Quentin has 14 dimes and 31 quarters.
Let x be the number of dimes, and y be the number of quarters. According to the problem, we have two equations: x + y = 45 (equation 1) 0.10x + 0.25y = 9.15 (equation 2)
To solve for x and y, we can use substitution or elimination method. Here, we'll use the elimination method:
Multiplying equation 1 by 0.10, we get: 0.10x + 0.10y = 4.50 (equation 3)
Subtracting equation 3 from equation 2, we get: 0.15y = 4.65, y = 31
Substituting y=31 in equation 1, we get: x + 31 = 45, x = 14
Therefore, Quentin has 14 dimes and 31 quarters.
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A van can ferry a maximum of 12 people. By setting up an inequality, find the maximum number of vans that are needed to ferry 80 people
By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.
To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.
Since a van can ferry a maximum of 12 people, we can write the inequality as:
12v ≥ 80
Now, let's solve for "v":
Divide both sides of the inequality by 12.
v ≥ 80/12
Simplify the inequality.
v ≥ 6.67
Since we cannot have a fraction of a van, we need to round up to the nearest whole number:
v ≥ 7
Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.
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Challenge paints ornaments for a school play. Each ornament is as shown and is made up of two identical cones. uses one bottle of paint to paint 210 . How many bottles of paint does he need in order to paint 50 ornaments? Use 3.14 for .
The number of paint bottles required is 49.716 bottles
Thus, 50 bottles are needed to paint the ornaments.
What is Surface Area?Surface area is the sum of all exterior surfaces on a three-dimensional object, representing the quantity of material that covers it. Computing an object's surface area entrails measuring each of its faces and then adding up their areas altogether.
If we take, for instance, a cube, its surface area would be calculated by multiplying the measurement of one face width by another and then multiplying this value by six (each cube has six sides). The units applied to measure surface area are usually in square feet or square centimeters.
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Solve for x WILL MAKE BRAINLIEST QUESTION IN PHOTI ALSO
The measure of x in the intersected chord is 16.
How to find the angle in an intersected chord?If two chords intersect in a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Using the chord intersection angle theorem,
5x - 7 = 1 / 2 (119 + 27)
5x - 7 = 1 / 2 (146)
5x - 7 = 73
add 7 to both sides of the equation
5x - 7 = 73
5x - 7 + 7 = 73 + 7
5x = 80
divide both sides of the equation by 5
x = 80 / 5
x = 16
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On the Employee Sales Summary sheet, the function used to add together the last employee's sales for the three months is ___________________.
Group of answer choices
=SUM(E16)
=E16+E16+E16
=SUM('Employee Sales October:Employee Sales December'!E16)
=SUM('Employee Sales January:Employee Sales March'!E5)
The function used to add together the last employee's sales for the three months on the Employee Sales Summary sheet is: =SUM('Employee Sales January:Employee Sales March'!E5)
SUM(E16): This function adds up the values in cells E16 from the current sheet. If the last employee's sales for the three months are stored in cells E16, E17, and E18, then this function would correctly calculate the total.
E16+E16+E16: This expression adds up the value in cell E16 three times. If the last employee's sales for the three months are stored in cells E16, E17, and E18, then this expression would not calculate the total correctly.
SUM('Employee Sales October:Employee Sales December'!E16): This function adds up the values in cell E16 from all sheets between Employee Sales October and Employee Sales December (inclusive). If the last employee's sales for the three months are stored in cells E16, E17, and E18 on different sheets, then this function could be used to calculate the total.
SUM('Employee Sales January:Employee Sales March'!E5): This function adds up the values in cell E5 from all sheets between Employee Sales January and Employee Sales March (inclusive).
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Full Question: On the Employee Sales Summary sheet, the function used to add together the last employee's sales for the three months is ___________________.
Group of answer choices
=SUM(E16)=E16+E16+E16=SUM('Employee Sales October:Employee Sales December'!E16)=SUM('Employee Sales January:Employee Sales March'!E5)Gross Monthly Income: Jackson works for a pipe line company and is paid $18. 50 per hour. Although he will have overtime, it is not guaranteed when or where, so Jackson will only build a budget on 40 hours per week. What is Jackson’s gross monthly income for 40 hours per week? Type in the correct dollar amount to the nearest cent. Do not include the dollar sign or letters.
