To find the area under the standard normal curve, we need to use a standard normal distribution table or a calculator with a normal probability distribution function.
(a) To find the area between z = -1.20 and z = 1.20, we can use the symmetry property of the normal distribution curve and find the area to the right of z = -1.20 and double it:
P(-1.20 < z < 1.20) = 2 * P(z < 1.20) - 1 = 2 * 0.8849 - 1 = 0.7698
Therefore, the area under the standard normal curve between z = -1.20 and z = 1.20 is approximately 0.7698.
(b) area between z = 1.23 and z = 1.87
P(1.23 < z < 1.87) = P(z < 1.87) - P(z < 1.23) = 0.9693 - 0.8907 = 0.0786
Therefore, the area under the standard normal curve between z = 1.23 and z = 1.87 is approximately 0.0786.
(c) area between z = -2.35 and z = -0.5
P(-2.35 < z < -0.5) = P(z < -0.5) - P(z < -2.35) = 0.3085 - 0.0094 = 0.2991
Therefore, the area under the standard normal curve between z = -2.35 and z = -0.5 is approximately 0.2991.
(d) To find the area to the right of z = 2.16
P(z > 2.16) = 1 - P(z < 2.16) = 1 - 0.9842 = 0.0158
Therefore, the area under the standard normal curve to the right of z = 2.16 is approximately 0.0158.
(e) To find the area between z = -0.8 and z = 1.53
P(-0.8 < z < 1.53) = P(z < 1.53) - P(z < -0.8) = 0.9370 - 0.2119 = 0.7251
Therefore, the area under the standard normal curve between z = -0.8 and z = 1.53 is approximately 0.7251.
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Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce
After Derek drinks 1/4 ounce of water, he is left with 95/3 ounces of water in his glass.
Derek initially had 10 2/3 ounces of water in his glass. To find out how much water is left after he drinks 1/4 ounce of water, we need to subtract 1/4 from 10 2/3. To do that, we need to convert the mixed number (10 2/3) into an improper fraction.
To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. In this case, we have:
10 x 3 + 2 = 32/3
Therefore, Derek initially had 32/3 ounces of water in his glass.
To subtract 1/4 from 32/3, we need to make sure the denominators are the same. We can convert 1/4 into twelfths by multiplying both the numerator and denominator by 3. This gives us:
1/4 x 3/3 = 3/12
Now that we have a common denominator of 12, we can subtract:
32/3 - 3/12 = 383/12 - 3/12 = 380/12
To simplify, we can divide both the numerator and denominator by 4:
380/12 ÷ 4/4 = 95/3
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Complete question is:
Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce of the water from his glass how much water is left in Derek's glass?
Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X ∼ N ( 153 , 14.5 ) . z-score when x = 108 is _____. The mean is 153 . The z-score tell you that x = 108 is _____ standard deviations to the left of the mean.
x = 108 is 3.10 standard deviations to the left of the mean.
What is standard deviation?The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.
The z-score when x = 108 is:
z = (108 - 153) / 14.5
z = -3.10
This tells us that x = 108 is 3.10 standard deviations to the left of the mean.
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A figure which has a sphare and cylinder. The total height of figure is 102mm and the height of cylinder is 76mm. Find Volume and Surface Area of the figure
The volume of the figure is approximately 50101mm^3 and the surface area is approximately 8253mm^2.
The figure consists of a sphere and a cylinder. We can find the volume and surface area of the figure by calculating the volume and surface area of each component separately and adding them together.
The height of the cylinder is given as 76mm, which means the remaining height of the figure must be occupied by the sphere. Thus, the radius of the sphere can be calculated as half the difference between the total height of the figure and the height of the cylinder:
Radius of sphere = (102mm - 76mm)/2 = 13mm
Now we can calculate the volume and surface area of each component:
Volume of cylinder = πr^2h = π(13mm)^2(76mm) ≈ 40899mm^3
Surface area of cylinder = 2πrh + 2πr^2 = 2π(13mm)(76mm) + 2π(13mm)^2 ≈ 6128mm^2
Volume of sphere = (4/3)πr^3 = (4/3)π(13mm)^3 ≈ 9202mm^3
Surface area of sphere = 4πr^2 = 4π(13mm)^2 ≈ 2125mm^2
Finally, we can find the total volume and surface area of the figure by adding the values for the cylinder and sphere:
Total volume = Volume of cylinder + Volume of sphere ≈ 50101mm^3
Total surface area = Surface area of cylinder + Surface area of sphere ≈ 8253mm^2
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Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in
Sandy's experiment.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
And please give me the answer
Answer: option C - Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips, is the most likely scenario.
