Therefore, your answer would be "30".
Hoped this helped.
Lesson 8 Practice Problems
1. A number line can represent positions that are north and south of a truck stop on a
highway. Decide whether you want positive positions to be north or south of the
truck stop. Then plot the following positions on a number line.
a. The truck stop
b. 5 miles north of the truck stop
c. 3.5 miles south of the truck stop
The graph can be viewed at the conclusion of the response. We want to graph a number line and certain points on it.
Let A denote the truck stop and then it is 0 miles away from the truck stop.
Let us take the north side of the truck stop as the negative side.
Then the south side of the truck stop is the positive side.
We are asked to represent the following positions on the number line:
a. The truck stop
b. 5 miles to the north of the truck stop
c. 3.5 miles to the south of the truck stop
Point A refers to the truck stop.
Let B denote the point 5 miles away from A towards the north side of the truck stop.
And let C denote the point 3.5 miles away from A towards the south side of the truck stop.
Refer to the attached image for the required number line.
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6. If rls and mZ1 = 35º, what is mZ2?
2
1
S
please help!!
Answer:
55
Step-by-step explanation:
along line s, r intersects it, and you can see a right angle
90+35+angle 2 =180
you end up with 55, which is the measure
use the spinner below to answer the question. assume that it is equally probable that the pointer will land on any one of the five numbered spaces. if the pointer lands on a borderline, spin again.
The probability that the arrow will land on 2 or 3 is given by the following option:
2/5.
How to obtain the probability?A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.
From the spinner given by the image shown at the end of the answer, we have that:
The total number of outcomes is given by the five regions of the spinner.The desired number of outcomes is given by 2, as there are two outcomes, 2 and 3, considering that all regions are equally as likely.Then the probability that the arrow will land on 2 or 3 is calculated as follows:
p = 2/5.
Meaning that the third option is correct.
Missing InformationThe complete problem, along with the options, is given by the image presented at the end of the answer.
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How can you decompose the composite figure to determine its area? as a circle, three rectangles, and a triangle as a circle, a trapezoid, and four triangles as a semicircle, three rectangles, and a square as a semicircle, a trapezoid, and two rectangles.
Answer:
The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:
Area of a semicircle = 21πr2, where r is the radius of the circle.
Area of a trapezoid = 21(b1+b2)h, where b1 and b2 are the bases and h is the height of the trapezoid.
Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.
Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.
Step-by-step explanation:
The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.
Option D is the correct answer.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as: 1/2 x sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
The given figure can be decomposed into the following figure.
- Semicircle
- Trapezoid
- Two rectangles
Thus,
A semicircle, a trapezoid, and two rectangles.
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Consider a sample with a mean of 48 and a standard deviation of 6 . Where rounding is required, round to 4 decimal places a. Assuming that the distribution is known to be normal or bell-shaped, what percentage of the data will fall between 42 and 54 ? b. What percentage of the data will be greater than 66 ? Assume the data is normally distributed. c. Now assume the distribution of the data is unknown. What percentage of the data can we assume falls between 36 and 60 ? d. Again assuming the distribution of the data is unknown, what percentage of the data will fall between 39 and 57 ? c. Suppose one of the individual elements in the data set is 33. Compute the z-score of this element and interpret it?
Approximately 68.27% of the data will fall between 42 and 54. 0.13% of the data will be greater than 66. A large percentage of the data falls between these values, but we cannot provide an exact percentage. The z-score of element 33 is -2.5 indicates that the element is 2.5 standard deviations below the mean.
To solve these questions, we can use the properties of the normal distribution and z-scores.
a. To find the percentage of data that falls between 42 and 54, we need to calculate the z-scores for these values and then find the area under the normal curve between those z-scores.
The z-score formula is:
z = (x - μ) / σ
For 42:
z1 = (42 - 48) / 6 = -1.0000
For 54:
z2 = (54 - 48) / 6 = 1.0000
Using a standard normal distribution table or a calculator, we can find the area between these two z-scores.
Area between z1 and z2 = P(z1 < Z < z2) = P(-1 < Z < 1) ≈ 0.6827
Therefore, approximately 68.27% of the data will fall between 42 and 54.
b. To find the percentage of data that will be greater than 66, we need to calculate the z-score for 66 and find the area to the right of that z-score.
