Answer:
The common ratio is 2Step-by-step explanation:
To find the common ratio of the geometric sequence divide the previous term by the next term
That's
0.9 / 0.45 = 2
1.8 / 0.9 = 2
Therefore the common ratio is 2
Hope this helps you
Carlo and Anita make mailboxes and toys in their wood shop. Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita. Each toy requires 1 hour of work from Carlo and 1 hour from Anita. Carlo cannot work more than 12 hours per week and Anita cannot work more than 24 hours per week. If each mailbox sells for $10 and each toy sells for $5, then what is their maximum possible revenue
Answer:
$80
Step-by-step explanation:
Let the number of hours required to make a mailbox = x
Let the number of hours required to make a toy = y
Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.
Each toy requires 1 hour of work from Carlo and 1 hour from Anita.
The table below summarizes the information for ease of understanding.
[tex]\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|[/tex]
We have the constraints:
[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]
Each mailbox sells for $10 and each toy sells for $5.
Therefore, Revenue, R(x,y)=10x+5y
The given problem is to:
Maximize, R(x,y)=10x+5y
Subject to the constraints
[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]
The graph is plotted and attached below.
From the graph, the feasible region are:
(0,0), (6,0), (4,8) and (0,12)
At (6,0), 10x+5y=10(6)+5(0)=60
At (4,8), 10(4)+5(8)=80
At (0,12), 10(0)+5(12)=60
The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.
The maximum possible revenue is $80.
Solve the one-variable equation using the distributive property and properties of equality.
-6(2 + a) = -48
What is the value of a?
O a = -6
O a = -3
O a = 5
Са= 6
Hey there! :)
Answer:
Last choice. a= 6.
Step-by-step explanation:
Starting with:
-6(2 + a) = -48
Distribute the -6:
-6(2) -6(a) = -48
Simplify:
-12 - 6a = -48
Add 12 to both sides:
-12 + 12 - 6a = -48 + 12
-6a = -36
Divide both sides by -6:
a = 6. Therefore, the last choice is correct.
Answer:
a = 6
Step-by-step explanation:
Solve the one-variable equation using the distributive property and properties of equality.
–6(2 + a) = –48
What is the value of a?
a = –6
a = –3
a = 5
a = 6
PLS HELP (pic included)
hope it helps uh.......
In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows: JG JH JM GJ GH GM HJ HG HM MJ MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The event A is defined as follows: A = event that Helen gets first prize List the outcomes that comprise the event ~A (not A).
Answer:
1. JG (Jim gets first prize, George gets second prize)
2. JH (Jim gets first prize, Helen gets second prize)
3. JM (Jim gets first prize, Maggie gets second prize)
4. GH (George gets first prize, Helen gets second prize)
5. GJ (George gets first prize, Jim gets second prize)
6. GM (George gets first prize, Maggie gets second prize)
7. MJ (Maggie gets first prize, Jim gets second prize)
8. MG (Maggie gets first prize, George gets second prize)
9. MH (Maggie gets first prize, Helen gets second prize)
Step-by-step explanation:
The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.
The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.
Will give brainliest answer
Answer:
Radius = 6.5cm
Diameter = 13cm
Step-by-step explanation:
The diameter is given (13)
Radius is half the diameter (13/2=6.5)
Answer:
Radius = 13 / 2 = 6.5 cmDiameter = 13 cmExplanation
RadiusThe straight line is drawn from the centre of a circle to a point on its circumference is called radius of the circle. The radius of a circle is half of its diameter.
DiameterThe chord that passes through the centre of a circle is called diameter of circle. Diameter is also called the largest chord of any circle. The length of diameter of a circle is two times it's radius.
Hope this helps...
Good luck on your assignment...
Find the surface area of this composite solid.
Answer:
C. 120 m²
Step-by-step explanation:
The surface area is equal to the area of 4 rectangles + area of 4 triangles + area of base.