Step-by-step explanation:
Based on the Law of Huge Numbers, the more times a coin is flipped, the closer the test likelihood will be to the hypothetical likelihood of 0.5 for heads and 0.5 for tails. In this manner, Sandy's exploratory likelihood is most likely to be closest to the hypothetical likelihood within the test with 1,000 flips.
In spite of the fact that it is conceivable that Sandy's exploratory likelihood might be near to the hypothetical likelihood within the explore with 100 flips or 500 flips, it is more likely that the bigger test measure of 1,000 flips will result in a more precise representation of the hypothetical likelihood.
Use the following data to answer questions 1-2.
1. Find the median, mean, and range of the elephant ages.
a) Median:.
b) Mean:,
Ages of 10 elephants (in years) living in zoos:
28, 14, 19, 20, 21, 28, 33, 36, 41
c) Range:.
years
years
years
Answer:
median - 28
mean - 26.6 (6 repeating)
range - 27
Step-by-step explanation:
The elephant ages would go in the order of 14, 19, 20, 21, 28, 28, 33, 36, 41. To find the median, you need to look for the center of the numbers, which would be 28, since 28 is the middle number. To find the mean, you add all the numbers up and divide them by however many numbers there are, in this case, they add up to 240, and there is 9 numbers, so you would do 240 divided by 9 = 26.66 (repeating so a line over the 6's after the decimal) and to find the range you subtract the highest number and the lowest, which is 41 and 14 and that would give you 27.
I'M SO SORRY IF THIS DIDN'T MAKE SENSE!
Determine the value of y-intercept of a line with the given slope -3 that is a tangent
line to the curve y = -x² - 5x -5.
a. 0
b. -1
c. -3
d. -4
The y-intercept of the tangent line is b. -1
What is the y intercept of a line?The y-intercept of a line is the value of y at which the line crosses the y axis
To determine the value of y-intercept of a line with the given slope -3 that is a tangent line to the curve y = -x² - 5x -5.
We proceed as follows
First we differentiate the equation of the curve.
So, y = -x² - 5x -5.
dy/dx = d(-x² - 5x -5)/dx
= d-x²/dx - d5x/dx - d5/dx
= -2x - 5 - 0
= -2x - 5
Since the derivative of the curve equals the value of the tangent at the point, we have that
dy/dx = -3
-3 = -2x - 5
-3 + 5 = -2x
2 = -2x
x = 2/-2
x = -1
So, substituting x = -1 into the equation for y to find the y intercept, we have that
y = -x² - 5x -5.
y = -(-1)² - 5(-1) -5
= -1 + 5 - 5
= -1 + 0
= -1
So, the y-intercept is b. -1
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Determine the point ths of the way from point A: (-3,-2) to point B. (4, -3) shown on the coordinate plane below.
Answer:
Step-by-step explanation:
To find the point that is a certain fraction of the way between two given points, we can use the midpoint formula and the scalar multiplication of vectors.
Let's first find the vector that points from point A to point B:
�
�
⃗
=
(
4
−
3
)
−
(
−
3
−
2
)
=
(
7
−
1
)
AB
=(
4
−3
)−(
−3
−2
)=(
7
−1
)
The scalar multiplication of a vector with a scalar value scales the length of the vector. To find the point that is 3/4 of the way from point A to point B, we can multiply the vector $\vec{AB}$ by 3/4:
3
4
�
�
⃗
=
3
4
(
7
−
1
)
=
(
21
4
−
3
4
)
4
3
AB
=
4
3
(
7
−1
)=(
4
21
−
4
3
)
Finally, we can add this vector to point A to get the point that is 3/4 of the way from point A to point B:
(
−
3
−
2
)
+
(
21
4
−
3
4
)
=
(
3
4
,
−
11
4
)
(
−3
−2
)+(
4
21
−
4
3
)=
(
4
3
,−
4
11
)
how is this answer wrong?
Answer:
its taking the immage on the right and moving it ounter clockwise 90°
Please could you help its due tommorow
Answer:
x = 52.5
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360.