A. Gross Annual Income: $
B. Gross Monthly Income: $
Jackson's gross monthly income for 40 hours per week is approximately $3,201.70 and gross annual income s $38,480.
To find Jackson's gross monthly income, we first need to find his gross weekly income.
Jackson's hourly wage is $18.50, so his weekly gross income for 40 hours of work is:
40 hours/week x $18.50/hour = $740/week
Calculate annual income:
To determine the gross annual income, we need to consider how many weeks there are in a year. Assuming 52 weeks in a year:
Annual income = Weekly income * Number of weeks in a year
Annual income = $740 * 52 = $38,480
To find Jackson's gross monthly income, we can multiply his weekly gross income by the number of weeks in a month (approximately 4.33):
$740/week x 4.33 weeks/month ≈ $3,201.70/month
Therefore, Jackson's gross monthly income for 40 hours per week is approximately $3,201.70.
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Which graph represents the function f {x} = -log (x-1) + 1?
Graph A
Graph B
Graph C
Graph D
y varies inversely as x. y= 27 when x=5 Find y when x=3
As y varies inversely as x, the value of y when x = 3 is 45.
What is the value of y when x = 3?Inverse proportionality is expressed as:
y ∝ 1/x
Hence:
y = k/x
Where k is the constant of proportionality.
First, we determine the constant of proportionality.
Using the information given in the problem.
When x = 5, y = 27
Substituting these values into the formula, we get:
y = k/x
27 = k/5
k = 135
Now that we have found the value of k, we can use the formula to find y when x = 3. Substituting x = 3 and k = 135, we get:
y = k/x
y = 135/3
y = 45
Therefore, the value of y is 45.
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If the area around the cylinder is 64 cm² and the area of the top is 16 cm², what is the surface area of the cylinder?
help me please lol
The surface area of the cylinder is 96cm²
Calculating the surface area of the cylinder?From the question, we have the following parameters that can be used in our computation:
The area around the cylinder is 64 cm² The area of the top is 16 cm²Using the above as a guide, we have the following:
Surface area of the cylinder = The area around the cylinder + 2 * The area of the top
Substitute the known values in the above equation, so, we have the following representation
Surface area of the cylinder = 64 + 2 * 16
Evaluate
Surface area of the cylinder = 96
Hence, the surface area of the cylinder is 96cm²
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Use the properties of logarithms to simplify as much as possible. 3) In(4x^5) – In (x^3)- In 4 4) The price of beef has inflated by 2%. If the price of beef inflates 2% compounded biannually, how lung will it take for the price of beef to triple?
3) The expression In(4x^5) - In(x^3) - In 4 can be simplified using the properties of logarithms. We know that ln(a) - ln(b) = ln(a/b) and ln(a^n) = n ln(a), so we can write:In(4x^5) - In(x^3) - In 4 = In[(4x^5)/(x^3)] - In 4= In(4x^2) - In 4= In(4x^2/4)= In(x^2)Thus, the simplified expression is In(x^2).4) To solve this problem, we need to use the formula for compound interest:A = P(1 + r/n)^(nt)where A is the final amount, P is the initial amount, r is the interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.We want to find t when A = 3P and r = 0.02 (since the price of beef has inflated by 2%). We are told that interest is compounded biannually, so n = 2. Plugging in these values and solving for t, we get:3P = P(1 + 0.02/2)^(2t)3 = (1.01)^2tln(3) = ln(1.01^2t)ln(3) = 2t ln(1.01)t = ln(3) / (2 ln(1.01))Using a calculator, we find t ≈ 34.64 years. Therefore, it will take about 34.64 years for the price of beef to triple at a 2% biannual inflation rate.
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It will take approximately 110 years for the price of beef to triple when inflating 2% compounded biannually.