For 66:
z = (66 - 48) / 6 = 3.0000
Using a standard normal distribution table or a calculator, we can find the area to the right of this z-score.
Area to the right of z = P(Z > z) = P(Z > 3) ≈ 0.0013
Therefore, approximately 0.13% of the data will be greater than 66.
c. When the distribution of the data is unknown, we cannot make exact calculations based on the normal distribution. However, if we assume that the data is approximately normally distributed, we can estimate the percentage of data falling between certain values.
Since the data is unknown, we can use a rough estimate based on the empirical rule (also known as the 68-95-99.7 rule). According to this rule, for a bell-shaped distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the mean is 48 and the standard deviation is 6, we can estimate that a large percentage of the data falls between 36 and 60. However, we cannot provide an exact percentage without knowing the specific shape of the distribution.
d. Similarly, assuming the distribution is unknown, we can use the rough estimate based on the empirical rule. The range between 39 and 57 is within two standard deviations of the mean. Therefore, we can estimate that a large percentage of the data falls between these values, but we cannot provide an exact percentage.
c. The z-score measures the number of standard deviations an individual element is away from the mean. To compute the z-score for an element of 33 in this case, we use the formula:
z = (x - μ) / σ
For 33:
z = (33 - 48) / 6 = -2.5
The z-score of -2.5 indicates that the element is 2.5 standard deviations below the mean. In terms of interpretation, it means that the value of 33 is relatively low compared to the mean and standard deviation of the data set. It falls in the lower tail of the distribution.
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Un carro utiliza 8 litros de gasolina para recorrer 96 kilómetros.Cuantos kilómetros recorre con 35 litros?
Answer:
415.625
Step-by-step explanation:
1. Yo dividida 35 por 8. La respuesta de eso es 4.375.
2. Yo multiplica 4.375 por 95. La respuesta es 415.625 km.
Raphael i h year old
a) Lily' age i Raphael' age divided by 3. Write an expreion in term of h for Lily' age
b) An expreion for Ethan' age i h6. Write a entence to decribe how Ethan' age compare with Raphael' age
a) When Lily's age is 20, and Raphael's age is divided by 3 then the expression of Lily's age in terms of h is h < 10.
b) Ethan's age is half of Raphael's age therefore, Ethan's age is half Raphael's age.
a) If Raphael is twice as old as his sister Lily, we can represent their ages as 2h and h, respectively, where h is Lily's age. The sum of their ages is less than 30, so we can write the equation:
2h + h < 30
Combining like terms, we get:
3h < 30
Dividing both sides by 3, we get:
h < 10
This is an expression of Lily's age in terms of h.
b) If Ethan's age is 16, and Raphael's age is twice Ethan's age, we can represent Raphael's age as 2 × 16 = 32.
Ethan's age is 16, which is half of Raphael's age of 32. Therefore, Ethan's age is half of Raphael's age.
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The question is -
Raphael is twice as old as his sister. The sum of their ages is less than 30.
a) Lily's age is 20, and Raphael's age is divided by 3. Write an expression in terms of h for Lily's age.
b) An expression for Ethan's age 16. Write a sentence to describe how Ethan's age compares with Raphael's age.
Please help!
What is the coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin?
Answer:
(- 5, 1 )
Step-by-step explanation:
under a clockwise rotation about the origin of 90°
a point (x, y ) → (y, - x ) , then
H (- 1, - 5 ) → H' (- 5, - (- 1) ) → H' (- 5, 1 )
use spherical coordinates. evaluate ∭E (x² + y²) dv, where e lies between the spheres x² + y² + z² = 9 and x² + y² + z² = 16.
The value of ∭E (x² + y²) dv over the region E between the given spheres.
To evaluate the integral ∭E (x² + y²) dv using spherical coordinates, we first need to express the volume element dv in terms of spherical coordinates.
In spherical coordinates, the volume element is given by dv = r² sin(φ) dr dφ dθ, where r represents the radial distance, φ represents the polar angle, and θ represents the azimuthal angle.
