Hello!
To expand:
==> we must multiply each variable with each other
[tex](x+2)(x+1)=x*x+x*1+2*x+2*1=x^2+x+2x+2=x^2+3x+2[/tex]
Thus: when (x+2)(x+1) is expanded and simplified
==> [tex]x^2+3x+2[/tex]
Answer:
Step-by-step explanation: First we will expand so
x times x = x^2
x times 1 = x ( don’t need to put 1 in front)
2 times x is = 2x
2 times 1 = 2
Now we line them all up and look out if there are any like terms.
x^2 + x + 2x + 2 = x^2 +3x + 2
at a sale, a sofa is being sold for of the regular price 33% the sale price is 184.80 what is the regular price?
The regular price is 275.82, according to given question.
What do you mean by regular price?
Regular price is the cost at which a provider continuously and actively sells goods or services to the general public over an extended period of time.
According to data in the given question,
We have the given information:
Sale discount 33% and the sale price 184.80.
Now, we will calculate the regular price:
Let Regular Price = x
33% Discount of x = 33/100 * x
33% Discount of x = 33x/100
Regular price - 33% Discount = Sale price
x-33x/100=184.80
(100x-33x)/100=184.80
67x/100=184.80
67x=18480
x=18480/67
x=275.82
Therefore, the regular price is 275.82.
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Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector
This set is closed under scalar multiplications. Statement 1 is false.
This set is a subspace. This statement is also false because this set does not contain a zero vector so it is not a subspace.
This set is closed under vector addition. This is false. Because let v and w be two vectors such that v=(v1,v2); w=(w1,w2).
The set contains the zero vector. Statement 4 is false because the sum of two zero vectors cannot be equal to 1.
Since v and w are vectors satisfying the condition of space so v1+v2=1;w1+w2=1
Now we check whether v+w also belongs to the same space or not.
v+w=(v1,v2)+(w1,w2)=(v1+w1, v2+w2)
We shall check whether components of v+w also add up to 1.
v1+w1+v2+w2=v1+v2+w1+w2=1+1=2
So it means that this space is not closed under addition too.
Consider a vector v=(v1,v2) from the space.
Obviously v1+v2=1
Now let us take a constant 'c' and consider the behavior of
cv=c(v1,v2)=(cv1,cv2)
Now we check whether components of this vector add up to 1.
cv1+cv2=c(v1+v2)=c\neq 1
which clearly indicates that vectors of this space are not closed under scalar multiplication.
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Please help! Question below
The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.
What is meant by linear equation?A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.
Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.
Sodium contains in a can of soup is 300mg
Sodium contains in a can of frozen dinners is 450mg
Let the number of cans of soup purchased be x
Then, the number of frozen dinners purchased=x+5
Total sodium purchased=6000mg
So, 300x+450(x+5)=6000mg
Therefore, the system is 300x+450(x+5)=6000mg
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The top and bottom margin of a poter are 6 cm and the ide margin are each 4 cm. If the area of printed material on the poter i fixed at 380 quare centimeter, find the dimenion of the poter with the mallet area
The dimensions of the poster found having the smallest area is H = 35. 87 cm and W = 25.63 cm.
Explain the term rate change of area?We understand that we are attempting to find the minimum of both the area function because we are instructed to locate the smallest area.Let "W" represent the poster's overall width and "H" represent its overall height.Area A = H.W
Its printed material is either W - 4(2) or W - 8.
Its printed material is H - 6(2)
height = H - 12
The printed area is therefore (W - 8)(H - 12) = 380.
(W - 8)(H - 12) = 380
WH - 12W - 8H + 96 = 380
W(H - 12) - 8H = 284
W = (284 + 8H)/(H - 12)
Put the values in the area;
A(H) = H(284 + 8H)/(H - 12)
A(H) = (284H + 8H²)/(H - 12)
Differentiate with respect to H to find the rate change of area.
A'(H) = [(284 + 16H)(H - 12) - (284H + 8H²)(1)]/(H - 12)²
A'(H) = (284H - 3408 + 16H² - 192H - 284H - 8H²)/(H - 12)²
A'(H) = (8H² - 192H - 3408)/(H - 12)²
A'(H) = 8(H² - 24H - 426)/(H - 12)²
Put A'(H) = 0
8(H² - 24H - 426)/(H - 12)² = 0
Solving;
H = 35. 87 cm
Thus, W = 25.63 cm
Thus, the dimensions of the poster found having the smallest area is H = 35. 87 cm and W = 25.63 cm.
