Answer:
Option B
Step-by-step explanation:
Function 'g' is,
g(x) = x²
Since, leading coefficient of this function is positive, parabola is opening upwards.
From the graph attached,
Function 'f' is opening upwards leading coefficient of the function will be positive.
Since, the graph of function 'f' is vertically stretched, equation will be in the form of f(x) = kx²
Here, k > 1
Since, function 'f' is formed by shifting the graph of function 'g' by 1 unit upwards,
f(x) = g(x) + 1
Combining all these properties, equation of the function 'f' should be,
f(x) = 4x² + 1
Option B will be the correct option.
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.8 years, and
standard deviation of 1.7 years.
The 10% of items with the shortest lifespan will last less than how many years?
Round your answer to one decimal place.
Answer:
Less than 3.6 years.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.8 years, and standard deviation of 1.7 years.
This means that [tex]\mu = 5.8, \sigma = 1.7[/tex]
The 10% of items with the shortest lifespan will last less than how many years?
Less than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 5.8}{1.7}[/tex]
[tex]X - 5.8 = -1.28*1.7[/tex]
[tex]X = 3.6[/tex]
Less than 3.6 years.
Find the distance between the points (-4, -2) and (-8, 6)
Answer:
distance=√[(x2-x1)²+(y2-y1)²]
√[{6-(-2)}²+ (-8-(-4))²]
√(64+16)
√[100]
10
Points given
(-4,-2)(-8,-6)Distance:-
[tex]\\ \sf \longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-8+4)^2+(6+2)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-4)^2+(8)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{64+16}[/tex]
[tex]\\ \sf \longmapsto \sqrt{80}[/tex]
[tex]\\ \sf \longmapsto 8.4[/tex]
The king and queen spent $1500 on decorations for the ball +8 dollars per guest for party favors. The king and queen are charging each guest $12 to enter the dance. How many guests must come to the ball for the king and queen to break even? (you must write an equation and then solve)
Answer:
375 guests
Step-by-step explanation:
costs: 1500 + 8g
income: 12g
They must be equal
1500+8g = 12g
Subtract 8g from each side
1500 +8g-8g =12g-8g
1500= 4g
Divide by 4
1500/4 = 4g/4
375 = g
An equal number of juniors and seniors are trying out for six spots in this year's decathlon
team. If the team must consist of four seniors and two juniors, then how many different
possible decathlon teams could result if five juniors try out?
50
55
75
100
There are 50 different possible debating teams that could be selected as obtained using COMBINATION.
Since there are EQUAL number of juniors and seniors ;
Then we have 5 of each.
Here, the order of arrangement DOES NOT matter, Hence, we use COMBINATION
since the team MUST contain 4 SENIORS and 2 JUNIORS
4 Seniors from 5 = 5C4 = 5
2 Juniors from 5 = 5C2 = 10
Hence, (5C4 * 5C2) = 5 * 10 = 50
Hence, there are 50 different possible debating teams that could be selected.
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In a particular year, a total of 46,601 students studied in two of the most popular host countries when traveling abroad. If 8483 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were ____ students who studied abroad in the most popular host country.
Answer:
31,783.5
Step-by-step explanation:
Half of 46601 = 23300.5
23300.5 + 8483 =31783.5
Find the degree of each polynomial and indicate whether the
polynomial is a monomial, binomial, trinomial, or none of these.
Answer:
1. Degree = 1, monomial
2. Degree = 2, monomial
3. degree = 2, trinomial
4. Degree = 2, binomial
5. Degree = 2, binomial
Step-by-step explanation:
If there are12 books on a rack,a person has to choose 5books.
In how many ways can he choose if one particular book is always selected?
Answer:
330
11 choose 4
[tex]=\frac{11!}{4!\left(11-4\right)!}\\= 330[/tex]
Step-by-step explanation:
Use the graphing calculator to graph the function f(x) = Vx. Which table of values contains points that lie on the
graph of the function?
9514 1404 393
Answer:
see below
Step-by-step explanation:
Assuming your Vx means √x, the values in the f(x) column will be the square root of the values in the x column. That is the case for the first table shown (also attached).
