x-intercept(s): (1/2, 0) or (0.5, 0)
y-intercept(s): (0, −2)
Q3. Express 984. 6080 correct to
a. 2 decimal places _______________
b. 4 significant figures _____________
c. 3 decimal places ________________
d. the nearest hundredth___________ help
Answer:
a) 984.6080 = 984.61 to 2 decimal places
b) 984.6080 = 984.6 to 4 significant figures
c) 984.6080 = 984.608 to 3 decimal places
d) 984.6080 = 984.61 to the nearest hundredth
Step-by-step explanation:
Answers to the approximation questions above are supplied below.
First, you needs to know approximation processes:
Step 1: Keep the required number of digits in question.
Step 2: Before rounding off the remaining digits, look at the next digit to the required number of accuracy, if it is 5 or more, increase the last digit of the number you're keeping by 1, otherwise leave it as it is and round down to zero all the unwanted digits.
Similarly, there is need know the meaning of each degree of accuracy.
1. Decimal places: These are the number of digits occurring after the decimal point. E.g. a set of figures in 1 decimal place has only one digit after decimal point, i.e. 65.4. In the case of the question above,
a) 984.6080 = 984.61 to 2 decimal places
c) 984.6080 = 984.608 to 3 decimal places
2. Significant figures: Basically, these are nonzero digits in a set of figures. However, when zero is in the middle of nonzero digits, i.e, 3045, such zero is a significant figure. In the question above,
b) 984.6080 = 984.6 to 4 significant figures
3. Hundredth: Under place value system, hundredth of a set of figures is located at two digits after the decimal point. In other words, hundredth is same as two decimal places so the same approach is required for the two. Thus;
d) 984.6080 = 984.61 to the nearest hundredth
You can see that the result for both 2 decimal places and nearest hundredth are the same, that is, 984.6080 = 984.61 to 2 decimal places and to the nearest hundredth respectively.
Therefore, the answers are summarized thus:
a) 984.6080 = 984.61 to 2 decimal places
b) 984.6080 = 984.6 to 4 significant figures
c) 984.6080 = 984.608 to 3 decimal places
d) 984.6080 = 984.61 to the nearest hundredth
Answer:
984.6080
a. 2 decimal places
984.61
b. 4 significant figures
984.6
c. 3 decimal places
984.608
d. the nearest hundredth
984.61
Prove that cos²(A-B)-sin²(A+B)=cos2Acos2B
Answer:
see below
Step-by-step explanation:
Prove : cos²(A-B)-sin²(A+B)=cos2Acos2B
LHS,
cos²(A-B) - sin²(A+B) (expand using double angle identities)
= [tex]\frac{1 + cos [2(A-B)]}{2} - \frac{1 - cos [2(A+B)]}{2}[/tex]
= [tex]\frac{1}{2} + \frac{1}{2} cos[2(A-B)] - \frac{1}{2} + \frac{1}{2} cos[2(A+B)][/tex]
= [tex]\frac{1}{2} cos[2(A-B)] + \frac{1}{2} cos[2(A+B)][/tex]
= [tex]\frac{1}{2} cos(2A-2B) + \frac{1}{2} cos(2A+2B)[/tex] (expand using sum/difference identities)
= [tex]\frac{1}{2} (cos2Acos2B + sin2Asin2B ) + \frac{1}{2} (cos2Acos2B - sin2Asin2B )[/tex]
= [tex]\frac{1}{2} cos2Acos2B + \frac{1}{2}sin2Asin2B + \frac{1}{2} cos2Acos2B - \frac{1}{2}sin2Asin2B[/tex]
= [tex]\frac{1}{2} cos2Acos2B + \frac{1}{2} cos2Acos2B[/tex]
= [tex]cos2Acos2B[/tex] (= RHS , Proven)
A frog sitting on a stump 3 feet high hops off and lands on the ground.
During its leap, its height h in feet is given by h= -0.5d^2 + 2d + 3, where d
is the distance from the base of the stump. How far is the frog from the
base of the stump when it landed on the ground? *
Answer: The distance of frog from the base of the stump is 5.16 feet ( approx)
Step-by-step explanation:
Given, A frog sitting on a stump 3 feet high hops off and lands on the ground.