3) To simplify the expression In(4x^5) - In(x^3) - In(4), we will use the properties of logarithms:
- In(a) - In(b) = In(a/b)
- In(a^b) = b * In(a)
So, we can rewrite the expression as:
In(4x^5 / (x^3 * 4))
Now, we can simplify the expression inside the natural logarithm:
(4x^5) / (4x^3) = x^(5-3) = x^2
Thus, the simplified expression is:
In(x^2)
4) To find how long it will take for the price of beef to triple when inflating 2% compounded biannually, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, we want the final amount to be triple the initial amount:
3P = P(1 + 0.02/2)^(2t)
To solve for t, we can divide both sides by P:
3 = (1 + 0.01)^(2t)
Now, take the natural logarithm of both sides and use the properties of logarithms:
ln(3) = ln((1 + 0.01)^(2t))
ln(3) = 2t * ln(1 + 0.01)
Finally, isolate t:
t = ln(3) / (2 * ln(1 + 0.01))
t ≈ 109.96
It will take approximately 110 years for the price of beef to triple when inflating 2% compounded biannually.
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1 ml =
a
litres
ii)
b
ml = 1 litre
iii) 1 cl =
c
litres
iv)
d
cl = 1 litre
v) 1 cl =
e
ml
vi)
f
cl = 1 ml
The corresponding measure of the parameters are;
i. 1ml = 0. 001 liter a.
ii. 1000ml = 1 liter b.
iii. 1 cl = 0. 01 liter c.
iv. 10dcl = 1 liter d.
v. 1cl = 100ml e.
v. 0. 01 cl = 1ml f.
How to determine the valuesTo convert the factors, we need to know the following conversion rates.
We have;
1 milliliter = 0. 001 liter
1 centiliter = 0. 01 liter
1 deciliter = 0. 1 liter
1 cubic centimeter = 1 millimeter
Hence, the sizes are determined by the corresponding factor.
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Complete question:
Convert the following to their equivalent measurement for each letter
i. 1 ml = a liters
ii) b ml = 1 liters
iii) 1 cl = c liters
iv)d cl = 1 liters
v) 1 cl = e ml
vi) f cl = 1 ml
Let f(x) = x² – 6x. Round all answers to 2 decimal places. = a. Find the slope of the secant line joining (2, f(2) and (7, f(7)). Slope of secant line = b. Find the slope of the secant line joining (6, f(6)) and (6 + h, f(6 + h)). Slope of secant line = c. Find the slope of the tangent line at (6, f(6)). Slope of the tangent line d. Find the equation of the tangent line at (6, f(6)). y =
The equation of the tangent line at (6, f(6)) is y = 6x - 48.
a. The slope of the secant line joining (2, f(2)) and (7, f(7)) is:
slope = (f(7) - f(2)) / (7 - 2)
We can find f(7) and f(2) by plugging in x = 7 and x = 2 into the expression for f(x):
f(7) = 7² - 6(7) = 7
f(2) = 2² - 6(2) = -8
Substituting these values into the slope formula, we get:
slope = (7 - (-8)) / (7 - 2) = 3
Therefore, the slope of the secant line joining (2, f(2)) and (7, f(7)) is 3.
b. The slope of the secant line joining (6, f(6)) and (6 + h, f(6 + h)) is:
slope = (f(6 + h) - f(6)) / ((6 + h) - 6) = (f(6 + h) - f(6)) / h
We can find f(6) and f(6 + h) by plugging in x = 6 and x = 6 + h into the expression for f(x):
f(6) = 6² - 6(6) = -12
f(6 + h) = (6 + h)² - 6(6 + h) = h² - 6h + 36 - 36 - 6h = h² - 12h
Substituting these values into the slope formula, we get:
slope = (h² - 12h - (-12)) / h = h - 12
Therefore, the slope of the secant line joining (6, f(6)) and (6 + h, f(6 + h)) is h - 12.
c. The slope of the tangent line at (6, f(6)) is the derivative of f(x) at x = 6:
f'(x) = 2x - 6
f'(6) = 2(6) - 6 = 6
Therefore, the slope of the tangent line at (6, f(6)) is 6.
d. To find the equation of the tangent line at (6, f(6)), we use the point-slope form of a line:
y - f(6) = f'(6)(x - 6)
Substituting f(6) and f'(6) into this equation, we get:
y - (-12) = 6(x - 6)
Simplifying, we get:
y = 6x - 48
Therefore, the equation of the tangent line at (6, f(6)) is y = 6x - 48.