22. The ratio in which (4, 5) divides the join of (2, 3)
and (7, 8) is :
(a) 4 : 3
(c) 3 : 2
(b) 5:2
(d) 2:3
Let the ratio be m:n
(x,y)=(4,5)Points be (x1,y1)=(2,3)(x2,y2)=(7,8)We know
[tex]\boxed{\sf (x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]
[tex]\\ \sf\longmapsto (4,5)=\left(\dfrac{7m+2n}{m+n},\dfrac{8m+3n}{m+n}\right)[/tex]
Now
.[tex]\\ \sf\longmapsto \dfrac{7m+2n}{m+n}=4\dots(1)[/tex]
[tex]\\ \sf\longmapsto \dfrac{8m+3n}{m+n}=5\dots(2)[/tex]
Adding both
[tex]\\ \sf\longmapsto \dfrac{7m+2n+8m+3n}{m+n}=4+5[/tex]
[tex]\\ \sf\longmapsto \dfrac{7m+8m+2n+3n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto \dfrac{15m+5n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9(m+n)[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9m+9n[/tex]
[tex]\\ \sf\longmapsto 15m-9m=9n-5n[/tex]
[tex]\\ \sf\longmapsto 6m=4n[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{6}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{3}{2}[/tex]
[tex]\\ \sf\longmapsto m:n=3:2[/tex]
Option B is correct
ANSWER THE QUESTIONS PLEASE IT IS ON BEARING
9514 1404 393
Answer:
(i) x° = 70°, y° = 20°
(ii) ∠BAC ≈ 50.2°
(iii) 120
(iv) 300
Step-by-step explanation:
(i) Angle x° is congruent with the one marked 70°, as they are "alternate interior angles" with respect to the parallel north-south lines and transversal AB.
x = 70
The angle marked y° is the supplement to the one marked 160°.
y = 20
__
(ii) The triangle interior angle at B is x° +y° = 70° +20° = 90°, so triangle ABC is a right triangle. With respect to angle BAC, side BA is adjacent, and side BC is opposite. Then ...
tan(∠BAC) = BC/BA = 120/100 = 1.2
∠BAC = arctan(1.2) ≈ 50.2°
__
(iii) The bearing of C from A is the sum of the bearing of B from A and angle BAC.
bearing of C = 70° +50.2° = 120.2°
The three-digit bearing of C from A is 120.
__
(iv) The bearing of A from C is 180 added to the bearing of C from A:
120 +180 = 300
The three-digit bearing of A from C is 300.
In a plane, line e is parallel to line f, line f is parallel to line g, and line h is perpendicular to line e. Which of the following cannot be true? e ⊥ h g ∥ h e ∥ g h ⊥ f
Answer:
g ∥ h
Step-by-step explanation:
since lines e,f,g are parallel to each other,
h is perpendicular to lines e,f,g
Find the radius of the circle containing 18
degree arc of a circle whose length is 15 Pi meters
9514 1404 393
Answer:
150 m
Step-by-step explanation:
The relationship between arc length (s), radius (r), and central angle (θ) is ...
s = rθ
Dividing by θ gives the formula for r:
r = s/θ = (15π m)/(18°(π/180°))
r = 150 m . . . . the radius of the circle
What does -3/8 > -1 indicate about the positions of -3/8 and -1 on the number line?!
Answer:
-3/8 is located on the right of -1
Step-by-step explanation:
-3/8 is left of -1 because -3/8 is larger than -1.
Which type of triangle will always have at least 1-fold reflectional symmetry?
right triangle
obtuse triangle
acute triangle
isosceles triangle
Answer:
D. isosceles triangle
Step-by-step explanation:
Ed22
A triangle with at least 1-fold reflectional symmetry is isosceles triangle, option D is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
An isosceles triangle will always have at least 1-fold reflectional symmetry.
This is because an isosceles triangle has two congruent sides and two congruent angles.
If we draw a perpendicular bisector of the base (the side that is not congruent), it will bisect the base and the angle opposite to the base.
This means that the triangle is symmetric with respect to this line of reflection, which is the line of symmetry.
Therefore, the correct answer is isosceles triangle.
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if qqq=90 what's qqqq+87
Answer: [tex]90\sqrt[3]{90}+87[/tex]
Step-by-step explanation:
[tex]qqq=90\\q^3=90\\\sqrt[3]{q^3} =\sqrt[3]{90}\\q= \sqrt[3]{90}\\\\qqqq+87\\q^3q^1+87\\90\sqrt[3]{90}+87[/tex]
một kho hàng có 927 chiếc quạt, đã chuyển đi 1/9 số quạt đó. Hỏi kho hnag còn lại bao nhiêu chiếc quạt?
Answer:
824
Step-by-step explanation:
Số quạt đã chuyển đi:
927 x 1/9 = 103 (chiếc)
Số quạt còn lại trong kho hàng là:
927-103 = 824 (chiếc)
Find the length of side
x
x in simplest radical form with a rational denominator.
Thanks In advance.
Answer:
Sorry I dont really understand wish I could help:(
Step-by-step explanation:
Answer:
[tex]\sqrt{10}[/tex]
[tex]\sqrt{5 } ^{2} + \sqrt{5 } ^{2} = x^{2}[/tex]
[tex]x^{2} =10[/tex]
Step-by-step explanation:
A vehicle purchased for $20700 depreciates at a constant rate of 6%.
Determine the approximate value of the vehicle 14 years after purchase.
Round to the nearest whole number.
Question Help: Viden M Message instructor
n Post to forum
Answer:
$22,000
Step-by-step explanation:
Please solve the problem
Answer:
does this have to do with graphs
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
-3y=3x-9
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Answer:
y = -3 m = -1 b = 3
Step-by-step explanation:
-3y=3x-9
To isolate the y variable, divide both sides by -3.
y = -1x + 3
y = -3
m = -1
b = 3
What is the factored form of the binomial expansion x3 + 9x2 + 27x + 27?
