Bob would take 5 hours to mow the law by himself.
Let us consider, the area of the lawn to be mowed to be x inch².
It is given that the law can be mowed by Abe alone in 3 hours.
We know that,
Rate of work = Work/Time
⇒ rate of work of Abe = area to be mowed(work)/time taken
= (x/3) inch²/hour
Now,
Abe has been working alone for 1/3 hour
⇒work done by Abe alone = rate of work of Abe x time
= (x/3) inch²/hour x 1/3 hour
= x/9 inch²
Remaining work = x - x/9 = 8x/9 inch²
Let, the rate of work of Bob be y inch²/hour.
It is given that the time taken by Abe and Bob to complete the remaining work together is 1 and 2/3 hours, i.e, 5/3 hours.
Therefore,
The rate of work of Abe and Bob when working together
= work ÷ time
=(8x/9) ÷ (5/3)
=8x/15 inch²/hour
⇒ Rate of work of Abe + Rate of work of Bob = 8x/15
⇒ x/3 + y = 8x/15
⇒ y = (8x/15) - (x/3)
⇒ y = 3x/15 = x/5 inch²/hour
Thus, the time taken by Bob to mow the law by himself
= work ÷ rate of work
= x inch² ÷ (x/5) inch²/hour
= 5 hours
So, it would take 5 hours for Bob to mow the lawn alone.
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the mass of a cylinder of water filled to the 19.65-ml mark was found to be 39.753 g. when a piece of the metal was immersed in the water, the level of the water rose to 20.37 ml and the mass of the cylinder with the metal was found to be____ 41.003 g.
The density of the unknown metal exists 8.9 g/mL.
What is meant by density?The mass of an object divided by its volume is how dense it is. The gram per cubic centimeter (g/cm³) unit of density is frequently used. How much mass is present in a given area is referred to as density. Try to picture a drawer full of socks. Its density is particular. Consider that when you remove a sock, the drawer's density changes. This is due to the socks' shifting mass while the drawer's remaining constant volume.
The definition of density is the mass of a substance per unit volume. The degree to which matter is packed together is fundamentally measured by density. It is a specific physical quality of a specific object. Greek scientist Archimedes is credited with discovering the density principle.
The density (D) is equal to mass (m) divided by volume (V): D = m/V
To find the mass of the object:
m = 156 g - 105.5 g = 50.5 g
To find the volume of the volume:
V = 30.7 mL - 25 mL = 5.7 mL
The density is:
D = m/V = 50.5 g / 5.7 mL = 8.9 g/mL
Therefore, the density exists 8.9 g/mL.
The complete question is:
A graduated cylinder was filled with water to the 25.0 mL mark and weighed. Its mass was 105.5g. An object made of an unknown metal was placed in the cylinder and completely submerged in the water. The water level rose to 30.7 mL. When reweighed, the cylinder, water and metal object had a total mass of 156.0g. Based on these measurement, what is the density of the unknown metal?
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I don’t understand this help?
Answer:
the first expression i think is the line going downwards
and the second is the line going upwards
Step-by-step explanation:
i think sorry if it wrong
hope the annotating will help you! If this is not the thing you want let me know so that I can edit the way the question actually is...
We want to find how the volume. V. of a balloon changes as it is filled with air. We know V(r)=4/3 πr^3, wherer is the radius in inches and V(r) is in cubic inches. The expression v(3)-v(1)/3-1 represents (a) The average rate of change of the radius with respect to the volume when the radius changes from 1 inch to 3 inches. (b) The average rate of change of the radius with respect to the volume when the volume changes from 1 cubic inch to 3 cubic inches. (c) The average rate of change of the volume with respect to the radius when the radius changes from 1 inch to 3 inches. (d) The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches.
Option D is the correct answer that is The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches.
The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches is represented in v(3)-v(1)/3-1.
The difference in volumes is
V(r+3) - V(r) = 4π [tex](r+3)^{3}[/tex] /3 - 4π [tex]r^3}[/tex]/3
= 4π/3( (r+3)[tex]^{3}[/tex] - [tex]r^{3}[/tex])
= 4π/3( [tex]r^{3}[/tex]+ 9[tex]r^{2}[/tex]+ 27r + 27 - r∧3 )
= 4π/3(9 [tex]3^{3}[/tex] + 27r + 27 )
= 12π( [tex]r^{2}[/tex]+ 3r + 3 ) in cube
A balloon is a sphere shape. A sphere is a solid figure where each endpoint is equidistant from the center. It is like a 3-Dimensional version of a circle shape. The volume of a sphere is 4/3πr∧3 and its surface area is 4πr∧2. Here r is the radius of the sphere.