Area of 4 rectangles:
4(5 × 4)
4(20) = 80
Area of 4 triangles:
4(3 × 4 × 1/2)
4(6) = 24
Area of base:
4² = 16
Add the areas.
16 + 24 + 80
= 120
The surface area of the composite solid is 120 m².
The surface area of this composite solid would be, 136 m². Hence, option D is true.
Used the formula for the surface area of the cuboid and the surface area of the 4 triangles,
The surface area of the cuboid = 2 (LW + LH + HW)
And, The surface area of the 4 triangles = 4 (1/2 × Base × Height)
Given that,
In a triangle,
Base = 4 m
Height = 3 m
And, In a Cuboid,
Length = 4 m
Width = 4 m
Height = 5 m
Hence, we get;
The surface area of the 4 triangles = 4 (1/2 × Base × Height)
= 4 (1/2 × 4 × 3)
= 4 × 6
= 24 m²
The surface area of the cuboid = 2 (LW + LH + HW)
= 2 (4 × 4 + 4 × 5 + 5 × 4)
= 2 (16 + 20 + 20)
= 112 m²
Therefore, The surface area of this composite solid would be,
24 m² + 112 m² = 136 m²
So, Option D is true.
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The following display from a graphing calculator presents the least-squares regression line for predicting the price of a certain commodity (y) from the price of a barrel of oil (x).
Y = a + bx
a = 4.95
b = 0.29
r2 = 0.53045
r = 0.72832
Predict the commodity price when oil costs $107 per barrel.
Answer:
35.98
Step-by-step explanation:
Fill in the numbers and do the arithmetic.
y = a + bx . . . . . . a=4.95, b=0.29, x=107
y = 4.95 + 0.29(107) = 35.98
The predicted price is 35.98.
what is the remainder when p(x) is divided by (x-3) please help
Answer:
1
Step-by-step explanation:
We will use polynomial remainder theorem or little Bézout's theorem. It states that reminder p(x) divided by (x - a) is p(a). In our case (a = 3) it is p(3) = 1
Not sure how to solve this
Answer:
The x-intercepts as shown on this graph are: (-3,0), (1,0), and (3,0). The y-intercept as shown on this graph is: (0,2).
Step-by-step explanation:
The intercepts refer to where the function intersects with either the x-axis or y-axis. Since the line crosses the y-axis at (0,2), that's the y-intercept. The same thing applies to the x-intercepts. On this graph, it's easier to identify because the intercepts are marked with dots.
Evaluate geometric series sigma1^20 4(8/9)^n-1
Answer:
32.5861
Step-by-step explanation:
I interpreted it this way:
20 - stop at n = 20 (inclusive)
1 - start at n = 1
4(8/9)^(n - 1) - geometric expression
There were 35,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold. If a total of 448,000 copies of the novel were sold in all, how many paperback copies were sold
Answer:
3,717,000
Step-by-step explanation:
The calculation of paperback copies is shown below:-
Let us assume hardback copies is x, so paperback copies will be 9x
now the equation is
35,000 + x + 9x = 448,000
10x = 448,000 - 35,000
10x = 413,000
[tex]= \frac{413,000}{10}[/tex]
= 41,300
Therefore, the paperback copies are
= [tex]9\times 41,300[/tex]
= 3,717,000
Hence, the paperback copies is 3,717,000
A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
The required length of the line is given as 14.4 feet, as of the given conditions.
As given in the question, A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow, to determine the length of the line.
What are Pythagorean triplets?In a right-angled triangle, its side, such as the hypotenuse, is perpendicular, and the base is Pythagorean triplets.
Here,
let the length of the line be x,
The scenario formed is right angle triangle,
Apply Pythagoras' theorem,
x² = 12² + 8²
x = √208
x = 14.4
Thus, the required length of the line is given as 14.4 feet, as of the given conditions.
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The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. For a 0.01 level of significance, what is the critical value for the rejection region? a. 7.173 b. 2.33 c. 6.635 d. 7.106
Answer:
Critical value: b. 2.33
As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
The significance level is 0.01.
