Answer:
[tex]4\frac{17}{24}[/tex] feet
Step-by-step explanation:
Total length of the board = [tex]7\frac{1}{3}=\frac{22}{3}[/tex] feet
Length of board that is removed from the larger board = [tex]2\frac{5}{8}=\frac{21}{8}[/tex]
When a smaller board is removed, the length of the remaining board can be calculated using subtraction as:
Remaining Length of board = Total Length - Length of smaller board
= [tex]\frac{22}{3}-\frac{21}{8}\\\\\text{Taking LCM, which is 24}\\\\ =\frac{8(22)-3(21)}{24}\\\\ =\frac{113}{24}\\\\ =4\frac{17}{24}[/tex]
This means [tex]4\frac{17}{24}[/tex] feet of board remains after removing the smaller board from it.
Which statement is true regarding the graphed functions?
ANSWER
[tex]f(0) = g(0)[/tex]
EXPLANATION
From the graph we
[tex]g(0) = - 2[/tex]
because this is where the line x= 0 meets the graph of g(x).
Also
[tex]f(0) = - 2[/tex]
because this is where the line x= 0 meets the graph of f(x).
This implies that,
[tex]f(0) = g(0)[/tex]
The correct choice is A.
Which of the following quadratic functions are in standard form?
(Picture attached)
E and F
The standard form for a quadratic function is f(x) = ax^2 + bx + c.
E follows this pattern. a = -2; b = -8; c = 3
F also follows this pattern. a = 1/2; b = -2; c = 0
Measure of angle LOI= 38 degrees
Measure of angle JOP= 84 degrees
Find measure of angle JKP
Answer:
The measure of angle JKP is 61°
Step-by-step explanation:
we know that
If the measure of angle m<LOI=38°
then
m arc IL=38° -----> by central angle
and
If the measure of angle m<JOP=84°
then
m arc JP=84° -----> by central angle
Remember that
The measure of the interior angle is the semi-sum of the arcs that comprise it and its opposite.
so
m<JKP=(1/2)[arc IL+arc JP]
substitute the values
m<JKP=(1/2)[38°+84°]=61°
Matt and his dad are building a tree house. They buy enough flooring material to cover an area of 36 square ft. What are all possible dimensions of the floor?
Answer:
Factor pairs of 36 are ...
1×36, 2×18, 3×12, 4×9, 6×6 . . . and the reverse of these
There is nothing in the problem statement limiting the dimensions to integer numbers of feet, so any dimensions x and 36/x will do. (x in feet)
Step-by-step explanation:
Area is the product of length and width. The desired dimensions are the length and width of the floor, so any pair of numbers resulting in a product of 36 will be a possible set of dimensions.
If the dimensions are supposed to be integer numbers of feet, then the possibilities for length×width are ...
1×36, 2×18, 3×12, 4×9, 6×6, 9×4, 12×3, 18×2, 36×1
_____
As a practical matter, the tree house probably needs to be wider than 2 feet, leaving 3×12, 4×9, and 6×6 as possible dimensions (length×width or width×length). Depending on the flooring material and the difficulty of cutting it, there may be other limitations on the dimensions.
The possible dimensions for the floor of the tree house that Matt and his dad are building are 1 ft x 36 ft, 2 ft x 18 ft, 3 ft x 12 ft, 4 ft x 9 ft, and 6 ft x 6 ft. These pairs are derived by identifying the factors of 36 square feet.
To determine all possible dimensions of the floor that Matt and his dad need to cover, we need to find pairs of whole numbers that multiply to 36 square feet. This is a classic problem in mathematics involving factors.
Here are the pairs of whole numbers that multiply to 36:
1 ft x 36 ft2 ft x 18 ft3 ft x 12 ft4 ft x 9 ft6 ft x 6 ftEach of these pairs represents a possible dimension for the tree house floor.
PLEASE HELP ASAP, I WILL MAKE U BRAINLIEST
The graph shows the normal distribution of the length of similar components produced by a company with a mean of 5 centimeters and a standard deviation of 0.02 centimeters. If a component is chosen at random, the probability that the length of this component is between 4.98 centimeters and 5.02 centimeters is about __%, and the probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is about __%.