During its leap, its height h in feet is given by [tex]h= -0.5d^2 + 2d + 3[/tex], where [tex]d[/tex] is the distance from the base of the stump.
When the stump landed on the ground, h= 0 .
So put h=0 in the given equation , we get
[tex]0=-0.5d^2 + 2d + 3\\\\\Rightarrow\ 0.5d^2-2d-3=0[/tex]
Multiply both sides by 2 , we get
[tex]d^2-4d-6=0\\\\\Rightarrow\ d=\dfrac{-(-4)\pm\sqrt{4^2-4(1)(-6)}}{2(1)}\\\\=\dfrac{4\pm\sqrt{16+24}}{2}\\\\=\dfrac{4\pm\sqrt{40}}{2}\\\\=\dfrac{4\pm2\sqrt{10}}{2}=2\pm\sqrt{10}[/tex]
[tex]i.e.\ d=2-\sqrt{10}\ \ or\ \ d=2+\sqrt{10}\\\\\ i.e. d=2-3.1622\ \ or\ \ d=2+3.1622\\\\ i.e. d= -1.1622\ \ or\ \ d=5.1622\approx5.16[/tex]
Since , distance cannot be negative.
Hence, the distance of frog from the base of the stump is 5.16 feet ( approx).
whats the least common denominator of 2/5 1/2 and 3/4?
Answer:
20
Step-by-step explanation:
Final answer:
The least common denominator for the fractions 2/5, 1/2, and 3/4 is 20, as it is the smallest number that all denominators can divide into without leaving a remainder.
Explanation:
The least common denominator (LCD) of the fractions 2/5, 1/2, and 3/4 is the smallest number that can be divided evenly by each of the denominators (5, 2, and 4, respectively). To find the LCD, we can list out the multiples of each denominator until we find a common multiple.
The multiples of 5 are 5, 10, 15, 20, 25, and so on. The multiples of 2 are 2, 4, 6, 8, 10, 12, and so on. The multiples of 4 are 4, 8, 12, 16, 20, and so on. When we look at these lists, the smallest number that appears in all three lists is 20. Therefore, 20 is the least common denominator for the fractions 2/5, 1/2, and 3/4.
A guinea pig weighs 1,130 grams.
What does the guinea pig weigh measured in kilograms?
The weight of the guinea pig measured in kilograms is A = 1.130 kg
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the measurement of unit be represented as A
Now , the weight of the guinea pig = 1,130 grams
where from the unit conversion
1000 grams = 1 kg
So , weight of the guinea pig measured in kilograms A = 1,130 grams / 1000
On simplifying , we get
The weight of the guinea pig measured in kilograms A = 1.130 kilograms
Therefore , the value of A is 1.13 kg
Hence , the measurement is A = 1.13 kg
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The guinea pig weight measured in kilograms is 1.13kgs.
To convert the weight of a guinea pig from grams to kilograms, you need to understand the relationship between these units:
In the metric system, 1 kilogram (kg) is equal to 1,000 grams (g).
Start with the weight of the guinea pig: 1,130 grams.
Use the conversion factor: 1,000 grams = 1 kilogram.
Divide the weight in grams by the conversion factor to find the weight in kilograms.
1,130 grams ÷ 1,000 = 1.13 kilograms.
The data set below shows the weights of some puppies, in pounds, at a kennel:
10, 10, 10, 11, 12, 12, 14, 14, 15
Which histogram represents the data set?
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 2, the bar for the second range goes to 4, the bar for the third range goes to 3.
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 3, the bar for the second range goes to 4, the bar for the third range goes to 2.
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 2, the bar for the second range goes to 3, the bar for the third range goes to 4.
A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 4, the bar for the second range goes to 2, the bar for the third range goes to 3.
Answer:
D. A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 4. The bar for the second range goes to 2, the bar for the third range goes to 3.
Find yhe difference 2/5 - 3/10
which expression is equivilent to 3x/x+1 divided by x+1?
