Explanation
[tex](10x+3)(2x+1)[/tex]Step 1
apply distributive property
[tex]\begin{gathered} (10x+3)(2x+1)=(10x\cdot2x)+(10x\cdot1)+(3\cdot2x)+(3\cdot1) \\ (10x+3)(2x+1)=20x^2+10x+6x+3 \end{gathered}[/tex]Step 2
add similar terms and order
[tex]\begin{gathered} (10x+3)(2x+1)=20x^2+10x+6x+3 \\ (10x+3)(2x+1)=20x^2+16x+3 \\ \text{the standard form is} \\ ax^2+bx+c,so \\ ax^2+bx+c\Rightarrow20x^2+16x+3 \end{gathered}[/tex]so, the answer is
[tex]20x^2+16x+3[/tex]I hope this helps you
Assume the TV warranty or replacement times for TV sets are normally distributed with a mean of 9.2 years and a standard deviation of 1.1 years. Find the probability that a randomly selected TV will have a replacement time of less than 6 years.
Firstly, let's draw a picture of the distribution:
Graphically, we want to calculate the blue area. To put it differently, we want to calculate
[tex]P(X<6).[/tex]To do this, we need to find the z-score associated with 6. We can calculate it by
[tex]\begin{gathered} z=\frac{6-\mu}{\sigma}\Rightarrow\begin{cases}\mu=\operatorname{mean} \\ \sigma=\text{standard deviation}\end{cases}, \\ \\ z=\frac{6-\mu}{\sigma}=\frac{6-9.2}{1.1}\approx-2.91. \end{gathered}[/tex]Now, we must check our favorite z-score table and look for the probability associated with the z-score we just found. It's 0.0018.
AnswerThe probability that a randomly selected TV will have a warranty of less than 6 years is 0.0018.
Sydney picked 28 raspberries and 35 blueberries to make two desserts.
She needs 4 raspberries for each raspberry tart and 5 blueberries for each
blueberry tart. She wants to know how many desserts she will be able to
make with the berries.
Answer:7 and
Step-by-step explanation:
Answer: 7 raspberry tarts and 7 blueberry tarts
Step-by-step explanation:
28 raspberries / 4 raspberries for each tart = 7 raspberry tarts
35 blueberries / 5 blueberries for each tart = 7 blueberry tarts
Which statement about nuclear fission is correct?(1 point)
Responses
Nuclear fission takes place in the nucleus of atoms.
Nuclear fission is used to generate water at nuclear power plants.
The fuel for nuclear fission is often helium.
Nuclear fission releases small amount of energy.
Answer:
(A) Nuclear fission takes place in the nucleus of atoms
Step-by-step explanation:
I took the test!
Please help me asap :)
Answer:
C = 62.8
Step-by-step explanation:
C = 2πr
π = 3.14
diameter = 20 ft
r = 10 ft
Get r or the radius by taking half of the diameter which is 20 ft and get 10 ft.
Plug this information in the formula and multiply to get C or the circumference.
C = 2(3.14)(10)
C = 62.8
f(x) = 4x3 + 6x2 – 3x – 4g(x) = 4x – 3Find (f - 9)(x).A. (f - g)(x) = 4x3 + 6x2 + x - 1B. (f - g)(x) = 4.23 + 6x2 – 7x – 7c. (f - g)(x) = 4x3 + 6x2 + x - 7O D. (f - g)(x) = 4x3 + 6x2 – 7x - 1SUBMIT
Step1:
You are to subtract g(x) from f(x)
Step2:
Simplify and collect like terms
therefore,
[tex]\begin{gathered} \\ (f-g)x=4x^3+6x^2\text{ - 3x - 4 - (4x - 3)} \\ =4x^3+6x^2\text{ - 3x - 4 - 4x + 3} \\ \text{Next add like terms} \\ =4x^3+6x^2\text{ -7x - 1} \end{gathered}[/tex]Option D is the correct answer
8. 6w — 8z = 16
3w — 4z = 8
Substation
Let the two equations be 6w — 8z = 16 and 3w — 4z = 8
Then the equation be
[tex]$6 \cdot w-(8 \cdot z)-16=0$[/tex]
To estimate the value of w, we get
[tex]$6 \cdot w=-(-8 \cdot z-16)=6$[/tex]
simplifying the above equation, we get
[tex]$w=\frac{(-(-8 \cdot z-16))}{6}$[/tex]
[tex]$w=\frac{(16-(-8 \cdot z))}{6}$[/tex]
We insert the solution into one of the initial equations of our system of equations We get a system of equations:
[tex]$3 \cdot\left(\frac{(16-(-8 \cdot z))}{6}\right)-(4 \cdot z)-8=0 \\[/tex]
Therefore, the value of
[tex]$w=\frac{(16-(-8 \cdot z))}{6}[/tex]
If the two equations be 6w — 8z = 16 and 3w — 4z = 8 then the system of equations has infinitely many solutions.