The sample 1 (women), of size n1=150 has a proportion of p1=0.62.
The sample 2 (men), of size n2=200 has a proportion of p2=0.24.
The difference between proportions is (p1-p2)=0.38.
[tex]p_d=p_1-p_2=0.62-0.24=0.38[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{93+48}{150+200}=\dfrac{141}{350}=0.403[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.403*0.597}{150}+\dfrac{0.403*0.597}{200}}\\\\\\s_{p1-p2}=\sqrt{0.001604+0.001203}=\sqrt{0.002807}=0.053[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.38-0}{0.053}=\dfrac{0.38}{0.053}=7.17[/tex]
The critical value for a right-tailed test with a signficance level of 0.01 is zc=2.33 (see picture attached).
As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
I AM GIVING + 20 POINTS !!!!! PLEASE ANSWER SOON!!!!! Which is NOT a good reason to perform step 1 in the solution shown? equation: 4x = 88 step 1: 4x/4 = 88/4 step 2: x = 22 a. divide by 4, because 4 is a factor of 88. b. dividing 4x by 4 isolates x on one side of the equation. c. dividing is the inverse of multiplying d. dividing both sides by 4 keeps the equation balanced
Answer:
c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.
If possible, find AB. & State the dimension of the result.
Answer:
Step-by-step explanation:
[tex]A=\begin{bmatrix}0 &0 &5 \\ 0 &0 &-3 \\ 0 &0 &3 \end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}8 &-12 &5 \\ 7 &19 &5 \\ 0 &0 &0 \end{bmatrix}[/tex]
A.B = A × B
[tex]A.B=\begin{bmatrix}0 &0 &0 \\ 0 &0 &0 \\ 0 &0 &0 \end{bmatrix}[/tex]
Dimension of the resultant matrix is (3 × 3)
Estimate the area under the graph of f(x)=1/x+4 over the interval [-1,2] using four approximating rectangles and right endpoints.
Answer:
Rn ≈ 0.6345
Ln ≈ 0.7595
Step-by-step explanation:
The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.
It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:
x = -1, -.25, 0.50, 1.25, 2
Of course, the spreadsheet can easily compute the sum of products for you.
__
The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:
Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)
Rn ≈ 0.6345
__
The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:
Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)
Ln ≈ 0.7595
_____
It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).
I need help fast this is my summer packet
Answer:
40 miles per hr.
Step-by-step explanation:
alll u have to do is divide the number of miles by the hrs.
ex.80/2=40
140/3.5=40
200/8=40
300/7.5=40
what number must add to the expression below to complete the square x^2-x
A.-1/2
B. 1/2
C. -1/4
D. 1/4
Answer:
Option D is correct.
1/4 completes the square.
Step-by-step explanation:
To complete the square for a quadratic function, we require a third term that will enable the solutions of the quadrstic equation to be 2 repeated roots.
For that to be so for the quadratic equation
ax² + bx + c = 0,
b² has to be equal to 4ac
For this question, x² - x + c
From b² = 4ac
c = (b²/4a)
a = 1
b = -1, b² = 1
c = ?
c = (1/4)
Hence, (1/4) is the number that must be added to the expression to complete the square.
Hope this Helps!!!