Since we are integrating over the region E between the spheres x² + y² + z² = 9 and x² + y² + z² = 16, the limits of integration for r, φ, and θ will be as follows:
r: from the lower sphere to the upper sphere, which corresponds to r = 3 to r = 4
φ: from 0 to π (since we are considering the entire range of polar angle)
θ: from 0 to 2π (since we are considering the entire range of azimuthal angle)
Now, let's substitute these values and evaluate the integral:
∭E (x² + y²) dv = ∭E (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ
Integrating over θ from 0 to 2π, and integrating over φ from 0 to π, we have:
∭E (x² + y²) dv = ∫[0,2π] ∫[0,π] ∫[3,4] (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ
Now, we can evaluate the integral by performing the integration step by step, starting from the innermost integral.
After evaluating the integral, the final result will give us the value of ∭E (x² + y²) dv over the region E between the given spheres.
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What is the percent of increase from 75 to 99?
Answer:
What is the percentage increase/decrease from 75 to 99? = 32.
Step-by-step explanation:
Solution for What is the percentage increase/decrease from 75 to 99:
(99-75):75*100 =
(99:75-1)*100 =
132-100 = 32
Now we have: What is the percentage increase/decrease from 75 to 99 = 32
Answer:
it would be 32
Step-by-step explanation:
i got my answer by adding the amount that makes up one percent and did that until i got from 75 to 99.
numbers in percentages are more than regular numbers
what is the last digit of 3 with a power of 2011
So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.
Find each of the following probabilities when n independent Bernoulli trials are carried out with probability of success p.(a) the probability of no successes(b) the probability of at least one success(c) the probability of at most one success(d) the probability of at least two successes(e) the probability of no failures(f) the probability of at least one failure(g) the probability of at most one failure(h) the probability of at least two failures
The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].
The probability of a success in one Bernoulli trial is given by p, and the probability of a failure is q = 1 - p.
(a) The probability of no successes is (1-p)^n.
(b) The probability of at least one success is 1 minus the probability of no successes, which is 1 - (1-p)^n.
(c) The probability of at most one success is the sum of the probabilities of 0 and 1 successes, which is (1-p)^n + np(1-p)^(n-1).
(d) The probability of at least two successes is 1 minus the probability of 0 or 1 success, which is 1 - [(1-p)^n + np(1-p)^(n-1)].
(e) The probability of no failures is the same as the probability of n successes, which is p^n.
(f) The probability of at least one failure is 1 minus the probability of no failures, which is 1 - p^n.
(g) The probability of at most one failure is the sum of the probabilities of 0 and 1 failures, which is p^n + nqp^(n-1).
(h) The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].
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A company manufactures water bottles the list below describes the number of water bottles manufactured in three months
.February 4,100 water bottles
. March 7% more water bottles than in February
.April: 500 more water bottles than in march
what is the percent increase to the nearest percent in the number of water bottles the company manufactured from February to April?
Answer:
19%
Step-by-step explanation:
First, find how many water bottles were manufactured in March:
4,100 x 1.07 = 4387
Add 500 to the March number
4387 + 500= 4887
Then divide the April number by February
4887/4100= 1.19195
This means that there is a 19 percent increase of water bottles manufactured from February to April
The shapes in this question are drawn on a centimetre grid.
a) What is the area of rectangle A?
b) What is the area of triangle B?
c) What is the area of trapezium C?
Picture included.
Answer:
A. 12 centimeters B. 4 centimeters C. 20 centimeters
Step-by-step explanation:
To find area you need to do the Height time the Length.
For A it is 3x4
For B it is 4x1
And for C it is 4x5
You get this equation by multiplying the amount of squares that the Height and Length measured!
Hope this helped!
:DD
The area of the rectangle is 12 units².
The area of the triangle is 2 units².
The area of the trapezium is 16 units.
We have,
The area of the rectangle.
= length x width
= 4 units x 3 units
= 12 units²
The area of the triangle.
= 1/2 x base x height
= 1/2 x 1 unit x 4 units
= 2 units²
The area of the trapezium.