How to estimate the value of w?Let the two equations be 6w — 8z = 16 and 3w — 4z = 8
Then the equation be
[tex]$6 \cdot w-(8 \cdot z)-16=0$[/tex]
To estimate the value of w, we get
[tex]$6 \cdot w=-(-8 \cdot z-16)=6$[/tex]
simplifying the above equation, we get
[tex]$w=\frac{(-(-8 \cdot z-16))}{6}$[/tex]
[tex]$w=\frac{(16-(-8 \cdot z))}{6}$[/tex]
We insert the solution into one of the initial equations of our system of equations We get a system of equations:
[tex]$3 \cdot\left(\frac{(16-(-8 \cdot z))}{6}\right)-(4 \cdot z)-8=0 \\[/tex]
Therefore, the value of
[tex]$w=\frac{(16-(-8 \cdot z))}{6}[/tex]
[tex]$&\frac{(3 \cdot(8 \cdot z+16))}{6}-4 \cdot z-8=0 \\[/tex]
simplifying the above equation, we get
8 - 8 = 0
0 = 0
The system of equations has infinitely many solutions.
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HELPPPP
Which of the following formulas can be used to determine the measure of the angle of rotation for a regular polygon with n sides?
Answer: [tex]m=\frac{360^{\circ}}{n}[/tex]
Step-by-step explanation:
This is a standard result.
The second option is the segment addition postulate.
The third option is the sum of the angles of a polygon with n sides.
The fourth option is the measure of each interior angle of a regular polygon with n sides.
The fifth option is the angle addition postulate.
2q/5 + 4 < 2q/3 - 9 what the answer?
Answer: 195/4
Step-by-step explanation:
20 = 4 (y + 8) - 8y solve for y and simplify your answer as much as possible
Answer:
y = 3
Step-by-step explanation:
20 = 4 (y + 8) - 8y
20 = 4y + 32 - 8y
20 - 32 = 4y - 8y
-12 = -4y
-4y = -12
-4y/-4 = -12/-4
y = 3
To check
20 = 4 (y + 8) - 8y
20 = 4 (3 + 8) - 8(3)
20 = 12 + 32 - 24
20 = 44 - 24
20 = 20
Correct~
Answer: y = 3
Step-by-step explanation:
1. Distribute the 4 to the terms in the parenthesis.
20 = 4y + 32 - 8y
2. Combine like terms (those containing y).
20 = -4y + 32
3. Isolate terms with y by subtracting 32 from both sides.
-12 = -4y
4. Divide both sides by -4.
3 = y
4. Mark's age, when doubled, is Peggy's age. Peggy is 6 years older than Chris. Chris is 6 years older than
Mark. How much older is Peggy than Mark?
Please help me,
Susan colored in the decimal grid shown below. Right a multiplication expression for the area she colored. Then multiply
AnswerAnswerAnswer:
mutiply 14 by 6704
Step-by-step explanation:
The multiplication expression for the area covered is 3 x 8 and the number of grids will be 24.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.
Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
As per the given decimal grid,
The number of colored raw = 8
The number of colored columns = 3
Total grids = 8 x 3 = 24
Hence "The multiplication expression for the area covered is 3 x 8 and the number of grids will be 24".
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Evelyn needs to order some new supplies for the restaurant where she works. The restaurant needs at least 769 glasses. There are currently 205 glasses. If each set on sale contains 12 glasses, write and solve an inequality which can be used to determine xx, the number of sets of glasses Evelyn could buy for the restaurant to have enough glasses.