Step-by-step explanation:
[tex] \frac{3x}{x + 1} \div (x + 1) \\ \\ = \frac{3x}{x + 1} \times \frac{1}{(x + 1) } \\ \\ = \frac{3x}{ {(x + 1)}^{2} } [/tex]
Antoine is designing a new, cylindrical drinking glass. If the glass has a diameter of 8 centimeters and a height of 12.8, what is it’s volume? Round to the nearest tenth
Answer:
643.4
Step-by-step explanation:
Answer:
The answer is: 643.4
Step-by-step explanation:
A rectangular stained glass window is made up of identical triangular parts as pictured below.
36 inches
48 inches
What is the area of the shaded triangular section?
18 square inches
36 square inches
72 square inches
144 square inches
Answer:
The area of the shaded triangular section is 72 square inches
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The rectangular stained glass can be divided into 24 identical triangular parts
step 1
Determine the area of complete rectangle
[tex]A=(48)(36)=1,728\ in^2[/tex]
step 2
Divide the area of complete rectangle by 24
[tex]1,728/24=72\ in^2[/tex]
therefore
The area of the shaded triangular section is 72 square inches
Answer:
72 square inches
Step-by-step explanation:
The image is shown below.
The area of a rectangle is length times width.
Length is 48 and width is 36
Hence, area of whole rectangle is:
Area = 48 * 36 = 1728
Now, the whole figure is broken down into
24 congruent triangles
So, each triangle's area is:
1728/24 = 72 square inches
The shaded region is ONE of the triangles, so the shaded region area is:
72 square inches
Write an algebraic expression that represents A less than 27.
Answer:
A=26
Step-by-step explanation:
well, A is less than 27 so A could be 26?
What is 6h-15 when h = 3
Answer:
H=3
Step-by-step explanation:
1. 6(3)-15
2.18-15
3. 3
4. Brainliest please
40 POINTS IF YOU ANSWER. YOU WILL GET BRAINLIEST!!! Plz need ASAP
Consider the following algorithm:
Step 1: Start with a list of the positive integers from 2 to 100, inclusive (meaning you include 2 and 100 in your list).
Step 2: For each n from 2 to 50, inclusive, do the following: Remove all multiples of n greater than n from the list.
Step 3: Output all of the numbers remaining in the list.
What is the tenth number in the list that gets output?
Answer:
29
Step-by-step explanation:
If all the multiples are removed, you'll be left with prime numbers only
2, 3, 5, 7, 11, 13, 17, 19, 23, 29..
The tenth prime no. is 29
Answer:
29
Step-by-step explanation:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100
Delete all even numbers greater than 2 since they are multiples of 2
2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99.
Now delete multiples of 3 greater than 3
2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, , 89, 91, , 95, 97,
We can skip all even numbers since they we all ready taken care of by deleting the evens
Now delete multiples of 5 greater than 5
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97,
Now delete multiples of 7 greater than 7
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
There are no more numbers to delete since these are all prime numbers
29 is the 10th number in the list
12 points, help plz.
Here is a number machine.
Input x5
Output -3
a) work out the output when the input is 8
b) work out the input when the output is 42
Answer:
thought it would be 7.8, could be wrong not sure
Step-by-step explanation:
42 -3= 39/5=7.8
Step-by-step explanation:
ty for the free points tho
F(x)= (x-2)(x-3)(x-5) simplify the right side. What is the equation?
Answer:
x³ - 10x² + 31x - 30
Step-by-step explanation:
Given
(x - 2)(x - 3)(x - 5) ← expand the second pair of factors using FOIL
= (x - 2)(x² - 8x + 15) ← distribute
= x³ - 8x² + 15x - 2x² + 16x - 30 ← collect like terms
= x³ - 10x² + 31x - 30
Calculate the final displacement from 0 if an object first
moves 3 cm to the left and then 5 cm to the right.
The final displacement is cm to the
Answer:
final displacement = - 3cm +5cm = + 2 cm
ie 2 cm towards right
For which values of x is the expression undefined?
X – 9
——————
X^2+9x + 18
Answer:
-3, -6
Step-by-step explanation:
Any number of x that makes the bottom 0 makes the expression undefined.
Factor the polynomial in the denominator:
(x+3)(x+6)
Values of x that makes the expression undefined are -3 and -6
Support me by choosing my answer as the brainiest :)
Royston plays a video game 7 times.His scores are 60,65,66,74,69,72 and 63.Which is the best measure of center of Royston's performance?