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Find the inverse of y=(2/3)x^5-10
The inverse of the function y= (2/3)x^5-10 is y = [3/2(x + 10)]^1/5
Finding the inverse of the functionFrom the question, we have the following parameters that can be used in our computation:
y= (2/3)x^5-10
Swap the ocurrence of x and y
so, we have the following representation
x = (2/3)y^5-10
Next, we have
(2/3)y^5 = x + 10
This gives
y^5 = 3/2(x + 10)
Take the fifth root of both sides
y = [3/2(x + 10)]^1/5
Hence, the inverse function is y = [3/2(x + 10)]^1/5
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The polynomial â 2x2 + 700x represents the budget surplus of the town of Alphaville.
Betaville's surplus is represented by x2 - 100x + 80,000. If x represents the tax revenue in
thousands from both towns, enter the expression that represents the total surplus of both
towns together.
The expression that represents the total surplus of both towns together is ?
The total surplus of both towns together is represented by the polynomial [tex]3x^2 + 600x + 80,000.[/tex]
The expression that represents the total surplus of both towns together is (â 2x2 + 700x) + (x2 - 100x + 80,000).?To find the total surplus of both towns together, we need to add the budget surplus of Alphaville and Betaville.
The budget surplus of Alphaville is represented by the polynomial [tex]2x^2 + 700x.[/tex]
The budget surplus of Betaville is represented by the polynomial x^2 - 100x + 80,000.
Therefore, the expression that represents the total surplus of both towns together is:
[tex](2x^2 + 700x) + (x^2 - 100x + 80,000)[/tex]
Simplifying this expression, we get:
[tex]3x^2 + 600x + 80,000[/tex]
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Mr. Woodley invested $1200 at 5% simple interest at the beginning of each year for a period of 8 years. Find the total accumulated value of all the investments at the end of the 8-year period.
It would be helpful if u used a geometric or arithmetic sequence formula.
Answer:
$1680
Step-by-step explanation:
PV = $1200
i = 5%
n = 8
Simple interest formula:
FV = PV (1 + i × n)
FV = 1200 (1 + 5% x 8)
FV = $1680
what is the product of -5 and -10 sign and result
Answer:
50, positive
Step-by-step explanation:
(-5) * (-10) = 50
When a negative multiplies by another negative, the answer is positive
So, the answer is 50 and the sign is positive
Sam makes mini pancakes for breakfast. Each pancake is a circle with a diameter of 6 centimeters.
a) Calculate the circumference of each pancake.
b) Calculate the area of each pancake.
Answer:
a) 18.84 cm
b) 28.26 cm²
Step-by-step explanation:
We Know
Each pancake is a circle with a diameter of 6 centimeters.
a) Calculate the circumference of each pancake.
Circumference of circle = d · π
d = 6 cm
We Take
6 · 3.14 = 18.84 cm
So, the circumference of each pancake is 18.84 cm.
b) Calculate the area of each pancake.
Area of circle = r² · π
r = 1/2 · d
r = 1/2 · 6 = 3 cm
We Take
3² · 3.14 = 28.26 cm²
So, the area of each pancake is 28.26 cm².
Liquid a has a density of 1. 2 g/cm'
150 cm of liquid a is mixed with some of liquid b to make liquid c.
liquid c has a mass of 220 g and a density of 1. 1 g/cm
find the density of liquid b.
If Liquid a has a density of 1. 2 g/cm³, 150 cm of Liquid a is mixed with some of Liquid b to make Liquid c whose mass is 220 g and has a density of 1.1 g/cm³, then the density of liquid B is 0.8 g/cm³.
To find the density of liquid B, you can follow these steps:
1. Calculate the mass of liquid A using its density and volume:
Liquid A has a density of 1.2 g/cm³ and a volume of 150 cm³.
Mass of A = Density of A × Volume of A = 1.2 g/cm³ × 150 cm³ = 180 g
2. Calculate the mass of liquid B using the mass of liquid C and mass of liquid A:
Liquid C has a mass of 220 g.
Mass of B = Mass of C - Mass of A = 220 g - 180 g = 40 g
3. Calculate the volume of liquid C using its mass and density:
Liquid C has a density of 1.1 g/cm³.