2x+100 +95+60 = 360
Combine like terms.
2x+255=360
Subtract 255 from each side
2x+255-255= 360-255
2x = 105
Divide each side by 2
2x/2 = 105/2
x = 52.5
Answer:
x = 52.5
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360°.
Accordingly, let us find the value of x.
2x + 100 + 95 + 60 = 360
2x + 255 = 360
Subtract 255 from both sides.
2x = 360 - 255
2x = 105
Divide both sides by 2.
x = 52.5
Can someone show me step by step correctly for a better grade
There are approximately 7.48 liquid gallons in a cubic foot. If a cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet, what is the approximate height of the water tank? Approximate using π = 3.14 and round to the nearest tenth.
4.6 feet
14.4 feet
46.0 feet
147.1 feet
The height of the cylindrical water tank is 4.6 feet. Therefore, the answer is A.
How to find the height of the water tank?The cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet.
Therefore, the height of the tank can be calculated as follows:
7.48 liquid gallons = 1 ft³
1100 liquid gallons = ?
cross multiply
volume of the tank = 1100 / 7.48 = 147.058823529 ft³
Therefore, let's find the volume of the cylindrical tank.
volume of the cylindrical tank = πr²h
where
r = radiush = heightTherefore,
r = 3.2 feet
h = ?
The volume of the cylindrical tank in feet cube is 147.058823529 ft³
Let's find the height, h
volume of the cylindrical tank = 3.14 × 3.2² × h
147.058823529 = 3.14 × 10.24 × h
32.1536h = 147.058823529
divide both sides by 32.1536
h = 147.058823529 / 32.1536
h = 4.57363405653
Therefore,
height of the water tank = 4.6 feet
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What is the value of x in the equation 2x + 3 = 11?
Answer: x=4
Step-by-step explanation:
Isolate x using opposite operations.
2x + 3 = 11
2x = 8
x = 4
Answer:
4
Step-by-step explanation:
subract 3 from 11
2x=8
divide by 2
x=4
Question 90
The quality of milk reaching the ultimate consumer is largely determined
a. at the plant, where processing and handling occurs
b. at the farm, where the milk is processed
c. by the USDA through stringent testing and laboratory analysis
d. by the FDA in accordance with Federal regulations
The quality of milk reaching the ultimate consumer is largely determined at the plant, where processing and handling occurs. a
Once milk is collected from the farm, it is transported to processing plants where it undergoes a series of treatments to ensure that it is safe for consumption.
This includes pasteurization, homogenization, and standardization.
The pasteurization process involves heating the milk to a specific temperature for a certain amount of time to kill harmful bacteria.
Homogenization helps to evenly distribute the milk's fat content, while standardization ensures that the milk meets certain regulatory requirements for fat content and nutritional value.
The plant, milk undergoes rigorous quality control testing to ensure that it meets certain standards.
This includes testing for bacterial count, somatic cell count, and antibiotic residue.
Any milk that fails to meet these standards is discarded.
The USDA and FDA also play a role in ensuring that milk reaching consumers is of high quality.
The USDA sets standards for milk production, while the FDA regulates the use of antibiotics and other drugs in milk production.
The primary responsibility for ensuring milk quality rests with the processing plant.
The USDA and FDA do play a role in ensuring the quality of milk reaching consumers, the majority of the responsibility lies with the processing plant.
It is at the plant where the milk undergoes treatments to ensure that it is safe for consumption and undergoes rigorous quality control testing to meet certain standards.
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Deondra is going to invest $64,000 and leave it in an account for 5 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $82,000?
Answer:
To the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount (in this case, $82,000)
P = the principal (the initial investment, in this case, $64,000)
r = the interest rate (what we're trying to find)
n = the number of times the interest is compounded per year (in this case, 4, since it's compounded quarterly)
t = the number of years (in this case, 5)
Plugging in the values we know and solving for r, we get:
$82,000 = $64,000(1 + r/4)^(4*5)
$82,000/$64,000 = (1 + r/4)^20
1.28125 = (1 + r/4)^20
Taking the 20th root of both sides, we get:
(1.28125)^(1/20) = 1 + r/4
0.0167 = r/4
r = 0.0668 (rounded to four decimal places)
Therefore, to the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.
Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
Polynomials expression explained.