Answer:
The mean will be the best instrument to measure Royston's performance
Step-by-step explanation:
The mean will be the best measure Royston's performance will be mean as it will help to decide how well Royston performed all round
A cash register contains $10 bills and $100 bills with a total value of $2010. If there are 30 bills total, then how many of each does the register contain? $10 bills
Answer:
there will be 19 $100 bills
and 11 $10 bills
Step-by-step explanation:
[tex]100*19=1900\\10*11=110\\1900+110=2010[/tex]
Answer:
11
Step-by-step explanation:
Let x be how many $10 bills there are.
Let y be how many $100 bills there are
x + y = 30
x = 30 - y
10x + 100y = 2010
10(30 - y) + 100y = 2010
300 - 10y + 100y = 2010
-10y + 100y = 2010 - 300
90y = 1710
y = 1710 / 90
y = 19
x = 30 - 19
x = 11
(i) Calculate the mean and standard deviation for these weekly incomes.
221 248 251 255 259 263 264 272 291 297 374
Answer:
Mean = 272.3
sd = 37.7
Step-by-step explanation:
Mean = sum/n
(221+248+251+255+259+263+264+272+291+297+374) ÷ 11
= 2995/11
= 272.2727273
Variance = (sum of x²)/n - mean²
[(221²+248²+251²+255²+259²+263²+264²+272²+291²+297²+374²)/11] - (2740/11)²
= (831067/11) - (2995/11)²
= 1419.107438
sd² = variance
sd = sqrt(1419.107438)
sd = 37.67104243
A cylinder with height 10 inches and radius 4 inches is filled with water. The water is poured into a bowl
(hemisphere) with radius 5 inches. Sketch a cylinder and a hemisphere with dimensions labeled. If all the water
will fit, tell how much empty space remains in the bowl. If all the water will not fit, tell how much water is left in
the cylinder. (leave your answer in terms of pi)
Answer:
Volume of water left in the cylinder=[tex]76\frac{2}{3}\pi \:in^3[/tex]
Step-by-step explanation:
Height of the Cylinder=10 inches
Radius of the cylinder=4 Inches
Volume of the Cylinder
[tex]=\pi r^2h\\=4^2*10\pi\\=160\pi\:in^3[/tex]
Radius of the Hemisphere=5 Inches
[tex]\text{Volume of a Hemisphere}=\frac{2}{3}\pi r^3\\ =\frac{2}{3}\pi *5^3\\=\frac{250\pi}{3} in^3[/tex]
Since the Volume of the cylinder is greater than the Volume of the bowl, all the water will not fit.
[tex]\text{Therefore: volume of water left} =160\pi-\frac{250\pi}{3}\\=76\frac{2}{3}\pi \:in^3[/tex]
A rectangle has an area of 80cm² and a perimeter of 48cm.
Find the length and width of the rectangle.
Answer:
20,4
Step-by-step explanation:
Suppose that x, y are the the length and width
Area=x*y=80
Parameter=2(x+y)=48....x+y=24
Xy=80...x(24-x)=80...x=20,y=4
Answer:
20,4
Step-by-step explanation:
20+20+4+4=48
20*4=80
Help worth 10 points!!
Answer:
the answer is B
Step-by-step explanation:
the line is a negative slope so therefore the answer must be negative, use the simple rise over run method to find the slope like normal! :)
We can find 2 points on the graph to solve for the slope; (-2, 0) and (2, -3)
Slope formula: y2-y1/x2-x1
= -3-0/2-(-2)
= -3/4
Therefore, the answer is B.
Best of Luck!
Quadrilateral PQRSis graphed in the coordinate plane.
To the nearest tenth, what is the perimeter of quadrilateral PQRS?