Answer: 769 bottles ≤ 12x + 205, or 564 bottles ≤ 12x
Step-by-step explanation:
➜ They need at least 769 bottles, so our inequality will use either ≤ or ≥ depending on how we set it up.
➜ They currently have 205 bottles, so we will use addition to show there are some glasses currently owned
➜ If each set contains 12 glasses, we will multiply x, the number of sets bought, by 12
With these details, we will write an inequality.
769 bottles ≤ 12x + 205
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which of the following coordinates represent a point on the Y - axis choose all that apply
Question 7:
The y-axis on a graph is the vertical line on a graph, it represents the dependent variable.
Any point on the y-axis of a graph, has an x-value of zero.
Therefore, from the list given, any coordinate with an x-value of zero is on the y-axis.
Apply the point form: (x, y)
The following coordinates represent a point y-axis:
(x, y) ==> (0, -4)
(x, y) ==> (0, 3)
ANSWER:
(0, -4)
(0, 3)
I need help with what's on the screen, thank you.
a) We know that in the northern Hemisphere we have 4 seasons: Summer where is more sun, Spring, and autumn that the sun is like 50/50 and winter that is the season with less sun. So we can made a graph with this so:
b) In this case if we have a simple interest is going to be a streight light that is going to increase. So the graph will be:
c) An item that increase it's price by 50% is going to be increasing each time more, so this case will be an exponential so the graph will be:
d) The high of a triangle and the base of the triangle are going to to have a constant rate. so the graph will be a horizontal line so:
please help math is an absolute pain
Answer: 3/5 cm
Step-by-step explanation:
Let the length of the base be x. Then, using the formula for the area of a triangle,
[tex]\frac{3}{25}=\frac{1}{2} \cdot \frac{2}{5} x\\\\\frac{3}{25}=\frac{1}{5}x\\\\x=\frac{3}{5}[/tex]
I need help with the 2nd g(x) one please
i need help please help tysm
Answer:
(2, 3)
Step-by-step explanation:
the work is all in the pic go check it out I am so sorry if it's incorrect also have a nice day:)
PLS HELP ME ANWSER THIS
Answer:
y=(5/2)x-4
Step-by-step explanation:
1) You would have to find the slope by using the slope equations
(x1-x2)/(y1-y2)
(6-1)/(4-2)
Slope =5/2
2) the next is to find the y-axis
the line land on the x=0 at -4
y-axis=-4
3) plug into slope intercept form
y=mx+b
m=slope
b=y-axis
y=(5/2)x+(-4)
y=(5/2)x-4
Answer:
[tex]y=\frac{5}{2}x-4[/tex]
Step-by-step explanation:
1. we pick 2 points from a graph...one is (0,-4) and the other is (1,2)
2. we find the gradient between the two points using this equation m=[tex]\frac{y2-y1}{x2-x1}[/tex]
3. we plug the value in the equation
4. m = 5/2
5. equation of a straight line is y = mx +c
-where c is the intercept of the graph and m is the gradient
-4=5/2(0)+c
c =-4
therefore [tex]y=\frac{5}{2}x -4[/tex]
5xº35°60°solve for x
In every triangle the addition of all internal angles is always 180 degrees.
So this means we can build this equation
5x + 35 + 60 = 180
now separate x values and numerical values
5x = 180 - 60 - 35
x= (180 - 60 - 35)/ 5 = 85/5 = 17
Hi, does anyone know the solution to this question?
Hello, in this question we will use the "Sinus Theorem".
The general formula of the Sine Theorem is as follows;
[tex]A=\frac{1}{2}.a.b.sin(C)[/tex]We are given the length of the two sides and the sine value of the angle of the unknown side. We also know the area of the triangle. Let's substitute the required values in this formula to get the result.
[tex]A=\frac{1}{2} (x+2)(2x-3)(sin45^o)[/tex][tex]4\sqrt{2}=\frac{1}{2}(x+2)(2x-3)(\frac{1}{\sqrt{2} } )[/tex][tex]16=(x+2)(2x-3)[/tex][tex]16=2x^2+x-6[/tex][tex]0=2x^2+x-22[/tex]In the last step, we are left with a quadratic equation with one unknown. To solve this equation, we need to calculate the discriminant value.