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skee ball refer to exercise 4. make a histogram of the probability distribution. describe its shape.
Ten to fifty is the range of the scores. The most frequent result is a 10 with a right-skewing bias.
Probability histogram
The height of each bar must be equal to the probability, the width of each bar must be the same, and the bars must be centered on the amount of money gathered.
The distribution is skewed to the right because the highest bar in the histogram is to the left and there is a tail of lower bars to its right.
The most frequent score is 10 due to the fact that the top bar in the histogram is centered at 10.
The result is:
Ten to fifty is the range of the scores.
The most frequent result is a 10 with a right-skewing bias.
Ten to fifty is the range of the scores.
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Helen is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $90. Helen will be earning a base salary of $55 per month from the gym, plus an additional $5 for every class she teaches. If Helen teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How many classes will that take? How much will Helen's expenses and earnings be?
To earn back the amount Helen spent on certification, she would need to earn $90. Since her base salary is $55 per month, she would need to teach an additional $90 - $55 = $35 in classes. Since she earns $5 per class, she would need to teach $35 / $5 = 7 classes.
So, Helen will need to teach 7 classes to earn back the amount she spent on certification.
Her total earning for teaching 7 classes would be $55 (base salary) + $5 (per class) * 7 (classes) = $110
Therefore Helen's expenses and earning would be $90 (certification cost) and $110 (earning) respectively.
What equation does this set of algebra tiles represent? x 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 Combine like terms on each side of the equation. For example, write 3 instead of 1 + 1 + 1. Like u don’t understand it at all can anyone help meeeeeeee””””””
The required solution of the given algebraic expression is x = 6.
What is an algebraic expression?The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.
Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1 = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1
Combining like terms on each side of the equation, we get,
According to the question
x + 7 = 13
x = 6
Thus, the required solution of the given algebraic expression is x = 6.
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Answer:
x + 7 = 13
Step-by-step explanation:
(in case you also need it) x = 6
during the first four summer olympic games attended by the united states, these medal counts were awarded. calculate the mean number of medals won during these olympic games. (round it to the nearest whole number.)
The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.
1904: 78 medals
1908: 82 medals
1912: 88 medals
1920: 94 medals
Mean = 86 medals
1. Add the total number of medals awarded to the US during the first four summer Olympic Games: 78 + 82 + 88 + 94 = 342
2. Divide the total number of medals by the number of Olympic Games (4): 342 / 4 = 85.5
3. Round the mean to the nearest whole number: 86 medals
The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.
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Use the given information to determine the number of elements in each of the four disjoint subsets in the following Venn diagram: n BAnBA' nB n(A) = 20 n(B) = 50, n(A nB) = 0, n(U) = 200 4' nB' (A) Find n(An B): n(An B) = (B) Find n(A n B'): n(Anb) = (C) Find n(A' n B): n(A' n B) =Ml (D) Find n(A' n B') n(A' 0 B') =
The value of the following venn expressions of sets is (A)=1 ,(B)=50,(C)=20 and (D)=130 respectively.
A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.
Symmetric difference between two sets A and B defined by,
AΔB=(A\B) ∪ (B\A)
AΔB=(A∩B') ∪(A'∩B).
we have n(A)=20 n(B)=50, n(A∩B)=0, n(U)=200
SO,
(A) Find n(A∩B)
n(A∩B) =0 (GIVEN)
(B) Find n(A∩B')
n(A∩B') =n(B)-n(A∩B)
= 50-0
=50
(C) Find n(A∩B')
n(A'∩B) =n(A)-n(A∩B)
=20-0
=20
(D) n(A'∩B') =n(U)-n(A'∩B)-n(A∩B)-n(A∩B')
=200-20-0-50
= 130.
thus, the above is the value of expression.
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QUICK I’LL MARK YOU BRAINLIEST!!
5-142. Use the similar figures at right to answer the questions.