= 1/2 x (sum of the parallel sides) x height
= 1/2 x (5 units + 3 units) x 4 units
=1/2 x 8 units x 4 units
= 4 x 4
= 16 units²
Thus,
The area of the rectangle is 12 units².
The area of the triangle is 2 units².
The area of the trapezium is 16 units.
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The volume of a fish tank is 30 cubic feet. if the density is 0.3fish over feet cubed, how many fish are in the tank? 100 10 9 3
Number of fishes in the tank are 9.
Given
Density (d)= 0.3 fish/ft³
Volume of a fish tank (V) = 30 ft³
number of units(n)= ?
Density, mass of a unit volume of a material substance. The formula for density is d = n/V, where d is density, n is quantity(number of units), and V is volume. Density is commonly expressed in units of grams per cubic centimetre.
d = n/V
d = n/V
n = d * V
n = 0.3 fish/ft³ * 30 ft³
number of units(n) = 9
Hence,
Number of fishes in the tank are 9.
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Answer: The correct answer is (c) 9.
Step-by-step explanation:
0.3 x 30 = 9
how to find hypotenuse?
Answer:
Given two right triangle legs
Use the Pythagorean theorem to calculate the hypotenuse from the right triangle sides. Take a square root of sum of squares: c = √(a² + b²)
Step-by-step explanation:
The hypotenuse can be discovered using Pythagoras' Theorem.
The meaning of hypotenuseThe definition of "the longest side of a right triangle" is simply "hypotenuse." The triangle's hypotenuse is the side that faces away from the right angle. It is also the triangle's longest side.
Where is the Hypotenuse located?The Pythagorean theorem is formalized mathematically via the hypotenuse formula. It states that the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the shorter two sides of the triangle, a and b: a2+b2=c2.
The 3:4:5 triangle is the only way to know for sure if an angle is 90 degrees. According to this rule, a triangle cannot be a right triangle if one side of the triangle measures 3 and the other side measures 4 and the diagonal connecting those two locations does not measure 5.
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What attributes do squares and
trapezoids always have in
common?
Answer:
There both quadrilaterals
Step-by-step explanation:
What is the area of the figure ?
a graph artist created the design for a rectangular poster. the design is 12 inches by 9 inches. The poster is 48 inches by 36 inches. What scale factor did the graph artist use to create the design
Answer:
The ratio of the areas of the design and the poster is
(12*9):(48*36) = 1:16
Which curves on the accompanying graphs may represent the temperature and ph profiles of an enzyme secreted by a bacterium that lives in a mildly alkaline hot springs at temperatures of 70°c or higher?.
The temperature and pH profiles of an enzyme secreted by a bacterium that lives in a mildly alkaline hot spring at temperatures of 70°C or higher can be represented by curves B and D.B and D curves on the graph can represent the temperature and pH profiles of an enzyme secreted by a bacterium that lives in a mildly alkaline hot spring at temperatures of 70°C or higher.
There are two graphs given for the question, which are described below.
Graph 1: This graph shows the temperature and pH of an enzyme's activity.
Temperature is plotted on the y-axis and pH on the x-axis.
The graph has four curves.
Curve A represents an enzyme secreted by a bacterium that lives in the intestines of a cow.
Curve B represents an enzyme secreted by a bacterium that lives in a mildly alkaline hot spring at temperatures of 70°C or higher.
Curve C represents an enzyme secreted by a bacterium that lives in the acidic contents of the human stomach.
Curve D represents an enzyme secreted by a bacterium that lives in the alkaline environment of a deep-sea hydrothermal vent at temperatures of 100°C or higher.
Graph 2: This graph shows the effects of temperature on the activity of three different enzymes. Enzyme A is from a bacterium that lives in the soil at temperatures of 20°C or lower.
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can anyone help me with this its really urgent!!
Answer:
h = 2 cm
402 over 3.14 x (8) to the power of two. SImplifies to about the answer of 2
Write an equation in slope-intercept form for a line perpendicular to y=-2 x+6 containing (3,2) .
The equation of a line perpendicular to y=-2 x+6 containing (3,2) in slope-intercept form: y = 0.5 x - 0.5
Two lines are perpendicular if their slopes are negative reciprocals of each other. The slope of y=-2 x+6 is -2, so the slope of the perpendicular line will be 1/2.