Volume of C = Mass of C ÷ Density of C = 220 g ÷ 1.1 g/cm³ = 200 cm³
4. Calculate the volume of liquid B using the volume of liquid C and the volume of liquid A:
Volume of B = Volume of C - Volume of A = 200 cm³ - 150 cm³ = 50 cm³
5. Calculate the density of liquid B using it's mass and volume:
Density of B = Mass of B ÷ Volume of B = 40 g ÷ 50 cm³ = 0.8 g/cm³
So, the density of liquid B is 0.8 g/cm³.
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A farmer wants to fence an area of 750 000 m² in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. How can this be done so as to minimize the cost of the fence?
The farmer should construct a rectangle that is twice as long as it is wide, with dimensions of 1216.56 m x 608.28 m, and should use 7301.36 m of fence to divide it in half parallel to the shorter side in order to minimize the cost of the fence.
To minimize the cost of the fence, the farmer should construct a rectangle that is twice as long as it is wide, with the dividing fence parallel to the shorter side. This will result in two identical rectangles each with an area of 375 000 m².
The perimeter of the rectangle can be calculated as follows:
P = 2L + 2W
where L is the length and W is the width.
Since the area of the rectangle is 750 000 m² and the length is twice the width, we can write:
L x W = 750 000
L = 2W
Substituting L = 2W into the equation for area, we get:
2W x W = 750 000
2W² = 750 000
W² = 375 000
W = 608.28 m
L = 2W = 1216.56 m
So the dimensions of the rectangle are 1216.56 m x 608.28 m.
The perimeter of each rectangle is:
P = 2L + 2W
P = 2(1216.56) + 2(608.28)
P = 3650.68 m
The total length of fence needed is twice the perimeter, since we are dividing the rectangle in half:
Total fence length = 2 x 3650.68 = 7301.36 m
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Monica deposits $ 300 into a savings account that pays a simple interest rate of 3.4%. Paul deposits $400 into a savings account that pays a simple interest rate of 3.3 %. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Monica's claim is incorrect. Even though her interest rate is higher, she will earn less interest, $10.20, after one year than Paul because her initial deposit is lower.
Paul will earn more interest of $13.20 because he deposited more money, even though his interest rate is slightly lower.
To determine who will earn more interest in one year, we shall calculate the interest earned by each person using the simple interest formula.
What is the simple interest formula?The formula for simple interest is:
I = P * r * t
where:
I = the interest earned
P = the principal (the amount deposited)
r = the interest rate (as a decimal)
t =s the time (in years)
For Monica, we are given:
P = $300
r = 0.034 (the interest rate is 3.4%)
t = 1 (the interest earned in one year)
Plugging these values, we have:
I = 300 * 0.034 * 1 = $10.20
So, Monica will earn $10.20 in interest after one year.
For Paul, we are given:
P = $400
r = 0.033 (interest rate = 3.3%)
t = 1 (interest earned in one year)
Plugging the values, we get:
I = 400 * 0.033 * 1 = $13.20
So, Paul will earn $13.20 in interest after one year.
Therefore, Monica's claim is incorrect. Monica will earn $10.20 in interest after one year while Paul will earn $13.20 in interest after one year.
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In triangle abc, point d is on side ac, ab=bd=dc=12 inches, and measurement of angle bdc= 2 times the measurement of angle abd. find ac
The length of AC in triangle ABC is 24 inches.
In triangle ABC, let point D be on side AC such that AB = BD = DC = 12 inches. We are given that the measure of angle BDC is twice the measure of angle ABD.
To find the length of AC, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we can apply the Law of Cosines to triangle ABD to find the length of AD:
AD^2 = AB^2 + BD^2 - 2 * AB * BD * cos(ABD)
Since AB = BD = 12 inches, we have:
AD^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(ABD)
AD^2 = 288 - 288 * cos(ABD)
Now, let's consider triangle BDC. We are given that the measure of angle BDC is twice the measure of angle ABD. Let's denote the measure of angle ABD as x. Therefore, the measure of angle BDC is 2x.