Answer:
1. P(A) = 0.6826
2. P(B) = 0.13591
Step-by-step explanation:
the first graph is given just as an example to show the percentage distribution values for bell shaped curve
Answer:
68.3%, 33.3%
Step-by-step explanation:
PLATO answer!! pls mark brainliest :)))
Find the area. The figure is not drawn to scale.
The answer is B. It is the most reasonable answer that I see.
Answer:
[tex]704 in^2[/tex]
Step-by-step explanation:
The figure is a parallelogram.
The area of a parallelogram is
[tex]=base\:\:\times\:\:height[/tex]
The base is 22 inches and the height is 32 inches.
We multiply to obtain:
[tex]22\times 32=704in^2[/tex]
the correct answer is B
If one dollar bill is 0.0001 meters thick how many meters tall would a stack of 4 trillion one dollar bills be?
Answer:
400,000,000
Step-by-step explanation:
4000000000000×.0001 is the answer above
Answer:
[tex]4 \times {10}^{8 }m \: or \: 400,000,000m[/tex]
Step-by-step explanation:
Put them both into standard form.
[tex]0.0001 = 1 \times {10}^{ - 4} \: and \: 4 \: trillion \: is \: 4 \times {10}^{12} [/tex]
Multiply them together.
[tex](1 \times {10}^{ - 4} ) \times (4 \times {10}^{12}) = 4 \times 10^{8} [/tex]
How does the range of g(x)=6/x compare with the range of the parent function f(x)=1/x?
The range of the function g(x)=6/x is the same as the range of the parent function f(x)=1/x, which is all real numbers except zero, despite the scaling factor '6'. This is because transformations other than shifts do not change the range.
Explanation:The comparison between the functions g(x)=6/x and f(x)=1/x lies in the understanding of how modifications to a parent function affect its range. The function f(x)=1/x is a parent function and its range is all real numbers except for zero. This is because as x approaches zero, the output of the function approaches infinity, thus, zero is not included in the range.
When we look at the function g(x)=6/x, the multiplier '6' just scales the values of the parent function by a factor of 6. This means the range will still be all real numbers except for zero, just like in the parent function. This is because the function transformations do not affect the range of the function that has a rational form like f(x)=1/x unless there are additional horizontal or vertical shifts.
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Does Red Increase Men’s Attraction to Women? A study1 examines the impact of the color red on how attractive men perceive women to be. In the study, men were randomly divided into two groups and were asked to rate the attractiveness of women on a scale of 1 (not at all attractive) to 9 (extremely attractive). Men in one group were shown pictures of women on a white background while the men in the other group were shown the same pictures of women on a red background. The results are shown in Table 1 and the data for both groups are reasonably symmetric with no outliers. Color n x¯ s Red 15 7.2 0.6 White 12 6.1 0.4 Table 1 Does red increase men’s attraction to women? To determine the possible effect size of the red background over the white, find a 95% confidence interval for the difference in mean attractiveness rating μR-μW, where μR represents the mean rating with the red background and μW represents the mean rating with the white background.
please attached is your answer
Preston wants to create a garden that backs up to an existing fence in his yard. He won't need to enclose the garden with fencing and he only has 85 feet of fencing available. What was the largest dimensions of the garden be if you could encloses the three sides of the garden and use the existing fence as the fourth side? If necessary, round answer to the nearest tenth.
Answer:
42.5 ft by 21.3 ft
Step-by-step explanation:
The largest area is obtained when half the available fence is used parallel to the existing fence, and the other half is used to fence the two ends of the rectangle. Here, that means the dimension parallel to the existing fence is ...
(85 ft)/2 = 42.5 ft
and the ends of the rectangular garden are ...
(42.5 ft)/2 = 21.25 ft ≈ 21.3 ft
_____
You can figure this as follows:
Let x represent the length of fence parallel to the existing fence. Then the other dimension of the fenced area is (85 -x)/2 and the fenced area is the product of these dimensions.
area = x(85-x)/2
This expression describes a downward-opening parabola with zeros at x=0 and at x=85. The vertex (maximum) will be found where x is halfway between these values, at x = (0 +85)/2 = 42.5.
Area is maximized when 42.5 ft of fencing is used parallel to the existing fence, and the other half of the fencing is used for the other two sides of the enclosure.