(x + 3)3
(x - 3)3
(x + 9)3
(X - 9)3
Answer:
A
Step-by-step explanation:
the factored form of the binomial expansion x^3 + 9x^2 + 27x + 27 is (x+3)^3
A potato chip manufacturer produces bags of potato chips that are supposed to have a net weight of 326 grams. Because the chips vary in size, it is difficult to fill the bags to the exact weight desired. However, the bags pass inspection so long as the standard deviation of their weights is no more than 3 grams. A quality control inspector wished to test the claim that one batch of bags has a standard deviation of more than 3 grams, and thus does not pass inspection. If a sample of 21 bags of potato chips is taken and the standard deviation is found to be 4.1 grams, does this evidence, at the 0.025 level of significance, support the claim that the bags should fail inspection
Following this pattern, type a number to show how many bags of wheat there will be on the sixth square.
Will pay 14 points
The number of bags of wheat that will be on the sixth square is 32wheats
The amount of wheat in each square are expressed in geometric sequence as shown.
1, 2, 4, 8, 16,....
Geometric sequence is a sequence where the ratio of the succeeding and the preceding term is equal to a common ratio.
The nth term is expressed as
Tn = ar^{n-1}
a is the first term
r is the common quantity
n is the number of terms
a = 1
n = 6 (sixth square)
r = 4/2 = 2/1 = 2
Substitute the given values into the formula
T6 = 1(2)^{6-1}
T6 = 2^5
T6 = 32
Hence the number of bags of wheat that will be on the sixth square is 32wheats
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Answer:
32
Step-by-step explanation:
https://www.yutube.com/watch?v=U3vLXdNdTJ8
link is broken add an o to yutube
Bob wants to replace a glass window in his restaurant. The window is in the shape of a square. Its side lengths are 6 feet. Suppose glass costs $7 for each square foot. How much will the glass cost to replace the window?
ANSWER: The glass window will cost $252.00 for window replacement.
EXPLANATION:
The area of a square is given by the formula:
s^2
where s is the side length.
If we were to replace the glass window, and it will cost $7.00 per square foot, the total price will be:
FIND AREA OF THE GLASS WINDOW:
6^2 = 36 square feet
$7 per square foot so:
36 x 7 = 252
Therefore it will cost $252.00 to replace the glass window.
Simplify: 2(6+1)-|-10|+3x2
Answer:
10
Step-by-step explanation:
2(6+1)-|-10|+3*2
First start with the absolute values and parentheses
2(7)-10+3*2
Then multiply from left to right
14 -10 +6
Then add and subtract from left to right
4 +6
10
1. Đường kính của một loại trục máy là một đại lượng ngẫu nhiên có phân phối chuẩn N (μ = 250mm, σ2 = 25mm2). Trục máy được gọi là hợp quy cách nếu đường kính từ 245mm đến 255mm. Cho máy sản xuất 100 trục. Tính xác suất để:
a. Có 50 trục hợp quy cách.
b. Có không quá 80 trục hợp quy cách
Answer:
please ask in English
Step-by-step explanation:
then I can help
lee is planning an event for 28 people, he wants to make a fruit drink and he thinks that each person will drink 3 glasses each. If he is correct , how many glasses of fruit should he make?
Answer:
84
Step-by-step explanation:
Since there will be 28 people, and each of them will drink 3 glasses, you just multiply the number of people times the number of glasses they will drink each, so 28*3. The result is 84.
I hope this helped! :D
Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let Lee needs to make x number of glasses of fruit.
From the question we can frame a linear equation in one variable:
x/3 = 28
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
After cross multiplication:
x = 28×3
x = 84 glasses
Thus, Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
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To make sky blue Sam uses two drops of blue paint for every eight drops of white paint. He wants to
make a large amount of sky blue paint. If he uses sixteen drops of blue, how many drops of white will he
need?
Answer:
64
Step-by-step explanation:
The Ratio of Blue to White drops is 2:8
16*4=64,... 16:64 Have a nice day!
Please help me with this on the picture
Answer:
1. 748
2. 901
3. 27
4. 672
Step-by-step explanation:
1. 1011-263=748
2. 653+248=901
3. 1161÷43=27
4. 48×14=672
A rectangular window is 48 in long and 36 in wide. Lisa
would like to buy a screen for the window. The cost of
the screen is based on the number of square feet the
screen is. Use the facts to find the area of the window in
square feet.
Conversion facts for length
1 foot (ft) 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
2
Х
$
?
[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto Area=48(36)[/tex]
[tex]\\ \sf\longmapsto Area=1728in^2[/tex]
[tex]\\ \sf\longmapsto Area=144ft^2[/tex]
[tex]\\ \sf\longmapsto Area=48yard^2[/tex]