[tex]Discriminant=b^2-4ac[/tex]There are only two roots of a quadratic equation with one unknown.
[tex]x_{1}=\frac{-b-\sqrt{Discriminant} }{2a}[/tex][tex]x_{2}=\frac{-b+\sqrt{Discriminant} }{2a}[/tex]Thus our x values;
[tex]x_{1}=\frac{-1-\sqrt{177} }{4}[/tex][tex]x_{2}=\frac{-1+\sqrt{177} }{4}[/tex]We cannot accept the first root [tex]x_1[/tex]. Because length cannot be a negative value.
Ans = [tex]x_{2}=\frac{-1+\sqrt{177} }{4}=3.076[/tex]
-2 = y + 5/6 solve for y and simplify your answer as much as possible
Step-by-step explanation:
Solve for y: -2 = y + 5/6
-2 = y + 5/6 subtract 5/6 from both sides:
-2 - 5/6 = y + 5/6 - 5/6
-2 - 5/6 = y
combine left side:
-17/6 = y
so:
y = -17/6
OR:
[tex]y = -2\frac{5}{6}[/tex]
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 335 people entered the park, and the admission fees collected totaled 940 dollars. How many children and how many adults were admitted?
Let
number of children admitted = x
number of adult admitted = y
Total number admitted = 335
[tex]\begin{gathered} x+y=335 \\ 1.5x+4y=940 \\ x=335-y \\ 1.5(335-y)+4y=940 \\ 502.5-1.5y+4y=940 \\ 502.5+2.5y=940 \\ 2.5y=940-502.5 \\ 2.5y=437.5 \\ y=\frac{437.5}{2.5} \\ y=175 \\ x+y=335 \\ x+175=335 \\ x=335-175 \\ x=160 \end{gathered}[/tex]number of children = 160
number of adult = 175
why is sampling with replacement used? to ensure that the sample size is as small as possible to ensure that individuals cannot be selected twice to ensure that the proportions of subgroups in the sample are exactly the same as their proportions in the population to ensure that the probability of selecting any specific individual stays constant
To determine probability with replacement, It uses sampling with replacement. In other words, you want to determine the likelihood of an event in which you choose a ball, card, or other object from a set of options and then swap it out after each choice.
Example:
Consider a scenario in which you wished to sample two people from a population of seven.
Those people are:
John, Jack ,Qiu, Tina, Hatty, Jacques, Des
Their names could be placed in a hat. If you sample with replacement, you would pick one name, put it back in the hat, and then pick a different name. Your two-name sample has the following potential outcomes:
John, John
John, Jack
John, Qui
Jack, Qui
Jack Tina
…and so on.
The two products you sample with replacement are independent. In other words, the outcome of one has no bearing on the other. The odds of picking the first name are 1/7, and the odds of picking the second name are 1/7.
P(John, John) = (1/7) * (1/7) = .02.
P(John, Jack) = (1/7) * (1/7) = .02.
P(John, Qui) = (1/7) * (1/7) = .02.
P(Jack, Qui) = (1/7) * (1/7) = .02.
P(Jack Tina) = (1/7) * (1/7) = .02.
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?????????? Image attached!
I will gladly take your help!
Answer:
-1/2; take both points which equals to -1/2
Step-by-step explanation:
Can somebody help me with number 11?
The unknown angles are as follows:
m∠EFH = 80°m∠EFG = 160°The value of ST in the line segment is 22 units.
How to find angles and mid points?An angle bisector is a bisector that bisect an angles into two equal parts.
Therefore, EF is the angle bisector of ∠EFG.
The bisector divides the ∠EFG equally into ∠EFH and ∠HFG.
Hence,
∠EFH = ∠HFG
m∠HFG = 80°
m∠EFH = 80°
m∠EFG = 80 + 80
m∠EFG = 160°
12.
Let's find ST in the line segment.
PT = 40
QS = 12
PQ = QR = RS = x
QR + RS = QS
2x = 12
x = 12 / 2
x = 6
Therefore,
PQ = QR = RS = 6 units
PS = PQ + QR + RS
PS = 6 + 6 + 6
PS = 18 units
Hence,
ST = PT - PS
ST = 40 - 18
ST = 22 units
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April is arranging place cards for a wedding reception on a table. The bride's family has 154 cards and the groom's family has 140 cards. She wants the arrangements for the two families to have the same number of cards in each row. What is the greatest number of cards that she can place in a row?
The greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is 14.
In the question ;
it is given that
number of card that Bride's family has = 154
number of cards that Groom's family has = 140 cards.
So , to find the greatest number of cards that April can place in a row we need to find the GCF(154,140) ,
to find the GCF (154,140)
prime factorization of 154 = 2*7*11
prime factorization of 140 = 2*2*5*7
common factors = 2*7
Hence the GCF(154,140) = 14
Therefore , the greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is 14.
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Oliver estimates the weight of his cat to be 16 pounds. The actual weight of his cat is 14.25 pounds. What is the percent error of Olver's estimate? Round the percent to the nearest tenth if necessary.
ANSWER
The percent error is 10.9 %
EXPLANATION
The percent error is:
[tex]\text{ \% error}=\frac{|approx-exact|}{exact}\times100[/tex]In this problem, the approximate value is 16 and the exact value is 14.25:
[tex]\begin{gathered} \text{ \% error}=\frac{|14.25-16|}{16}\times100 \\ \text{ \% error}=\frac{1.75}{16}\times100 \\ \text{ \% error}=0.109375\times100 \\ \text{ \% error}=10.9375\approx10.9\text{ \%} \end{gathered}[/tex]Answer:
10.9%
Step-by-step explanation:
14.25/16 = 0.890625
0.890625 * 100 = 89.0625
1 - 89.0625 = 10.9375%
-7u^2+12u+4 factor the following expression
-( ( 7 - u )( u - 2 ) ) is the factorized form of the polynomial -7u² + 12u + 4, using the AC method.
How to factor a polynomial?Given the polynomial in the question;
-7u² + 12u + 4
Factor out -1 out of the polynomial
-1( 7u² - 12u - 4 )
Compare to the form ax² + bx + c
a = 7b = -12 c = -4To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;
a × c = 7 × -4 = -28
and whose sum is;
b = -12
Now, factor -12 out of -12x
-1( 7u² - 12(u) - 4 )
We know that -13 is the same as 2 plus -14
-1( 7u² - ( 2 - 14 )u - 4 )
Apply distributive property
-1( 7u² - 2u - 14u - 4 )
Group the terms
-1( u(7u - 2) - 2(7u - 2 ) )
-1( (7-u)(u-2) )
-( (7-u)(u-2) )
Therefore, the factorized form of the polynomial is -( ( 7 - u )( u - 2 ) ).
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-(7u+2)(u-2) is the factorized form of expression -7u²+12u+4.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is -7u²+12u+4.
We need to find the factors of this expression.
-7u²+12u+4.
This can be written as
-7u^2+14u-2u+4.
Take 7u from first two terms and 2 from last two terms in the expression.
-7u(u-2)-2(u-2)
(-7u-2)(u-2)
-(7u+2)(u-2)
Hence -(7u+2)(u-2) is the factorized form of -7u^2+12u+4.
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The surface area S(r) in square units of a cylinder with a volume of 18 cubic units is a function of its radius r in
units where S(r) = 2rr²+36. What is the surface area of a cylinder with a volume of 18 cubic units and a
radius of 3 units
The surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 68.52 units².
How to calculate the surface area?The volume of a cylinder is calculated as:
= πr²h
In this case, the volume is given as 18 units³. The computed height is 0.637 units.
The surface area will be:
= 2πr² + 2πrh
= 2(3.14 × 3²) + (2 × 3.14 × 3 × 0.637)
= 56.52 + 12
= 68.52 units²
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Complete the explanation of the error.
If x²=81, then x = 9.
The value of x could also be
The square root of a number can also be negative number so x could also be -9
Taking square root of a numberSquare root of a number is the number such that if it is multiplied by itself we get the square. The opposite of squaring an integer is finding its square root. As we know multiplication of two negative numbers produce a positive number. this is the reason why square of both positive and negative numbers are both positive. therefore, square root of a number can also be positive or neegative both. That is why we can't take square root of negative numbers.
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