Since the sum of angles in a triangle is 180 degrees, we can write:
x + 2x + angle BCD = 180
3x + angle BCD = 180
angle BCD = 180 - 3x
Now, let's apply the Law of Cosines to triangle BDC to find the length of BC:
BC^2 = BD^2 + CD^2 - 2 * BD * CD * cos(BDC)
BC^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(2x)
BC^2 = 288 - 288 * cos(2x)
Since AD = DC, we have AD = 12 inches. Now we can write the equation for the total length AC:
AC = AD + DC
AC = 12 + 12
AC = 24 inches
Therefore, the length of AC in triangle ABC is 24 inches.
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Which is a reasonable estimate for the difference 5 1/2- 3 5/9? Circle
the letter of the correct answer
A between 1/2 and 1
B between 1 and 1 1/2
C between 1 1/2 and 2
D between 2 and 2 1/2
Elise chose D as the correct answer. How did she get that answer?
Step-by-step explanation:
To estimate the difference between 5 1/2 and 3 5/9, we can first round the fractions to the nearest whole number or simpler fractions. In this case, we can round 1/2 to 1/2 and 5/9 to 1/2 as well. Now, we have:
5 1/2 − 3 1/2
Subtracting the whole numbers, we get:
5−3=2
Subtracting the fractions, we get:
1/2 − 1/2 = 0
So, the estimated difference is 2, which falls between 2 and 2 1/2. Therefore, Elise chose option D as the correct answer.
12. A normal distribution has a mean of 34 and a standard deviation of 7. Find the range of
values that represent the middle 95% of the data.
F. 27
G. 20 X 48
H. 13
J. 6
The range of values that represent the middle 95% of the data is from 20.18 to 47.82 or (20.18, 47.82).
What is Hypothesis test?A measurable speculation test is a strategy for factual deduction used to conclude whether the information within reach adequately support a specific speculation. We can make probabilistic statements about the parameters of the population thanks to hypothesis testing.
According to question:The middle 95% of a normal distribution is located within 1.96 standard deviations from the mean in both directions.
Therefore, the lower limit is:
34 - 1.96(7) = 20.18
And the upper limit is:
34 + 1.96(7) = 47.82
So the range of values that represent the middle 95% of the data is from 20.18 to 47.82 or (20.18, 47.82).
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Asap!!!! Solve the equation for v. v over 8 minus 4 equals negative 12 (18 points)
v = -128
v = -64
v = 16
v = 92
Answer:
v = -64
Step-by-step explanation:
First, you add 4 to both sides to isolate the variable term:
v/8 = -8
Next, you multiply both sides by 8 to isolate the variable on one side:
v = -64
So, the solution to the equation v/8 - 4 = -12 is v = -64.
El 91 no es un número primo porque tiene más divisores que el 1 y el 91 verdadero o falso
The statement''El 91 no es un número primo porque tiene más divisores que el 1 y el 91'' is true because 91 is not a prime number.
A prime number is a positive integer that has only two divisors, 1 and itself. To check if 91 is a prime number, we need to find its divisors. We can start by dividing 91 by 2, but we find that 2 is not a divisor of 91. Next, we can try dividing it by 3, and we get 30 with a remainder of 1. This means that 3 is not a divisor of 91 either.
We continue dividing by 4, 5, 6, and so on until we reach 13, which gives us 7 as a quotient and 0 as a remainder. Therefore, the divisors of 91 are 1, 7, 13, and 91, which means that 91 is not a prime number because it has more than two divisors. Hence, the statement is true.
91 ÷ 2 = 45 r 1
91 ÷ 3 = 30 r 1
91 ÷ 4 = 22 r 3
91 ÷ 5 = 18 r 1
91 ÷ 6 = 15 r 1
91 ÷ 7 = 13 r 0
Since 91 has more than two divisors, it is not a prime number.
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A circle is centered at c(0,0)c(0,0)c, left parenthesis, 0, comma, 0, right parenthesis. the point m(0,\sqrt{38})m(0, 38 )m, left parenthesis, 0, comma, square root of, 38, end square root, right parenthesis is on the circle.where does the point n(-5,-3)n(−5,−3)n, left parenthesis, minus, 5, comma, minus, 3, right parenthesis lie
The point N(-5,-3) lies inside the circle centered at C(0,0) with radius √38.