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1. From the window of one building, the angle of elevation to the top of a second building
is 41° and the angle of depression to the bottom is 54°. The buildings are 56 m apart.
a. How tall is the second building?
b. How high up is the window?
Answer:
a) the second building is 118.69 m tall
b) the height of the window from the ground is 70.077 m
Step-by-step explanation:
Attached is a sketch of the building. Look over the sketch before reading the explanation.
Use SOH CAH TOA.
Let [tex]O_{1}[/tex] be the height of the window from the ground.
Therefore we can say that [tex]O_{1}+O_{2}[/tex] is the height of the second building.
We can say that
[tex]O_{1}=tan(x_{1} )*A_{1}[/tex]
Therefore
[tex]O_{1}=tan(54)*56[/tex]
[tex]O_{1}=70.077[/tex]
[tex]O_{2}=tan(x_{2} )*A_{2}[/tex]
[tex]O_{2}=tan(41)*56[/tex]
[tex]O_{2} =48.68[/tex]
[tex]70.007+48.68=118.69[/tex]
By using compatible numbers, the estimate is
Use a calculator to multiply 92 × 12. What do you get?
Circle whether the estimates were all less than or greater than
the actual product.
Answer:
92*12=1104
Step-by-step explanation:
a probability distribution has a mean of 22 and a standard deviation of 2. use chebychev's inequality to estimate the probability that an outcome of the experiment lies between 13 and 31. a) 0.9506 b) 0.9917 c) 0.0494 d) 0.0083 e) 0.2222 f) none of the above
Using Chebychev's inequality the probability shows an outcome of the experiment between 13 and 31 is equal to 0.9506.
As given in the question,
Mean 'μ' = 22
Standard deviation 'σ' = 2
Apply Chebychev's inequality we have,
P ( | X - μ | ≤ kσ ) ≥ 1 - (1/k²)
Where 'k' is the constant value.
Estimation of probability with outcome lies between 13 and 31 using Chebychev's inequality is :
P ( 13 < X < 31 )
= P ( 13 -22 < X - μ < 31 - 22 )
= P ( -9 < X - μ < 9 )
= P ( | X - μ |≤ 9)
= P [ |X - μ | ≤ (9/2) ×2 ]
= P( |X - μ | ≤ Kσ)
≥ 1 - ( 1/k²)
here k = 9/2
= 1 - (1 / (9/2)²)
= 1 - 4/81
= (81 -4) / 81
= 77/ 81
= 0.9506
Therefore, the probability for which outcome lies between 13 and 31 using Chebychev's inequality is equal to 0.9506.
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Ms. Apple bought a new chair that was 25% off and saved $14. What was the sale price of the chair? What was the original price?
Answer:
Original price was $56
Step-by-step explanation:
If $14 is 25% then to find 100% multiply $14 by 4
then you will get $56
1.numbers going up in value descending order 2.the number being divided dividend 3.numbers going down in value estimation 4.an approximate value close to the actual value divisor 5.the number divided by ascending order
1. Numbers going up in value - Ascending order
2. The number being divided - Dividend
3. Numbers going down in value - Descending order
4. An approximate value close to the actual value - Estimation
5. The number divided by - Divisor
When the value of numbers is increasing then it's said to be in ascending order. Similarly, when the value of numbers is decreasing then it's said to be in descending order.
The number which is getting divided is called a dividend and the number through which we divide the dividend is called the divisor.
Estimation is said to be the approximate value or the value which is close to the actual value.
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The complete question is -
Match the following-
1. numbers going up in value
2. the number being divided
3. numbers going down in value
4. an approximate value close to the actual value
5. the number divided by
Options - descending order, dividend, estimation, divisor, ascending order.
A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
Using the equation y=x/4+16, it is possible to estimate how many minutes will pass after 4:00 pm when she reaches her destination.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Let x be the time of original flight before delay.
Let y be the new time of flight after delay.
She will to arrive 4 times faster that in original flight time,
y=x/4
The flight is delayed by 16 minutes,
y=x/4+16
The equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination will be y=x/4+16.