A polynomial expression is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. The term "polynomial" comes from the fact that the expression can be thought of as a sum of many terms, each of which is a product of one or more variables raised to a non-negative integer power.
For example, the expression 3x^2 + 4x - 1 is a polynomial in one variable, x, with three terms. The first term is 3x^2, the second term is 4x, and the third term is -1. The highest power of the variable in this expression is 2, which makes it a polynomial of degree 2.
Polynomial expressions can be written in standard form, where the terms are arranged in descending order of degree and the coefficients are written with the highest power of the variable first. For example, the expression above could be written in standard form as 3x^2 + 4x - 1.
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
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6(4x - 3) > 30
need help pls?
Answer:
[tex]6(4x - 3) > 30 \\ divide \: both \: sides \: of \: the \: \\ inequality \: by \: 6 \\ = 4x - 3 > 5 \\ = 4x > 5 + 3 \\ = 4x > 8 \\ = x > \frac{8}{4} \\ = x > 2[/tex]
hope it helps
2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
-5
N
The answer of the given question based on the rectangle is , The MNOP congruence is shown by Side-Angle-Side (SAS) and the steps are given below.
What is Diagonal?In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon or a polyhedron. In other words, a diagonal is a line segment that joins two corners or vertices of a shape that are not next to each other. For example, in a rectangle, the diagonals are the line segments that connect opposite corners of the rectangle.
To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following steps:
Draw the diagonal MO and the diagonal NP.Since MNOP is a rectangle, we know that angles M and N, as well as angles O and P, are right angles. Therefore, we have four right triangles: triangle MNO, triangle NOP, triangle OPM, and triangle PMN.Since each of these triangles shares side OP, we can use the Side-Angle-Side (SAS) congruence criterion to show that triangles MNO and OPM are congruent, and triangles NOP and PMN are congruent.Since these triangles are congruent, we know that their corresponding sides are congruent. In particular, we know that segment MP is congruent to segment NO.Since MO and NP intersect at point Q, we know that Q is the midpoint of both segments MO and NP. Therefore, the diagonals of rectangle MNOP bisect each other.Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent.
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(I NEED THIS ASAP)
3. Select all the transformations that produce congruent images.
(A.) dilation
(B.) horizontal stretch
(C.) reflection
(D.) rotation
(E.) translation
(C.) reflection and (D.) rotation produce congruent images.
What three transformations are congruent?
We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.
(A) Dilation, (B) horizontal stretch, and (E) translation do not produce congruent images because they change the size, shape, and/or orientation of the original object.
(C) Reflection produces congruent images because the resulting image is a mirror image of the original object, and therefore has the same size and shape.
(D) Rotation produces congruent images because the resulting image is the same shape and size as the original object, just rotated to a different orientation.
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The function y=5. 45+1. 05(x+7) can be used to determine the cost in dollars for a prepaid cell phone plan of x minutes What is the rate of change with respect to the number of minutes purchased
According to the function, the rate of change with respect to the number of minutes purchased is $1.05 per minute.
The function given in the problem is y = 5.45 + 1.05(x + 7), where y represents the cost in dollars for a prepaid cell phone plan of x minutes. This means that if you want to know how much it will cost to purchase a certain number of minutes, you can simply plug in that number for x and the equation will give you the corresponding cost in dollars.
Now, the rate of change with respect to the number of minutes purchased is also known as the slope of the function. This tells us how much the cost will change for each additional minute purchased. To find the slope, we need to take the derivative of the function with respect to x.
The derivative of y with respect to x is given by:
dy/dx = 1.05
This means that for each additional minute purchased, the cost will increase by $1.05.
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Classify each number below as an integer or not.
Whoever answers it first ill give u brainliest
And if you dont figure the question ill report you so please help me
Answer:-91 is an integer
1/2 is not an integer
51 is an integer
-6/2 is not an integer
-99.34 is an integer
Step-by-step explanation: An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Answer:
-91 - yes
1/2 - no
51 - yes
-6/2 - yes
-99.34 - no
ASAP PLEASE!
1.
Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 3.8, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 2.4, 2.1
Determine the scale factor used.
one half
2
one fourth
3
2.
Question 4(Multiple Choice Worth 2 points)
(Dilations MC)
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.
6
one sixth
3
one third
The first option, "one half," corresponds to the scale factor of 0.5.
How to find the scale factor?Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.