How we find the point lies inside the circle?Since the point M(0, √38) lies on the circle with center C(0,0), we can find the radius of the circle by finding the distance between M and C:
r = √[tex]((0 - 0)^2[/tex] + (√[tex]38 - 0)^2)[/tex] = √38
Now that we know the radius of the circle is √38, we can determine where the point N(-5,-3) lies relative to the circle. We can find the distance between N and the center of the circle:
d = √[tex]((-5 - 0)^2[/tex] + [tex](-3 - 0)^2)[/tex] = √34
Since the distance between N and the center of the circle is less than the radius of the circle, the point N is inside the circle. Therefore, N lies inside the circle centered at C(0,0) with radius √38.
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Ariana has 144 peaches. She has to pack 9 boxes with an equal number of peaches. How many peaches should she pack in each box.
Answer:
16 peaches
Step-by-step explanation:
Let's break this down:
Total: 144 peaches
Number of boxes she has to fill evenly: 9
Question: How many peaches are able to fit into each box evenly?
144 peaches/9 boxes = 16 peaches
So, Ariana should pack 16 peaches into each box
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The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.\
The statement that is true is: "The range of the function is all real numbers less than or equal to 9
What is the function about?This quadratic function is indicated by a downward-opening parabola due to the negative coefficient of the squared term.
Found at coordinates (-2, 9), the vertex will be the highest point on this curved graph
Located on the x-axis at points (-5, 0) and (1, 0), each one serves as an intersection. Because of these intersections the following statement can be confidently said: "The range of the function consists of all actual numbers that are lesser or equal to 9."
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Un árbol ha sido roto por el viento de tal manera que sus dos partes forman un triángulo rectángulo. la parte superior tiene una longitud de 10 m, y la distancia medida sobre el piso hasta la cúspide del árbol es de 6 m. hallar la altura que tenía el árbol.
Se puede utilizar el teorema de Pitágoras para resolver este problema. Si se considera que la altura del árbol es la hipotenusa del triángulo rectángulo,
entonces la parte superior de la parte rota del árbol es uno de los catetos, y la distancia medida sobre el piso hasta la cúspide del árbol es el otro cateto.
Por lo tanto, se tiene que:
[tex]altura^2 = cateto1^2 + cateto2^2[/tex]
Reemplazando los valores conocidos, se tiene:
[tex]altura^2 = 10^2 + 6^2[/tex]
[tex]altura^2 = 136[/tex]
Tomando la raíz altura^2 = 136, se obtiene:
[tex]altura = √136[/tex]
altura ≈ 11.66 m
Por lo tanto, la altura que tenía el árbol antes de ser roto por el viento es de aproximadamente 11.66 metros.
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10% of people are left handed. If 800 people are randomly selected, find the likelihood that at least 12% of the sample is left handed
The likelihood of at least 12% of the sample being left-handed is approximately 0.007 or 0.7%.
Let X be the number of left-handed people in a sample of 800 individuals. Since the probability of a person being left-handed is 0.1, the probability of a person being right-handed is 0.9. Then, X follows a binomial distribution with n = 800 and p = 0.1.
P(X ≥ 0.12*800) = P(X ≥ 96)
where 96 is the smallest integer greater than or equal to 0.12*800.
[tex]P(X > =96)-P(X < 96)=1-[K=0 to 95](800 CHOOSE )(0.1^{k} (0.9)^{2} (800-k)[/tex]
This is the complement of the probability of getting less than 96 left-handed people in the sample. Using a calculator or statistical software, we can find that:
P(X ≥ 96) ≈ 0.007
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Use the rules to find derivatives of the following functions at the specified values
h(x) = 8x at x = 4
h'(4) = _____
To find the derivative of h(x) = 8x, we use the power rule, which states that the derivative of x^n is nx^(n-1). Applying this rule to h(x), we get h'(x) = 8.
To find the value of h'(4), we simply plug in x = 4 into our derivative expression: h'(4) = 8.
Therefore, the derivative of h(x) = 8x at x = 4 is h'(4) = 8.
To find the derivative of the function h(x) = 8x at x = 4, you can use the power rule for differentiation. The power rule states that if h(x) = x^n, then h'(x) = n * x^(n-1).
For h(x) = 8x, n = 1, so:
h'(x) = 1 * 8x^(1-1) = 8
Now, to find h'(4), just plug in x = 4:
h'(4) = 8
So, h'(4) = 8.
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