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Answer:b
Step-by-step explanation: did the test
kyra's math instructor told the class to refer to the unit conversion charts in the textbook when completing the homework assignment. however, she discovered that these charts weren't in the assigned chapter. where will kyra most likely find the unit conversion charts in her math textbook?
Kylie will most likely find the unit conversion charts in the appendix of her math textbook.
The correct answer option is option C
What is an appendix?An appendix can be defined as a text that is added to the end of a book or an article which provides additional information that was best left as an addition or complement at the end rather than being included somewhere in the book or article, that is, appendix is an information supplementing the texts. The plural form of appendix is appendicitis.
Foreword: This is an introductory section preceding the main text of a book or other document, also known as a preface or introduction.
Introduction: An initial section of a book or article, which introduces the subject material.
Glossary: This is a list of terms in a particular domain of knowledge with their definitions.
Complete question:
Kylie's math instructor told the class to refer to the unit conversion charts in the textbook when completing the homework assignment. However, she discovered that these charts weren't in the assigned chapter. Where will Kylie MOST likely find the unit conversion charts in her math textbook?
A. Foreword
B. Introduction
C. Appendix
D. Glossary
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There are 60 seconds in a minute and 60 minutes in an hour. How many seconds are in one hour?
Answer:
3600
Step-by-step explanation:
we just have to multiply 60 by 60.
the mean and standard deviation of the heights of american women are 63.8 inches and 4 inches, respectively. find an approximate probability that the mean height of a randomly selected 100 american women is between 63 and 64 inches (round off to second decimal place).
The probability that the mean height of the American women is between 63 and 64 is 0.6687
The probability of an event occurring is defined by probability. There are numerous instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.
Mean = 63.8
S = 4
n = 100
P(63 <=X-bar<=64) = P(63.638/4/[tex]\sqrt{100}[/tex] < z < 64.638/4/[tex]\sqrt{100}[/tex])
=P(0.2 < z < 0.5)
=P(z<0.5) - P(z<-2)
0.6915 - 0.0228
0.6687
So, the probability is 0.6687
p-values from the z table
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At a candy store, erika bought kilograms of cinnamon red hots and kilogram of gummy bears for. Meanwhile, irene bought kilograms of cinnamon red hots and kilograms of gummy bears for. What is the cost of one kilogram of each type of candy?.
The cost of one kilogram of each type of candy is 9 dollars per kilogram and 4 dollars per kilogram.
Given that,
Erika spent $21.00 at a candy store to purchase 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears. Irene spent $39.00 on 3 kilograms of gummy bears and 3 kilograms of cinnamon red hots.
We have to find how much would one kilogram of each kind of candy cost.
We know that,
Let's change the price of cinnamon red hots per kg to c and the price of gummy bears per kg to b.
3c+1b=21
3c+3b=39
By substitution method
-3c-b=-21 (Multiply one of the equation's terms by -1 to eliminate c.)
3c+3b=39
We get
2b=18
b=9 dollars per kilogram
To find c you can plug the value of b back into one of the equation above and 3c+9=21 which lead to 3c =12 so c=4 dollars per kilogram.
Therefore, the cost of one kilogram of each type of candy is 9 dollars per kilogram and 4 dollars per kilogram.
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day weight (ounces) monday 23 22 23 24 tuesday 23 21 19 21 wednesday 20 19 20 21 thursday 18 19 20 19 friday 18 20 22 20 what is the mean of the sampling distribution of sample means when this process is in control?
The value of the required mean of the sampling distribution of sample means is approx. 21 ounces when this process is in control.
Sample mean: The arithmetic mean of the values of the variables in the sample. If the samples are drawn from probability distributions with a common expected value, the sample mean is an estimate of that expected value.
Sample means for all days using formula,
Monday = (23+22+23+24)/4 = 23
Tuesday = (23+21+19+21)/4 = 21
Wednesday = (20+19+20+21)/4 = 20
Thursday = (18+19+20+19)/4 = 19
Friday = (18+20+22+20)/4 = 20
We have to calculate the mean of sampling distribution of sample means.
Mean of the sampling distribution of sample means = Sum of sample means of all days / Number of days
= (23+21+20+19+20)/5
= 20.6 = 21 ounces
Hence, the required mean is approx. 21 ounces.
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Suppose a school has three periods (called 1, 2, and 3) during which a class can be scheduled. For each class, there are three variables. For example, for class A, there are variables XA1, XA2, and XA3. Setting XA2 = 1 represent scheduling class A during period 2. a. give a boolean expression that evaluates to 1 if and only if a is scheduled in at least one of the three periods.