What is the solution to 8/x+2=2/x-4
Answer:
x=-1
Step-by-step explanation:
8/x+2=2/x-4
8/x=2/x-6
8=2-6x
6=-6x
-1=x
Answer:
x=6
Step-by-step explanation:
8/x+2=2/x-4
Using cross products
8*(x-4) = 2 (x+2)
Distribute
8x - 32 = 2x+4
Subtract 2x
8x-2x -32 = 2x-2x+4
6x-32 = 4
Add 32
6x-32+32 = 4+32
6x = 36
Divide by 6
6x/6 = 36/6
x = 6
A. Translation: (x,y) → (x – 5,y); Reflection across y-axis
B. Translation: (x,y) → (x,y + 5); Reflection across x-axis
C. Translation: (x,y) → (x,y – 5); Reflection across y-axis
D. Translation: (x,y) → (x,y + 5); Reflection across y-axis
Answer:
Option D
Step-by-step explanation:
Let's choose a point A to understand the transformations given in the picture attached,
Coordinates of A → (2, -1)
Coordinates of image A' → (-2, 4)
From these coordinates of A and A' we can calculate the vertical shift of point A = [4 - (-1)] = 5 units
Rule used for the translation,
(x, y) → (x, y + 5)
A(2, -1) → A"(2, 4)
Followed by the reflection across y - axis,
Rule for the reflection of a point across y-axis,
(x, y) → (-x, y)
By this rule, A"(2, 4) → A'(-2, 4)
Therefore, There is a translation of 5 units upwards and reflection across y-axis.
Option D will be the answer.
Add and write the fraction or mixed number in its simplest form: 2/5 + 1/4 + 7/10
Answer:
The LCM of 5, 4, and 10 is 20 so we can rewrite this expression as:
8/20 + 5/20 + 14/20 = (8 + 5 + 14) / 20 = 27 / 20 = [tex]1\frac{7}{20}[/tex]
Adding all the three fractions ,
Simplest form is
[tex]1\frac{7}{20}[/tex]
Given :
[tex]\frac{2}{5}+\frac{1}{4} +\frac{7}{10}[/tex]
Step-by-step explanation:
To add all the fractions , the denominators should be same
Lets find out LCD of 5,4 and 10
[tex]5= 1,5\\4=2,2\\10=5,2\\LCD=5\cdot 2\cdot 2=20[/tex]
Least common denominator = 20
Multiply the first fraction by 4 and second fraction by5 and third fraction by 2 to get same LCD 20
[tex]\frac{2}{5}+\frac{1}{4}+\frac{7}{10}\\\frac{8}{20}+\frac{5}{20}+\frac{14}{20}\\\\\frac{8+5+14}{20}\\\frac{27}{20}[/tex]
We cannot simplify the fraction further . So we write it in mixed form
[tex]1\frac{7}{20}[/tex]
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Quadrilateral DEFG is rotated 180° about the origin to create quadrilateral D'E'F'G'. In which quadrant does G' lie? A. I B. II C. III D. IV
Answer:
B. II
Step-by-step explanation:
G is in quadrant IV. The quadrant that is across the origin from that is quadrant II.
G' will lie in quadrant II
Answer:
B. 11
Step-by-step explanation:
Jane entered a raffle at a festival and hopes to win a new TV. The odds in favor of winning a new TV are 4/7 . Find the probability of winning a new TV.
Answer:
4/11
Step-by-step explanation:
The probability of winning a new TV is the number of times you will win a TV over the total number of times you try to win a TV. In this case, the odds of winning a new TV are 4/7, or 4 wins every 7 loses. (Odds are probability of success to failure) Therefore, there are 4 wins for every 4 + 7 raffles, or 4/11.
please tell ans of attached photo
Answer:
192 m^2.
Step-by-step explanation:
We can split this up into 3 rectangles:
Area of the bottom rectangle = 27 * (9-3)
= 27 * 6 = 162 m^2.
Area of rectangle on the left = (18-6)*2
= 24 m^2
Area of small rectangle on the right = 3*2
= 6 m^2
Total area = 162+24+6
192 m^2.