Find the perimeter of a triangle with sides measuring 5 centimeters , 9 centimeter, and 11 centimeters
Perimeter is the distance around an object, so you would add 5+9+11 to get 25 cm
A cricular arena is lit by 5 lights equally spaced around the perimeter of the arena. What is the measure of each angle formed by the lights on the perimeter?
Answer:
108°
Step-by-step explanation:
Suppose that circle with center A is a circular arena. Points B, C, D, E and F are 5 lights. These 5 points form regular pentagon (because these 5 lights are equally spaced around the perimeter of the arena).
The sum of all interior angles of pentagon can be calculated using following formula
[tex](n-2)\cdot 180^{\circ},\\ \\(5-2)\cdot 180^{\circ}=3\cdot 180^{\circ}=540^{\circ}[/tex]
All interior angles in regular pentagon are of equal measure, so
[tex]\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
Thus, the measure of each angle formed by the lights on the perimeter is 108°.
Answer:
D. 108
Step-by-step explanation:
I just did the test yourself
A mother who is 40 years old has a daughter and a son. The son is twice as old as the daugther. In 15 years the sum of all their ages will be 100 years. How old are the siblings now?
Answer:
Step-by-step explanation:
Let's call the ages D for daughter and S for son.
We know that the son is twice as old as the daughter, so:
S = 2D
We also know that in 15 years, their ages add up to 100, so:
(40+15) + (S+15) + (D+15) = 100
55 + S + 15 + D + 15 = 100
85 + S + D = 100
S + D = 15
Substituting the first equation:
2D + D = 15
3D = 15
D = 5
Therefore:
S = 2D = 10
The son is 10 and the daughter is 5.
Answer:
son = 10
daughter = 5
Step-by-step explanation:
Let the daughter = d
Let the son = s
s = 2*d
there ages in 15 years
Mother = 40 + 15 = 55
Son = s + 15
daughter = d + 15
Total: s + 15 + d+15 + 55 = 100 Combine the like terms.
s + d + 85 = 100 Subtract 85 from both sides.
s + d = 100 - 85
s + d = 15
s = 2*d Substitute for son
2d + d = 15
3d = 15
d = 15/3
d = 5
son = 2*5
son = 10
Check
son = 15 = 25
daughter + 15 = 20
Mother + 15 = 55
Total 100 just as it should be.
If the terminal side of an angle In standard position passes through the point (20, -21), then which of the following functions will be positive?
A. Cosecant
B. Secant
C. Tangent
Answer:
B
Hope This Helps! Have A Nice Day!!
Answer:
b
Step-by-step explanation:
Which figure shows how a shape can be rotated about an axis to form a hemisphere?
Answer:
A. (first choice)
Step-by-step explanation:
Examine all options:
A. The diagram shows the arc (1/4 from a circle). While rotating this arc about the given axis, we get the hemisphere.
B. The diagram shows the semicircle (1/2 from a circle). While rotating this semicircle about the given axis, we get the whole sphere.
C. The diagram shows the segment (perpendicular to the axis). While rotating this segment about the given axis, we get the circle (lying in a plane).
D. The diagram shows the segment. While rotating this segment about the given axis, we get the cone.
Dalia has 9 hamsters and 4 fish at her house. Choose the ratio of fish to the total number of pets. (Select all that apply.)
A) 4 to 9
B) 4 to 13
C) 9 to 13
D) 4:9
E) 4:13
F) 13:4
Answer:
4 to 13
4:13
Step-by-step explanation:
I finished my test and these were the answers
The ratio of the number of fish to the total number of pets Dalia has is 4 to 13 or 4:13.
Explanation:The subject of this question is the calculation of a ratio. In this case, the asked ratio is the number of fish to the total number of pets that Dalia has. Dalia has 4 fish and a total of 9 hamsters + 4 fish = 13 pets. Therefore, the correct answer is the ratio of 4 (fish) to 13 (total pets). This ratio can be represented in two ways: B) 4 to 13 or E) 4:13. The other options represent different ratios and do not correctly answer the question.
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Can someone please help me with this problem
Answer:
745.5 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the trig function relating the hypotenuse and the side opposite an angle. It tells you ...