The boolean expression that evaluates to 1 if and only if A is schedule in at least one of the three periods is [tex]x_{ A1}+x_{ A2} +x_{ A3}[/tex].
A logical assertion that can only be TRUE or FALSE is called a Boolean expression. As long as both sides of the expression have the same fundamental data type, boolean expressions can compare data of any kind. Data can be tested to check if it is more than, less than, or equal to other data.
An expression that may only be evaluated as true or false is called a boolean expression (after mathematician George Boole). Let's examine some examples in everyday language: Pink is one of my favorite colors. I'm apprehensive about programming computers. • It's entertaining to read this book.
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Solve -6 = a/-4 the a/-4 is in fraction form by the way
Answer:
a = 24
Step-by-step explanation:
1. Multiply all terms by the same value to eliminate fraction denominators
-6 = [tex]\frac{a}{-4}[/tex]
-4(-6) = -4 · [tex]\frac{a}{-4}[/tex]
2. Cancel multiplied terms that are in the denominator
-4(-6) = -4 · [tex]\frac{a}{-4}[/tex]
-4(-6) = a
3. Multiply the numbers
-4(-6) = a
24 = a
4. Move the variable to the left
24 = a
a = 24
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the purpose of a short-term measurement is to substitute for a long-term measurement. for this purpose, which do you think is more relevant, the confidence interval or the prediction interval? explain.
Prediction interval is more relevant than confidence interval.
Given,
Short term measures;-
Short-term actions and choices undoubtedly serve as significant beginning points for both concrete accomplishments and symbolic commitments. Several short-term actions appear to have the best potential of moving in the direction of wise growth over the long run, taking into account the obstacles, strengths, and weaknesses that have been identified.
Long term measures;-
Long-Term Performance Measures refers to the performance indicators created and used by the Committee to assess the Company's performance in order to determine the number of shares of Common Stock that will be paid to the Participant at the conclusion of a Restriction Period.
Here,
Prediction intervals must take into consideration both the random variation of the individual values and the uncertainty in predicting the population mean. Consequently, a prediction interval is always larger than a confidence interval. Additionally, as the sample size grows, the prediction interval won't condense to a single value.
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Lin runs 5 laps around a track in 6 minutes
a. How many minutes per lap is that
Answer: 0.83 laps per minute.
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.83 is the answer
Suzy is competing in a long-distance au
bicycle race. In the first 6 hours, she completed 132 miles of the race. If she
plans to ride 7 hours per day, how many
days will it take for her to complete the
616-mile race at the same rate?
A 2
B 4
C 6
D 8
Alina invests $1300 in one account and $1200 in an account paying 2 % higher interest. At the end of one year she had earned $99 in interest. At what rates did she invest?
Answer:
3%
Step-by-step explanation:
Apply distributive property as shown on all products-
All equations need to be distributed equally
x=3%
As shown, this should be what you do...
It's fine if you don't, but a little birdie said you should, just sayin'...
1300x+1200(x+0.02)=99
Rearrange
2500x+24=99
2500=75
[tex]75/100\\Properties[/tex]
[tex]3/100\\Prioritized(mathematically)[/tex]
Determine whether the given point is on the line. Explain your reasoning. (6, -2); y= 1/2x-5
The point (6, -2) lie on the given line segment y= 1/2x-5.
What is point and line segment?A point denotes exact location on any surface,
and the collection of points in the definite pattern is called line.
So, every line itself have infinite points.
Given point = (6, -2)
Hence, the given line = y= 1/2x-5
So, to find whether any point is on the line or not,
we have to put the point on line.
If it satisfies it will lie on line segment.
If not it will not pass through given line segment.
y= 1/2x-5
Putting x= 6 and y= -2
-2 = 3- 5
Hence, -2 = -2
Hence the (6, -2) lie on the given line segment y= 1/2x-5
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254.4 / 0.001 what is the solution?
Answer: 254400
Step-by-step explanation:
We notice that dividing by 0.001 is the same as multiplying by 1000.
So we take 254.4 timed 1000= 254400
Answer:
254,400
Step-by-step explanation:
1. Count how many zeros are in 0.001
0.001 = 3 zeros
2. Move the decimal point according to the zeros
(There are 3 zeros, so move the decimal point to the right 3 times):
254.4
2,544.