1. What is the scale factor?______
2. Find the lengths of the missing sides on the similar shapes below.
X=______ Y=_______ Z=_____
Answer:
Z = 22.5, Y = 81, X = 26.7
Step-by-step explanation:
Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.
[tex]Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7[/tex]
The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized
deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,562.
Assume that the standard deviation is a $2167. Use z-table.
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample
mean within $157 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to
four decimals.
n = 30
n = 50
n = 100
n = 400
b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four
decimals.
A larger sample increases
for a
the probability that the sample mean will be within a specified distance of the population
mean. In this instance, the probability of being within 157 of μ ranges from
for a sample of size 30 to
sample of size 400.
A. The probability that a sample of taxpayers from this income group are:
n = 30: 0.8159
n = 50: 0.8796
n = 100: 0.9332
n = 400: 0.9984
B. Advantages of a larger sample size are:
it increases precision
reliability of estimate of the population mean
standard error of the mean decreases
How do we determine the probabilities?Using the z-score below:
For a sample size of 30, the z-score is 1.28.
For a sample size of 50, the z-score is 1.64.
For a sample size of 100, the z-score is 2.33.
For a sample size of 400, the z-score is 3.29.
a. The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $157 of the population mean for each of the following sample sizes:
n = 30: 0.8159
n = 50: 0.8796
n = 100: 0.9332
n = 400: 0.9984
b. The advantage of a larger sample size when attempting to estimate the population mean is that it increases the precision and accuracy of the estimate. As the sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the standard error of the mean decreases.
In this case, as the sample size increases from 30 to 400, the probability of the sample mean being within 157 of the population mean increases from 0.8159 to 0.9984.
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determine the number of cycles per day and the production quantity per cycle for this set of vehicles: product daily quantity a 18 b 16 c 6 d 14 click here for the excel data file use the sequence a-b-c-d.
The number of cycles per day and the production quantity per cycle.
Number of cycles per day = (Product Daily Quantity/Production Quantity per Cycle)
For Product A:
Number of cycles per day = (18/Production Quantity per Cycle)
For Product B:
Number of cycles per day = (16/Production Quantity per Cycle)
For Product C:
Number of cycles per day = (6/Production Quantity per Cycle)
For Product D:
Number of cycles per day = (14/Production Quantity per Cycle)
Using the data from the excel file, we can calculate the production quantity per cycle and the number of cycles per day.
For Product A:
Production Quantity per Cycle = 18/3.75 = 4.8
Number of cycles per day = 3.75
For Product B:
Production Quantity per Cycle = 16/2.5 = 6.4
Number of cycles per day = 2.5
For Product C:
Production Quantity per Cycle = 6/1.5 = 4
Number of cycles per day = 1.5
For Product D:
Production Quantity per Cycle = 14/2.25 = 6.2
Number of cycles per day = 2.25
Therefore, for this set of vehicles, the number of cycles per day and the production quantity per cycle are as follows:
Product A: 3.75 cycles per day, 4.8 units per cycle
Product B: 2.5 cycles per day, 6.4 units per cycle
Product C: 1.5 cycles per day, 4 units per cycle
Product D: 2.25 cycles per day, 6.2 units per cycle
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The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
About 80 necklaces have more than 28 beads. Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.
P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)
P(x > 28) = P(x - 24 / 4 > 1)
P(x > 28) = 1 - ∅1
P(x > 28) = 1 - 0.8413
P(x > 28) = 0.1587
Multiply both sides by 500, then we have
500 P(x > 28) = 0.1587 × 500
500 P(x > 28) = 79.35
500 P(x > 28) ≈ 80
About 80 necklaces have more than 28 beads. Then the correct option is C.
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The missing options are given below.
A. About 24 devices have more than 28 beads.
B. About 48 necklaces have more than 28 beads.
C. About 80 necklaces have more than 28 beads.
D. About 96 necklaces have more than 28 beads.
If f(x)=5x^6-2x^2-5, then what is the remainder when f(x) is divided by x+2?
Answer:
To find the remainder when f(x) is divided by (x-a) , we substitute x = a in the polynomial f(x) and we get the remainder.
remainder = f(a)
In this case, we have f(x)=5x^6-2x^2-5, and x+2 is the divisor and we substitute x=-2
so, remainder = f(-2) = 5*(-2)^6-2*(-2)^2-5 = -643
So, the remainder when f(x) is divided by x+2 is -643
Triangle ABC has sides that are 6 cm and 11 cm.The third is represented by the inequality 5 < ×
if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that Triangle ABC has sides that are 6 cm and 11 cm
The third is represented by the inequality 5 < ×.