We can plug the point (3,2) into the slope-intercept form of a line, y = mx + b, to solve for b, the y-intercept.
```
2 = (1/2) * 3 + b
```
```
2 = 1.5 + b
```
```
b = 2 - 1.5 = 0.5
```
Therefore, the equation of the perpendicular line is y = 0.5 x + 0.5.
Here is a graph of the two lines:
```
[asy]
unitsize(1 cm);
draw((-1,0)--(6,0));
draw((0,-1)--(0,4));
draw((3,2)--(3,0.5));
draw((-0.5,4)--(5.5,-0.5),dashed);
label("y = -2 x + 6", (6,4), E);
label("y = 0.5 x + 0.5", (3,0.5), NE);
dot("(3,2)", (3,2), SW);
[/asy]
```
As you can see, the two lines intersect at the point (3,2), and their slopes are negative reciprocals of each other.
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Answer question below please
Answer:
Homework
Step-by-step explanation
I got the answer by telling you to TRY and do your own homeowrk, Have you TRIED at least?!?!?
help please! will mark brainliest
Answer:
C
Step-by-step explanation:
Each output is 3 more than the input
Answer: the answer is c, y + 3
Consider this expression.
√a³ - 7+ |b|
When a = 2and b
=
-4, the value of the expression is
The value of the expression when a = 2 and b = -4 is 5
Evaluating an expressionFrom the question, we are to determine the value of the expression for the given values of a and b
The given expression is
√(a³ -7) + |b|
From the given information,
we are to determine the value of the expression, when a = 2 and b = -4
Putting the values of a and b into the expression, we get
√((2)³ -7) + |-4|
√(8 -7) + 4
√(1) + 4
1 + 4
= 5
Hence, the value of the expression when a = 2 and b = -4 is 5
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Is -59+8 positive or negative
Answer:
Negative
Step-by-step explanation:
It's negative because there are 59 negatives and 8 positives. Since there are more negatives the sum is negative.
-59+8 = -51
Hope this helps ya!
Equipment costing $135,000 with a book value of $124,000 is sold for $125,000. What is the gain or loss on sale and how is it recorded for this transaction?
There is gain of $1,000 on the sale. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers are believed to be able to be described by the four fundamental operations, often known as "arithmetic operations". Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.
We are given that an equipment costing $135,000 has a book value of $124,000 and it is sold for $125,000.
Since, the sale value is higher than the book value, therefore there is a gain.
Using arithmetic operations, we get
Gain on sale = $125,000 - $124,000
Gain on sale = $1,000
Hence, there is gain of $1,000 on the sale.
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The second part of the question i.e. how is it recorded for this transaction is related to the subject accountancy and not mathematics.
if the actual increase in total sea otters was 1,400 individuals between 1985 and 2005, how many new sea otters were added to the population (on average) each year? if the actual increase in total sea otters was 1,400 individuals between 1985 and 2005, how many new sea otters were added to the population (on average) each year? 2 2,700 28,000 70
If the actual increase in total sea otters was 1400 individuals between 1985 and 2005 and 70 more sea otters were added to the population.
We must divide the overall increase of 1,400 individuals by the total number of years between 1985 and 2005 to determine the average annual addition to the sea otter population:
There have been 1,400 more sea otters overall.
There were 20 years between 1985 and 2005.
The average annual increase is calculated as follows: 1,400 / 20 years, or 70 new sea otters each year.
Hence, each year, there are typically 70 more sea otters added to the population.
Therefore, if the actual increase in total sea otters was 1400 individuals between 1985 and 2005 and 70 more sea otters were added to the population.
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Which system of equations has no solution?
Answer:
4x-5y=3
-3=4x-5y
Step-by-step explanation:
4x-5y = 3
4x-5y = -3
both statements have different answers but has the same problem making the statement x=x and 0=0 making it have no solution
I need help I keep getting it wrong
Find the area of the triangle and multiply by the length of the prism.
Area = 1/2 x 8x3 = 12 square yds.
Volume = 12 x 6 = 72 cubic yards.