We can contrast the side lengths of triangles D and D′ to determine the scaling factor.
Let's contrast the side lengths for the two triangles.
Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.
Scale factor = (Side length of triangle D′) / (Side length of triangle D)
Scale factor = 2.1 / 4.2
Scale factor = 0.5
The first option, "one half," corresponds to the scale factor of 0.5.
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the median home cost in the us in 1975 was $40,000. in 1990, an equivalent home cost $140,000. the trend continued into 2005 when the median home cost in the us was approximately $240,000. assuming that this data's relationship is steady in the future, what is a reasonable estimate of the median home cost in the us in 2025?
The reasonable estimate of the median home cost in the US in 2025 is $340,000
To assess the middle domestic taking a toll within the US in 2025, ready to utilize the verifiable drift and expect that the relationship between the middle domestic fetched and time (measured in a long time since 1975) is straight.
Let`s begin with calculating the rate of increment in median domestic fetched per year utilizing the information from 1975 to 2005. Ready to utilize the equation for the slant of a direct relapse line:
slant(slope) = (y2 - y1) / (x2 - x1)
where
y1 and y2 are the middle domestic costs in 1975 and 2005,
separately, and x1 and x2 are comparing a long time (0 and 30).
incline = ($240,000 - $40,000) / (30 - 0) = $6,000
This implies that the middle domestic taken a toll expanded by a normal of $6,000 per year amid this period.
Presently, ready to utilize this rate of increment to appraise the middle domestic taken a toll in 2025, which is 50 long times after 1975.
The year 2025 will be 50 a long time after 1975, so the number of a long time since 1975 will be x = 50. Utilizing the incline we fair calculated, able to assess the middle domestic fetched in 2025 as takes after
y = y1 + slant(slope) * x = $40,000 + $6,000 * 50 = $340,000
Therefore, a sensible assessment of the middle domestic taking a toll within the US in 2025, based on the presumption that the slant watched from 1975 to 2005 proceeds, is $340,000.
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To landscape his 70 ft by 60 ft backyard, Austin is planning first to put down a 4 inch layer of topsoil. He can buy bags of topsoil at $2.50 per 3-ft3 bag, with free delivery. Or he
can buy bulk topsoil for $22.00/yd, plus a $20 delivery fee. Which option is less expensive?
I need volume of soil, cost of bags and cost of bulk
Answer:
To calculate the volume of soil needed, we first convert the dimensions of the backyard to feet:
Length = 70 ft
Width = 60 ft
Depth = 4 in = 4/12 ft = 1/3 ft
Volume = Length x Width x Depth
Volume = 70 ft x 60 ft x (1/3) ft
Volume = 1400 ft³
Option 1: Bags of topsoil
Each bag of topsoil contains 3 ft³ of soil, so the number of bags needed is:
Number of bags = Volume / Bag size
Number of bags = 1400 ft³ / 3 ft³ per bag
Number of bags = 467 bags
The total cost of bags of topsoil is:
Cost = Number of bags x Cost per bag
Cost = 467 bags x $2.50 per bag
Cost = $1167.50
Option 2: Bulk topsoil
The volume of topsoil needed is 1400 ft³, which is equivalent to:
Volume = 1400 ft³ / 27 ft³ per yd³
Volume = 51.85 yd³ (rounded to two decimal places)
The cost of bulk topsoil is:
Cost = Volume x Cost per yd³ + Delivery fee
Cost = 51.85 yd³ x $22.00 per yd³ + $20.00 delivery fee
Cost = $1153.70
Therefore, buying bulk topsoil is less expensive than buying bags of topsoil. The cost of bulk topsoil is $1153.70, while the cost of bags of topsoil is $1167.50
Answer:
Bulk is less expensive
Step-by-step explanation:
First convert inches to feet: 4 in x 1 ft/12 in =0.333 ft
Volume of topsoil needed = 70 x 60 x 0.333 = 1400 ft³
Bagged topsoil: 1400 ft³ x $2.50/3 ft³ = $1166.67
Bulk: 1400 ft³ x 1 yd³/27 ft³ x $22.00/yd³ + $20 = $1160.74
Bulk is just a little cheaper
Estimate the measure of this
angle within 15°
Surface area of rectangular pyramid 2(½ ×w×h)+2(½×l×h)+(l×w)
The first term represents area of the two triangular faces having base of pyramid, second term represents area of two triangular faces having length of the rectangle, third term represents area of rectangular base.