25,440.
254,400
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? select two options. x2 (y – 3)2 = 36 x2 (y – 5)2 = 6 (x – 4)² y² = 36 (x 6)² y² = 144 x2 (y 8)2 = 36
The equation of the circle on the y-axis is x² +(y-3)² = 36.
Here we have to find the equation of the circle
Data provided:
diameter(d) = 12 units
so radius(r) = 6 units
The center lies on the y-axis
The general equation of the circle:
(x-x1)² + (y - y1)² = r²
where (x1, y1) is the point on the circle.
So by putting x1 = 0 and y1 = 3 and r = 6 as the center lies of y-axis
x² + ( y - 3)² = 6²
x² + (y-3)² = 36
Therefore we get the equation as x² + (y-3)² = 36
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A triangle has 2 angles that measure 60 degrees, what is the measurement of the opposite exterior angle?
Answer:
Step-by-step explanation:
Helppp I need an answer fast
Answer:6
Step-by-step explanation: PQRS is 2x the size of ABCD
Rejecting the null hypothesis when it is true is called a ________ error, whereas not rejecting a false null hypothesis is called a ________ error.
a. Type II; Type I
b. Type I; Type II
c. minor; major
d. significant; nonsignificant
The correct option is b.Type I; Type II.
Rejecting the null hypothesis when it is true is called a type I error, whereas not rejecting a false null hypothesis is called a u type II error.
A type I error occurs when a null hypothesis that is true in the population is rejected. A false positive is an example of this type of error. A type II error occurs if a null hypothesis that is actually false in the population is not rejected. This type of error is known as a false negative.A type II error differs from a type I error in that a type I error rejects the null hypothesis when it is true (i.e., a false positive). The likelihood of making a type I error is equal to the level of significance set for the hypothesis test.
Thus, for the given question, option. b is the correct answer for the blanks in the question.
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Another karaoke location, Sounds of the Sea, is charging $15 for 5 songs. Construct a graph to model the relationship between cost and number of songs.
The function that represent the proportional relationship between cost and number of songs is y = 3x and it's graph is attached below
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
'm' is the slope of the line'b' is the y-intercept of the line'x' is the independent variable'y' (or f(x)) is the dependent variableTo find the relationship between cost and number of songs, we can write a proportional relationship for this
y = mx
m = constant of proportionality
15 = m(5)
m = 15 / 5
m = 3
The constant of proportionality is 3
The function to represent the relationship between the cost and number of songs is
y = 3x
The graph of the function is attached below
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Given f(x) = |x|, g(x)=|x+4|-2 is what kind of
transformation ?
The transformation of the function g ( x ) = | x + 4 | - 2 is
Horizontal shift : Left by 4 units
Vertical shift : Down by 2 units
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching shift:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be f ( x )
The value of f ( x ) = | x |
Now , the transformation from the first function f ( x ) to g ( x ) is of the form
g ( x ) = | x + 4 | - 2
And , transformation is
y = a | x - h | + k
where the values of y , a , x , h and k are
The value of a = 1
The value of h = -4
The value of k = -2
Now , The Horizontal shift is given by
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
So , h = -4 means left shift by 4 units
And , The Vertical shift is given by
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
So , k = -2 means down shift by 2 units
Hence , The transformation of the function g ( x ) = | x + 4 | - 2 is
Horizontal shift : Left by 4 units
Vertical shift : Down by 2 units
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the difference of two numbers is 6 . two times the smaller is 3 more than the larger. find the two numbers.
The larger number is 15 and the smaller number is 9.
What is substitution method?
In order to solve a system of equations, the substitution method is typically used in mathematics. This approach involves first solving the equation for one variable, then changing the value of the variable in the second equation.
Suppose
'a' be the larger number and 'b' be the smaller number.
As the difference of two numbers is 6.
⇒ a - b = 6 ..(1)
As two times the smaller is 3 more than the larger.
⇒ 2b = 3 + a ..(2)
From equation (2),
a = 2b - 3
Substitute the value of 'a' in equation (1)
2b - 3 - b = 6
b - 3 = 6
b = 6 + 3
b = 9
Substitute b = 9 in equation (1),
a - 9 = 6
a = 6 + 9
a = 15
Hence, the larger number is 15 and the smaller number is 9.
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