Sin = Opposite/Hypotenuse
The line marked x (the hypotenuse of the triangle) is a transversal crossing the two parallel horizontal lines. That means the interior angle of the triangle at lower right (the angle of elevation) has the measure 28°. That angle is opposite the side marked 350 ft. So, you have ...
sin(28°) = (350 ft)/x
Multiplying by x/sin(28°), this equation becomes ...
x = 350 ft/sin(28°)
x ≈ 745.5 ft
Suppose you graphed every single point of the form $(2t + 3, 3-3t)$. For example, when $t=2$, we have $2t + 3 = 7$ and $3-3t = -3$, so $(7,-3)$ is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.
Answer:
see below for explanation
3x +2y = 15
Step-by-step explanation:
The x-coordinate and the y-coordinate are both linear functions of t, so their relationship to each other is linear. A graph of those (x, y) points must be a line.
___
You can find an equation by solving one of the expressions for t, then substituting that into the other.
x = 2t +3
t = (x -3)/2
Substituting into the y expression, we get ...
y = 3 -3(x -3)/2
y = (-3/2)x + 15/2
3x +2y = 15 . . . . . . . add 3/2x and multiply by 2 to put into standard form
_____
The attached graph shows a portion of the line defined parametrically (0 ≤ t ≤ 1). It is dotted so you can see it overlays the line defined by the linear equation in x and y.
Can someone please help me on this
Answer:
• The function is a linear function
• The function changes at a constant rate
Step-by-step explanation:
A graph of the function shows it to be a straight line (linear function). Such a function always changes at a constant rate. The line goes downward to the right, so the function is a decreasing function.
___
"changes at a constant rate" and "linear function" are two different ways of saying the same thing: the graph of the function is a straight line.
If 2n + 3(2- 2n) = 14 what is the value of n? (Please give the correct answer, I will give brainliest)
Answer:
n = -2
Step-by-step explanation:
Eliminating parentheses, you have ...
2n +6 -6n = 14
Combining terms and subtracting 6, you get ...
-4n = 8
Dividing by the coefficient of n gives ...
n = -2
_____
Check
2(-2) +3(2 -2(-2)) = 14
-4 +3(2+4) = 14
-4 +3(6) = 14
-4 +18 = 14 . . . . answer checks OK
Which of the following is the third term of the expansion (a + b)^n ?
C(n, 2)a^n - 2b^2
C(n, 3)a^n - 3b
C(n, 2)a^2b^n - 2
Answer:
C(n, 2)a^(n-2)b^2
Step-by-step explanation:
Generally, the expansion is written in decreasing powers of "a", so the first few terms would have variable constellations that look like ...
a^n, a^(n-1)b, a^(n-2)b^2, ...
The coefficients would be (in order), C(n, k) for k increasing from 0, so the coefficient of the 3rd term would be C(n, 2).
How would you convert 276 yards to inches?
Add up the digits
Multiply by 36
Change the unit measure
Answer:
9936 inch.
Step-by-step explanation:
Note the measurements:
1 Yard = 3 Feet
1 Feet = 12 Inch
1 Yard = 3 Feet = (12)(3) Inches = 36 Inches; 1 Yard = 36 Inches
Multiply 276 with 36
276 x 36 = 9936
9936 inches is your answer.
~
the kerns pen company makes ballpoint pens. the fixed cost of operation for one month averages $53500. the cost of producing one pen is $.75 and the pens are sold for $1.05 each. how many pens must be sold in order for the oay to break even?
Answer:
178,334 pens
Step-by-step explanation:
The company makes $0.30 above the variable cost on each pen, so must sell $53,500/$0.30 ≈ 178,334 pens to cover the cost of operation.
_____
Sale of 178,333 pens will result in a total cost of $0.10, so doesn't quite make the company break even. Sale of 178,334 pens will result in profit of $0.20.
What is 125% of 332?
Answer:
W = 415
Step-by-step explanation:
Is means equals and of means multiply
W = 125% * 332
Change to decimal form
W = 1.25 *332
W = 415
For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?
Answer:
0.335
Step-by-step explanation:
1. There is a 30 percent chance of a flight being delayed because of icy weather ,then the probability of being delayed is 0.3 and of being not delayed is 0.7.
2. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem, then the probability of being delayed is 0.1 and the probabilty of not being delayed is 0.9.
3. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem (MP), then the probability of being delayed is 0.05 and the probabilty of not being delayed is 0.95. (See attached probability tree)
Delayed of icy weather - 0.3
Delayed of MP when weather is not icy - 0.7·0.05=0.035
Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is
0.3+0.035=0.335
The probability that the flight selected will have at least one of the two types of delays is [tex]0.335[/tex].