We know that the sum of sides of a triangle must be greater than the third side.
5<6+11
5<17
Hence, if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.
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Two investments totaling $64,500 produce an annual income of $3270. One investment yields 8% per year, while the other yields 2% per year. How much is invested at each rate?
Answer:
The amount invested at 8% is 64,500-32,000 = 32,500
Step-by-step explanation:
one investment: 3%, amount: x
the other: 8%, amount: 64,500-x because x is invested at 3%
0.03x+0.08(64,500-x) = 3,560
0.03x+5,160-0.08x = 3,560
-0.05x = -1,600 divide both sides by 0.05 and remember that -/- = +
x = 32,000 This is the amount invested at 3%
The amount invested at 8% is 64,500-32,000 = 32,500
f(x) 10 3 5 2 Let glx) be a twice differentiable function defined by another differentiable function f(x), such that 9 (2) = 21+ J' f (t) dt: Selected values of f(x) are given in the table above
The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.
f(x) 10 3 5 2 Let glx) be a twice differentiable function defined by another differentiable function f(x), such that 9 (2) = 21+ J' f (t) dt: Selected values of f(x) are given in the table above.
We can calculate g'(x) as follows:
g'(x) = 2f'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3
1. Start by taking the derivative of g(x) with respect to x. This is done using the chain rule, since g(x) is defined by another differentiable function f(x):
g'(x) = d/dx[21 + J' f(t) dt] = 2f'(x)
2. Now, substitute the function f(x) into the equation for g'(x):
g'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3
The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.
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The measure of a base angle of an isosceles tri-
angle is 13 more than 3 times the measure of the
vertex angle. How many degrees are in the vertex
angle?
The vertex angle of the isosceles triangle is 22°.
What is isosceles triangle?
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
We know that an isosceles triangle is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180degrees.
Base angle = 3vertex angle+13.
=> 2base angle + vertex angle = 180°
=> 2(3 vertex angle +13)+vertex angle = 180°
=> 6 vertex angle+26+vertex angle = 180
=> 7 vertex angle = 180-26
=> 7 vertex angle = 154
=> vertex angle = 154/7 = 22°.
Hence the vertex angle of the isosceles triangle is 22°.
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you have 10 bags full of coins. in each bag are infinite coins. but one bag is full of forgeries, and you can't remember which bag. but you do know that genuine coins weigh 1 gram, but forgeries weight 1.1 grams. you have to identify the bag with the forgeries in minimum readings. you are provided with a digital weighing machine.
If there are no forgeries, then total weight will be
= (1+2+3+4+5+6+7+8+9+10) = 55 grams
given that
they have 10 bags full of coins
in each bag are infinite coins.
but one bag is full of forgeries, and you can't remember which bag.
you know that genuine coins weigh= 1 gram
forgeries weight = 1.1 gram
now, we need to find which bag has forgeries in minimum readings
then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag
If there are no forgeries, then total weight will be
= (1+2+3+4+5+6+7+8+9+10) = 55 grams
Therefore total weight should be 55 grams if the total weight is more than 55 grams then it has forgeries coins
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Total weight=55gm ,then there is no forgeries coin bag
1 bag with forgeries = take 1 coin from first bag
from 2 bag = take 2 coin
and similarly with all 10 bags.....
from 10th bag = take 10 coin
if there is no forgeries ,then total weight = (1+2+3+4+5+6+7+8+9+10)
=55gm
If bag weight 55.3 than we know that there are 3 forgeries.
So total weight=55 ,then there is no forgeries coin bag if weight is more than 55 than there is forgeries coin.
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the present age of Neha is 4 times the age of a son for gives ago if her son is 14 years ago find the present age of Neha.
Answer:
I didn't understand the question
Step-by-step explanation:
I think u have written wrong question..
during the last 3 years consolidated oil company expanded its gasoline stations into convenience food stores (cfss) in an attempt to increase total sales revenue. the daily sales (in hundreds of dollars) from a random sample of 10 weekdays from one of its stores are:
One kind of average is the mean. It is calculated by dividing the total number of values in a list of values, such as measurements or numbers, by the total number of values in the list.