Answer:
33.6
Step-by-step explanation:
As we can see in the graph, the points:
P is located at (-2, 8)Q is located at ( 6, 8) R( is located at (6, 2) S is located at (-5, 0)To find a distance between two points or the length of the segment, we use the following formula:
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
Because the two points P and Q are located at the same libe y = 8
=> the lenght of PQ = [tex]\sqrt{(6- (-2))^{2} } = \sqrt{8^{2} } = 8\\[/tex]
Because the two points R and Q are located at the same libe x = 6
=> the length of RQ = [tex]\sqrt{(8-2)^{2} } = \sqrt{6^{2} } = 6\\[/tex]
The lenght of RS is: [tex]\sqrt{(-5-6)^2+(0-2)^2} = \sqrt{-11^{2} +(-2)^{2} }[/tex] = [tex]\sqrt{125} = 11.1[/tex]
The lenght of SP is: [tex]\sqrt{(-5-(-2))^2+(0-8)^2} = \sqrt{-3^{2} +(-8)^{2} } = \sqrt{73}[/tex] = 8.5
=> the perimeter of quadrilateral PQRS = PQ+RQ+RS+SP
= 8+6+11.1+8.5
= 33.6
Answer:33.7
Step-by-step explanation:
8+8.5+6+11.2=33.7
Which algebraic expression represents the phrase below?
Five times the difference of one-half of a number and two
05-(3x-2)
Answer:
[tex]5( \frac{1}{2}x - 2)[/tex]
How to solve 8z+6=7z+4
Answer:
z= -2
Step-by-step explanation:
Answer:
z = -2 (plz give branliest i need to level up)
Step-by-step explanation:
8z-7z +6 = 4
z = 4 -6
z = -2
Anna is shopping for a new backpack. The probability that the backpack is pink is 0.7, and the probability that it is canvas is 0.7. The probability that it is pink and canvas is 0.5. What is the probability that it is pink or canvas. A) 0.3 B) 0.5 C) 0.9 D) 1.4
The probability that the backpack is pink or canvas is option (c) 0.9.
The probability that the backpack is pink or canvas can be calculated using the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B).
According to the question,
A represents: the event that the backpack is pink
B represents: the event that the backpack is the canvas
Substituting the given probabilities, we get:
P(pink or canvas) = 0.7 + 0.7 - 0.5 = 0.9.
So, the probability that the backpack is pink or canvas is option (c) 0.9.
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There are 3 less than twice as many cats than dogs in the local animal shelter. If there are 210 cats and
dogs combined, how many dogs are in the animal shelter?
There are 71 dogs in the local animal shelter.
To determine the number of dogs and cats in the shelter, let's denote the number of dogs by D and the number of cats by C. According to the problem statement, there are twice as many cats as dogs, minus three. Mathematically, this is represented as C = 2D - 3. We also know that the combined total of cats and dogs is 210, which can be expressed as C + D = 210. To find the number of dogs, we can solve these two equations simultaneously.
From the first equation, we solve for C in terms of D: C = 2D - 3.
Substitute C into the second equation: (2D - 3) + D = 210.
Combine like terms: 3D - 3 = 210.
Add 3 to both sides of the equation: 3D = 213.
Divide both sides by 3 to solve for D: D = 71.
Therefore, there are 71 dogs in the local animal shelter.
Judy is baking a round cake for her niece's birthday and the recipe requires her to coat the bottom of the pan with flour. If the cake pan has an 8-inch diameter, what is the area that she will need to cover with flour on the bottom of the pan?
Answer:
A = 50.24
Step-by-step explanation:
Diameter = 8
8/2 = 4
4 is the radius
A = πr2
A = 3.14 x 42
4 x 4 = 16
A = 3.14 x 16
A = 50.24
Answer:
A = 50.24
Step-by-step explanation:
Diameter = 8
8/2 = 4
4 is the radius
A = πr2
A = 3.14 x 42
4 x 4 = 16
A = 3.14 x 16
A = 50.24
Dr. Strauss has a bottle that contains 18 ounces of medicine. How many one-fourth ounce doses are
in 18 ounces?
There are doses.
Answer:72 IS THE ANSWER
Step-by-step explanation:
BRAINLIEST????? PLEASE
Number of one-fourth ounce doses are in 18 ounces is 72 doses
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What is Division?Division is a simple operation in which a number is divided.
Given,
Bottle contains 18 ounces of medicine
Therefore
Number of one-fourth ounce doses are in 18 ounces = [tex]\frac{18}{0.25}=72[/tex] doses
Hence, Number of one-fourth ounce doses are in 18 ounces is 72 doses
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