
temperature is heated half an hour
19°c+71°c=90°c
{since its increased by 71°c}
90°c-[2°c*30]=30°c
so the final temperature is 30°cPLEASE HELP ME ANSWER THIS QUESTION ASAP!! Will mark as brainliest if correct!
Answers
answer attached
see below
please give brainliest it will be much appreciated
x + 4y = 9
-x - 2y = 3
Answers
Hope it helps :)
[tex]x + 4y = 9 \\
-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)[/tex]
I don’t understand how to do this ?
Answers
The value of the derivative of the composite function h(x) = f[g(x)] is equal to h'(3) = 2.
How to find the exact value of the derivative of a composite function
In this problem we find a function in the form of a composite function of the form h(x) = f[g(x)], whose derivative is defined by the chain rule:
h'(x) = f'(g) · g'(x)
If we know that g'(3) = 2 and f'(2) = 1, then the exact value of the derivative of the composite function is:
h'(3) = 2 · 1
h'(3) = 2
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What is the solution set of 6x-24 =0? x^2
Answers
The solution to the Quadratic equation x², when x satisfies the equation 6x - 24 = 0, is x²= 16.
What is Quadratic equation?A quadratic equation is a polynomial equation of the second degree, meaning it contains one or more terms that involve a variable raised to the power of two. The standard form of a quadratic equation is:
ax^2 + bx + c = 0,where a, b, and c are constants, and x is the variable.
According to given informationThe given equation is 6x - 24 = 0.
To solve for x, we can isolate x on one side by adding 24 to both sides of the equation:
6x - 24 + 24 = 0 + 24
6x = 24
Then, we can solve for x by dividing both sides by 6:
6x/6 = 24/6
x = 4
Therefore, the solution to the equation 6x - 24 = 0 is x = 4.
Now, to solve for x², we can simply substitute x = 4 into the equation x²:
x² = 4²
x^2 = 16
Therefore, the solution to the equation x², when x satisfies the equation 6x - 24 = 0, is x² = 16.
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8 cm
*****
The dimensions of a triangular prism are shown in the diagram.
12 cm-
4/10
10 cm,
34 cm
What is the volume of the triangular prism in cubic centimeters?
10 cm
✓
✓
Answers
The volume of the triangular prism shown below is 48 cm²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The area of triangular base = (1/2) * 12 cm * 8 cm = 48 cm²
The volume of triangular prism = area of base * height
Volume = 48 cm² * 34 cm = 1632 cm³
The volume of the triangular prism is 48 cm²
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Find the surface area of the composite solid to the nearest hundredth.
Answers
The surface area of the composite solid is calculated to the nearest hundredth as: 113.09 square feet.
How to Find the Surface Area of a Composite Solid?To find the surface area of the composite solid which is composed of a cone and a cylinder, do the following:
Find the surface area of the cone:
Surface area of cone = πrl
radius (r) = 4 ft
l = √(3² + 4²) = 5 ft
Plug in the values:
Surface area of cone = π * 4 * 5 ≈ 62.83 square feet.
Find the surface area of the cylinder:
Surface area of cylinder = 2πr(h + r)
radius (r) = 4 ft
h = 2 ft
Plug in the values:
Surface area of cylinder = 2 * π * 4 * (2 + 4) ≈ 150.80 square feet.
Find area of the surface both meet:
Area = πr² = π * 4² ≈ 50.27 square feet.
Surface area of the composite solid = 62.83 + 150.80 - 2(50.27)
= 113.09 square feet.
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(4a-ts)(2a+2ts) what is the solution
Answers
Answer:
8a^2 + 6ats - 2t^2s^2
Step-by-step explanation:
(4a-ts)(2a+2ts)
4a(2a+2ts) -ts(2a+2ts)
8a^2 + 8ats - 2ts - 2t^2s^2
= 8a^2 + 6ats - 2t^2s^2
find the surface area to the nearest whole number. do not round until the end. X=4 units Y= 13 units Z= 7 units (giving brainliest!!!)
Answers
The Surface area of figure is 396.896 unit².
We have,
x = 4 unit, y = 13 unit and z = 7 unit.
First Surface Area of Cylinder
= 2πrh
= 2(3.14)(4)(7)
= 175.84 unit²
and, Surface Area of Cone
= πrl
= (3.14)(4)(13.6)
= 170.816 unit²
Thus, the Surface area of figure is
= 175.84 + 170.816 + 50.24
= 396.896 unit²
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If the diameter of a tree trunk is growing 1/4 inch each year, how many years will it take for the diameter to grow 8 inches? Explain how you found your answer.
Answers
The number of years that it will take to grow 8 inches is 32 years.
How many years will it take for the diameter to grow 8 inches?We know that the diameter grows at a constant rate of 1/4 inches per year.
Then the amount that the diameter grows after x years is given by the linear equation:
D(x) = x*(1/4) in
We want to find the number of years that it takes to grow 8 inches, then we need to solve the linear equation:
8in = x*(1/4) in
Now we can solve that equation for x, we will get:
8in/((1/4) in) = x
8*4 = x
32 = x
It will take 32 years.
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A fifth grade teacher believes that 12% of her students are late for class. If the teacher is right, what is the probability that the proportion of late students in a sample of 538 students would differ from the population proportion by less than 3%? Round your answer to four decimal places.
Answers
Answer:
Step-by-step explanation:
Given:
Proportion of students who are late for class in the population: p = 0.12
Sample size: n = 538
Margin of error: E = 0.03
The standard error of the proportion can be calculated using the formula:
SE = sqrt(p*(1-p)/n)
SE = sqrt(0.12*0.88/538)
SE = 0.019
The margin of error corresponds to a z-score at the 97.5th percentile (since we want the probability of the sample proportion being within 3% of the population proportion in either direction, which gives us a two-tailed test with an alpha level of 0.025 on each side). This z-score can be found using a standard normal distribution table or calculator and is approximately 1.96.
The margin of error can also be calculated using the formula:
E = z*(SE)
0.03 = 1.96*(0.019)
To find the probability that the sample proportion differs from the population proportion by less than 3%, we need to find the area under the standard normal distribution curve between the z-scores of -1.96 and 1.96. This area is equivalent to the probability of the sample proportion being within 3% of the population proportion. This probability can be found using a standard normal distribution table or calculator and is approximately 0.8534.
Therefore, the probability that the proportion of late students in a sample of 538 students would differ from the population proportion by less than 3% is 0.8534 or 85.34% (rounded to four decimal places)
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
From the information provided, according to the table, if the purchase price of a car was less than $20,000, what is the probability that its Trepair costs were less than about 46%.
If a car had total repair costs of less than $10,000, what is the probability that its purchase price was more than $40.000 Express your about 20%.
How did we get these values?Probability is a measure of the likelihood of an event happening. It is a numerical value between 0 and 1, where 0 indicates an event is impossible, and 1 indicates an event is certain.
So, calculating the probability of the events above happening in percentage is as follows:
A. 86/ (86+67+35) =
18/188 ≈ 46%.
Therefore, Blank 1 is about 46%
B. 40/(88+71+40) =
40/197 ≈ 20%.
Therefore, Blank 2 is about 20%.
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what is the circumference i need a refresh of how to do it i kinda forgot sum1 give answer and explanation
Answers
Answer:
102
Step-by-step explanation:
34 is d so 34×3=102
pls correct me if im wrong