What is the mean in maths?There are various mean types in mathematics, particularly in statistics. Each mean helps to summarise a certain set of data, frequently to help determine the overall significance of a specific data set.The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.Given data :
a ) Mean =
x = [tex]\frac{\left \{ {{i=10} \atop {i=1}} \right.}{n} Xi[/tex] = 101 / 10 = 10.1 hundreds of dollars
The median is the 50th percentile To determine the location index for the median (2nd
quartile (p =50) we do the following:
The index is
i = [tex]\frac{p}{100}[/tex] (n) = [tex]\frac{50}{100}[/tex] (10) = 5 integer
Since the index, 5, is an integer, the 2nd quartile is determined by finding the average of
the 5th and 6th values from the lower or higher end of the sorted data. This is:
Median = [tex]Q_{2}[/tex] = [tex]\frac{10 + 11}{2}[/tex] = 10.5 hundreds of dollar
Mode = most frequently occurring observation = 11 hundreds of dollars ( two times )
Here i attached graph
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"
Can anyone help me solve this question?
Calculate sin 300° − cos 945° + tan(−675°) without using calculator �
Answer:
Step-by-step explanation:
sin 300° = sin (300° - 360°) = sin (-60°) = -sin 60° = -(1/2)
cos 945° = cos (945° - 360°) = cos (585°) = cos (-295°) = -cos 295°
tan (-675°) = -tan (675° - 360°) = -tan 315°
so
sin 300° − cos 945° + tan(−675°) = -(1/2) - (-cos 295°) + (-tan 315°)
It is not a trivial task to simplify the above equations without using a calculator.
= -(1/2) + cos 295° + tan 315°
As we know that cos(x) = cos(360°-x) = -cos(x) and tan(x) = -tan(360°-x) = -tan(x)
= -(1/2) - cos 295° - tan 315°
As we know that cos(295°) = cos(360°-65°) = cos(65°) and tan(315°) = tan(360°-45°) = tan(45°)
= -(1/2) - cos(65°) - tan(45°)
= -(1/2) - 0.4226 - 1
= -0.5 - 0.4226 - 1
= -1.4226
.
Zip codes are assigned by region. In Colorado, all zip codes begin with the number 7 while the second
digit is restricted to 1-5. There is no restrictions on the remaining digits. How many zip code combos
are there?
Answer:4999 combos
Step-by-step explanation:
max:75999
min:71000
*zip codes are 5 digits long
75999-71000=4999
graphing y ≥ |x| - 4?
The graph for the given mode function, y ≥ |x| - 4 is attached below.
What is a modulus function?In mathematics, the modulus function is a function for which any input value of x, output will be always positive
Given that,
The modulus function,
y ≥ |x| - 4
We can write given function in a following two ways-
y ≥ x - 4
y ≥ -x - 4
So, for any value of x
y should be greater than modulus functions value
Plotting graph for y ≥ x - 4
So first draw line x - 4
Now, here we have inequality sign
So left side region will be our desired space
Similarly, Plotting graph for y ≥ -x - 4
So first draw line -x - 4
Now, here we have inequality sign
So right side region will be our desired space
Hence, Graph is drawn for the given function
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which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?
The potential energy of the spring-mass system is equal to 1/2kx². Thus, figure I is a correct representation.
where x is the mass's deviation from the average location, or O.
Consequently, the graph would be symmetric about a vertical line that passes through O and would exhibit a quadratic variation with respect to x.
Thus, figure I is a correct representation.
The graph illustrates how the potential and kinetic energy of a block coupled to a spring that follows Hooke's law changes over time.
Due to the potential and kinetic energy's x2 variation, both graphs are parabolas.
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Given that the expression f(x)=2x³+px² 8x+q is exactly divisible by 2x²-7x+6, evaluate p and q and factorise completely
The values of p and q are given as follows:
p = 3.5, q = 6.
Hence the factored expression is given as follows:
2(x - 1.5)(x - 2)(x + 2).
How to obtain the values of p and q and factor the function?The function f(x) is divisible by 2x² - 7x + 6, which has the roots given as follows:
x = 1.5 and x = 2.