A rectangular pyramid is a solid figure with a rectangular base and four triangular faces that meet at a single point, known as the apex. To find the surface area of a rectangular pyramid, we need to calculate the area of each face and add them together.
The formula for the surface area of a rectangular pyramid is:
Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base)
The first term, 2(1/2 x base x height), represents the area of the two triangular faces that share the base of the pyramid. The second term, 2(1/2 x length x height), represents the area of the two triangular faces that share the length of the rectangle. The third term, (length x base), represents the area of the rectangular base.
By multiplying each term by its appropriate values and adding them together, we can find the total surface area of the rectangular pyramid.
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Complete question is:
Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base). Explain what each term represents?
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Question 7
O 500
An ice cream factory makes 200 quarts of ice cream in 10 hours. How many quarts could be made
in 36 hours?
O 720
360
9
620
The ice cream factory could make 720 quarts of ice cream in 36 hours.
How many quarts could be made in 36 hours?We can use a proportion to solve this problem:
quarts / hours = constant rate of production
Let x be the number of quarts that could be made in 36 hours. Then we have:
200 quarts / 10 hours = x quarts / 36 hours
Cross-multiplying, we get:
10x = 200 * 36
Simplifying, we get:
10x = 7200
Dividing both sides by 10, we get:
x = 720
Therefore, the ice cream factory could make 720 quarts of ice cream in 36 hours.
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The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. (b) What is the probability that the arrival time between vehicles is 12 seconds or less? (Round your answer to four decimal places.) (c) What is the probability that the arrival time between vehicles is 4 seconds or less? (Round your answer to four decimal places.) (d) What is the probability of 30 or more seconds between vehicle arrivals? (Round your answer to four decimal places.)
The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.6321.
Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1.
The exponential probability distribution with a mean of 12 seconds is given by
f(x) = (1/12) × e^(-x/12)
where x represents the time between arrivals of vehicles.
To find the probability that the arrival time between vehicles is 12 seconds or less, we need to integrate the probability density function from 0 to 12
P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] f(x)dx
= [tex]\int\limits^{12}_0[/tex] (1/12) × e^(-x/12) dx
= [(-e^(-x/12))]_[0,12]
= (-e^(-12/12)) - (-e^(0/12))
= 1 - e^(-1)
≈ 0.6321
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The given question is incomplete, the complete question is:
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. What is the probability that the arrival time between vehicles is 12 seconds or less?
find fy , the y-component of force that the wall exerts on the beam ( f ), using the axis shown. remember to pay attention to the direction that the wall exerts the force.
The y-component of the force that the wall exerts on the beam (f) is -400.5 N.
The y-component of the force that the wall exerts on the beam (f) can be found using the following steps:
Step 1: Calculate the magnitude of the force (f):
f = √[f_x² + f_y²]
f = √[(-500 N)² + (-300 N)²]
f = 600 N
Step 2: Calculate the angle of the force relative to the y-axis:
θ = tan-1(-300 N/500 N)
θ = -53.13°
Step 3: Calculate the y-component of the force (fy):
fy = f × sin(θ)
fy = 600 N × sin(-53.13°)
fy = -400.5 N
Therefore, the y-component of the force that the wall exerts on the beam (f) is -400.5 N.
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Rita’s adding 3+ -8+1 Siri writes the expression is 3+-1+8 what is Rita’s error
Answer: 3+(-8+1) or 3+-8+1
Step-by-step explanation: Rita rewrote the equation so instead of it being negative 8 it is negative 1.
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The average rate of change of each function on the interval 2 ≤ x ≤ 6 is given as follows:
f(x): -1.25.g(x): -0.715.How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For the function f(x), we have that:
When x = 2, y = 7.When x = 6, y = 2.Hence the rate is given as follows:
r = (2 - 7)/(6 - 2)
r = -5/4
r = -1.25.
For the function g(x), we have that:
When x = 2, y = 2(-5/7) - 6 = -7.43.When x = 6, y = 6(-5/7) - 6 = -10.29.Hence the rate is given as follows:
r = (-10.29 - (-7.43))/(6 - 2)
r = -0.715
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The circumference of a circle is 7(pie)cm. What is the area, in square centimeters?
Express your answer in terms of TT(pie).