1. There is a [tex]30[/tex]% chance of a flight being delayed because of icy weather, [tex]\therefore[/tex] probability of being delayed is [tex]P(a)=0.3[/tex]
probability of not being delayed is [tex]P(a')=1-0.3=0.7[/tex].
2. If a flight is delayed because of icy weather, there is [tex]10[/tex]% chance the flight will also be delayed because of a mechanical problem,
[tex]\therefore[/tex] probability of being delayed is [tex]P(b)=0.1[/tex]
probability of not being delayed is [tex]P(b')=1-0.1=0.9[/tex].
3. If a flight is not delayed because of icy weather, there is [tex]5[/tex]% chance that it will be delayed because of a mechanical problem ,
[tex]\therefore[/tex]probability of being delayed is [tex]P(c)=0.05[/tex]
probability of not being delayed is [tex]P(c')=1-0.05=0.95[/tex].
Delayed of mechanical problem when weather is not icy is:
[tex]P(a'\cap c)=P(a').P(c)=0.7\times 0.05=0.035[/tex]
Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is
[tex]P(a'\cap c)+P(a)=0.035+0.3=0.335[/tex]
Learn more about Probability.
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write a function to model the situation.
a digital image is reduced or enlarged by dragging the corner. the height to width ratio is always maintained as that the width is 1.25 times the height. write a function to model the area of the image as a function of its height.
please help and thank you !!
Answer:
a(h) = 1.25h²
Step-by-step explanation:
The formula for the area of a rectangle is ...
A = HW . . . . . where H represents the height and W represents the width
If the image has a height of h, then the width is 1.25 times that, or 1.25h. Putting these values into the formula, we have ...
A = h·(1.25h)
A = 1.25h²
In function form, we can write a(h), area as a function of height, as ...
a(h) = 1.25h²
Someone explain to me how I do this law of sines problem
Answer:
44.1 cm
Step-by-step explanation:
In order to find the length of side "a", you need to know the measure of angle A. That is found by making use of the fact that the sum of angles in a triangle is 180°.
102° + 28° + A = 180°
A = 180° -130° = 50°
Now, you can fill in the given information in the given equation and solve for "a":
sin(A)/a = sin(B)/b
sin(50°)/a = sin(28°)/(27 cm)
Multiplying by a(27 cm) gives ...
sin(50°)(27 cm) = a·sin(28°)
Dividing by the coefficient of "a", we get ...
a = (27 cm)sin(50°)/sin(28°) ≈ 44.0563 cm
Rounded to the nearest tenth, this is ...
a ≈ 44.1 cm
_____
Since we're looking for a side length (not an angle), I prefer to write the Law of Sines formula "upside down" from that shown:
a/sin(A) = b/sin(B) = c/sin(C)
Then it is one step to get to ...
a = b·sin(A)/sin(B) . . . . . . multiply by sin(A)
Please help!! 30 points!! Will mark brainliest!!
Answer:
x = ab/c
Step-by-step explanation:
The product of the distances from the point of intersection of the chords (secants) to the circle is the same for both chords (secants). (This is true whether the point of intersection is inside or outside the circle.)
ab = cx
x = ab/c
find the area of the yellow region round to the nearest tenth
Please help! For my little sister
Answer:
So first, we need to find the area of the whole circle since we already had the radius:
A = πr² = 3.14 . 7.53² = 178.040826 (cm²)
Now our next job is to find the area of the square inside the circle.
Looking at the picture, we can see that the radius of the circle is also half of the diagonal of the square, so the whole diagonal of the square should be: 7.53 . 2 = 15.06 (cm)
*Now this is where things get a little bit more complicated:
Imagine that x is the length of the side of the square.
Using Pythagorean theorem, knowing that d is the diagonal of the square and also the hypotenuse of the right triangle inside the square, we have the equation:
a² + a² = d²
2a² = d²
a² = d²/2
a² = 226.8036/2 = 113.4018
So a², which is also the area of the square, is 113.4018 (cm²)
So the are of the yellow region is: 178.040826 - 113.4018 ≈ 64.6 (cm²)
*I could be wrong though
solve the equation n+5=2n-1
n+5=2n-1
5=n-1
6=n <— Answer