(using a quadratic equation calculator with coefficients a = 2, b = -7 and c = 6).
Hence the following relation holds true, considering the linear factors of the function:
2x³ + px² + 8x + q = 2(x - 1.5)(x - 2)(x - a).
In which a is the third root.
Hence:
2x³ + px² - 8x + q = 2(x² - 3.5x + 3)(x - a)
2x³ + px² - 8x + q = 2(x³ - x²(3.5 + a) + x(3.5a + 3) - 3a)
2x³ + px² - 8x + q = 2x³ - x²(7.5 + 2a) + x(7a + 6) - 3a.
Hence the system of equations is given as follows:
p = 7.5 + 2a.7a + 6 = -8.q = -3a.From the second equation, the value of a is given as follows:
7a = -14
a = -2
Then the value of q is given as follows:
q = -3a = 6.
The value of p is given as follows:
p = 7.5 - 4
p = 3.5
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An ice cream cone with a 2cm radius has a volume of 75.36 cubic cm how tall is the ice cream cone
Step-by-step explanation:
reading the question thoroughly, we find out that volume (V) and radius (r) of the cone is given, and we just have to find out the length (h) of the cone
V = πr²h/3
Putting the given values in place,
V = 75.36 cm³
V = 75.36 cm³r = 2 cm
V = 75.36 cm³r = 2 cmπ = 3.14
Now, since we calculating for h, we can interpret the formula in the terms of h, i.e.
h = 3V/(πr²)
h = 3×75.36/(3.14×2²)
h = 226.08/12.56
h = 18 cm
Thus, the height of the ice cream cone is 18cm
Hope this helped!
For statistics:a group of college a group of college students believes that herbal tea has restorative powers they test their Theory by making visits weekly to a nursing home they serve the residents tea after several months it's determined that the residents are more cheerful and healthy which of the following could be concluded from that study a there is some evidence that the herbal tea May improve ones emotional state the results could be completely convincing if a scientist had concluded the study rather than a group of college students be herbal tea does improve ones emotional state at least the residents of nursing homes see the results of the study are not convincing because only a local nursing home was used and only for a few months or D the results of the study are not convincing because the effects of herbal tea is confounded with several other factors
a. visits of the college students, b. herbal tea, d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.
What is herbal tea?Despite the name, herbal tea is not actually "tea" as these beverages typically do not contain the leaves or leaf buds of tea plants. Herbal teas are made from tisanes, which are blends or infusions of dried fruits, flowers, spices or herbs in water.
The lurking variable in this experiment is - a. visits of the college students.
The explanatory variable in this experiment is - b. herbal tea
Which of the following may be correctly concluded from this study - d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.
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Atmospheric pressure P
in pounds per square inch is represented by the formula P=14.7e−0.21x
, where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.164 pounds per square inch? (Hint: there are 5,280
feet in a mile)
The mountain is ___ feet high?
The peak of the mountain has a height of 14805 feet.
How to determine the height of a mountain according to atmospheric pressure model
In this problem we find the case of an exponential function for atmospheric pressure (p), in pounds per square inch, in terms of height (x), in miles, whose expression is introduced below:
[tex]p(x) = 14.7 \cdot e^{- 0.21\cdot x}[/tex], for x ≥ 0.
If we know that p(x) = 8.164 lb / in², then the height of the peak of a mountain is:
[tex]8.164 = 14.7\cdot e^{-0.21 \cdot x}[/tex]
[tex]0.555 = e^{-0.21\cdot x}[/tex]
Then, by relationship between exponential and logarithmic functions and logarithm properties:
㏑ 0.555 = - 0.21 · x · ㏑ 1
㏑ 0.555 = - 0.21 · x
x = - (1 / 0.21) · ㏑ 0.555
x ≈ 2.804
Finally, convert miles into feet:
x = 2.804 mi × (5,280 ft / 1 mi)
x = 14805.12 ft
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Given quad QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0).
What is the best name for quad QRST?
Square
Rectangle
Trapezoid
Kite
The best name for quadrilateral QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0) include the following: C. Trapezoid.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidNext, we would use an online graphing calculator to construct (plot) quadrilateral QRST on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral QRST on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a trapezoid.
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Help pls it’s imaginary numbers
Answer:
Why don't you use this app and take a picture and see if someone got the answer