can someone help me solve this problem
Answer:
D
Step-by-step explanation:
Using a Graph to Find Positive or Negative Intervals
Answer:
Step-by-step explanation:
The second is correct
f(x) <0 on ( _ infinit, -2.7) and ( -1, 0.8)
Four horizontal forces of magnitudes 1 N, 2 N, 3N and 4N act at a point in the direction whose bearings are 000, 060, 120 and 270 respectively. a Calculate the magnitude of their resultant. b. A 5th horizontal force of magnitude 3 N now acts at the same points so that the resultant of all five forces has a bearing of 090. Find the bearing of the 5th force
Answer:
resultant = 0.356N 202.1°
Step-by-step explanation:
Resultant force = √((x component)² + (y component)²)
X component= 1 cos 90 + 2 cos 30 + 3 cos 30 -4 cos 0
X component = 0 + 1.732 + 2.598 - 4
X component = 0.33
Y component = 1 sin 90 + 2 sin 60 -3sin 60 + 3 sin 0
Y component= 1+1.732-2.598
Y component= 0.134
Resultant = √( (0.33)² +(0.134)²)
Resultant= √(0.1089+0.017956)
Resultant= √ 0.126856
Resultant= 0.3562 N
Tan tita = 0.134/0.33
Tan tita = 0.406
Tita = 22.1°
Tab is positive In the third quadrant and first quadrant but the magnitude of the force lies mainly on the third so resultant = 0.356N 202.1°
For the fifth force.
X component =- 0.356 cos 67.9 +x
X component= -0.134 +x
Y component = 0.356sin22.1 +0
Y component= 0.1334
Tan tita = 0.1334/(-0.134+x)
Tita = tan^-1 0.1334/(-0.134+x)
90 = 0.1334/(-0.134+x)
Tan 90 is undefined so no more solution
In quadrilateral ABCD, AD || BC
What must the length of segment AD be for the
quadrilateral to be a parallelogram?
B
8 units
O 16 units
3x + 7
5x - 9
31 units
62 units
С
D
Answer:
31 units
Step-by-step explanation:
I just did it
The length of segment AD must be 31 units for ABCD to be a parallelogram.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Now, When the figure is a parallelogram, opposite sides have the same measure:
That is,
⇒ AD = BC
Plug the given values we get;
⇒ 3x +7 = 5x -9
⇒ 16 = 2x
⇒ 8 = x
Hence, Use this value of x in the expression for AD to find its required length:
AD = 3(8) +7 = 24 +7
AD = 31 . . . . units
Thus, The length of segment AD must be 31 units for ABCD to be a parallelogram.
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how many different four letter permutations can be formed using four letters out of the first 12 in the alphabet?
Answer:
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Permutations of four letters from a set of 12 letters. So
[tex]P_{(12,4)} = \frac{12!}{(12-4)!} = 11800[/tex]
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Answer: it’s 11,880
not 11800
Find an equation of the tangent line to the curve at the given point. y = x , (16, 4) Step 1 To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16, 4), we know that (16, 4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula mtan = lim x→a f(x) − f(a) x − a . In this situation, the function is f(x) = and a =
The question is incomplete. The complete question is:
Find an equation of the tangent line to the curve y = [tex]\sqrt{x}[/tex] at the given point (16,4). To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16,4) we know that (16,4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula m tan = lim x↔a f(x) - f(a)/ x - a.
Answer: y = [tex]\frac{x}{8} + 2[/tex]
Step-by-step explanation: The tangent line is a line that intercepts a curve in only one point. The point-slope formula for a line is [tex]y-y_{0} = m(x-x_{0})[/tex], where m is the slope of the line and can be calculated by the first derivative of the given curve. For this case:
y = [tex]\sqrt{x}[/tex]
f'(x) = [tex]\frac{dy}{dx} = \sqrt{x}[/tex]
f'(x) = [tex]\frac{1}{2\sqrt{x} }[/tex]
At point (16,4), the slope will be:
m = f'(16) = [tex]\frac{1}{2.\sqrt{16} }[/tex]
m = [tex]\frac{1}{8}[/tex]
With slope and a point, the line function will be:
[tex]y-y_{0} = m(x-x_{0})[/tex]
y - 4 = [tex]\frac{1}{8}[/tex](x - 16)
y = [tex]\frac{x}{8}[/tex] - 2 + 4
y = [tex]\frac{x}{8}[/tex] + 2
The tangent line to the curve is y = x/8 + 2