Answer:
4.086 < 5.025 true
6.37 = 6.370 true
64.28 > 64.281 false
11.716 < 11.708 false
64.28 > 64.281 false
3,756.082 < 3,756.802 true
Step-by-step explanation:
First, let's define how the symbols work.
a < b means that a is strictly smaller than b
a > b means that a is strictly greater than b
Also, for rounding up or down:
Suppose that we want to round to the second decimal after the decimal point.
Then, we need to look at the third one, if it is 5 or larger, we round up.
if it smaller than 5, we round down.
We need to see if each statement is true or not.
a) 4.086 < 5.025
This is true, the number 5.025 is larger than 4.086 (you only need to see at the units digit) So this statement is true.
b) 6.37 = 6.370
Because the third digit is equal to zero, we can round down the right number to 6.37, then the equality is true.
c) 11.716 < 11.708
11.716 is actually larger than 11.708, so this statement is false
d) 64.28 > 64.281
We have that:
64.28 + 0.001 = 64.281
Then 64.281 is larger than 64.28, so this statement is false.
e) 3,756.082 < 3,756.802
By looking at the numbers after the decimal point, we can see that the right number is larger than the left one, then the statement is true.
Find the value of x
Answer:
Hello! answer: x = 4
Step-by-step explanation:
Because this is a 180 degree angle it will add up to 180 so 8 × 4 = 32 and 32 + 120 = 152 and 7 × 4 = 28 and 28 + 152 = 180 so 4 is x HOPE THAT HELPS!!
180 degree line-
180 = (8x + 120)
-120
60 = 8x
/8
7.5
x = 7.5
7(7.5) = 52.5
what is the value of x over 20 = 5 over 8
Answer:
x = 12.5
Step-by-step explanation:
The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors have prices that were less than $3.12 per gallon
Answer:
[tex]P(x<3.12)= 0.21186[/tex]
Step-by-step explanation:
Mean [tex]\=x=\$3.20[/tex]
Standard deviation [tex]\sigma =\$0.10[/tex]
Estimated price [tex]y=\$3.12[/tex]
Generally the equation for P(x<3.12) is mathematically given by
[tex]P(x<3.12)=P(\frac{y-x}{\sigma}<-\frac{3.12-3.20}{0.10})[/tex]
[tex]P(x<3.12)=(z<-0.8)[/tex]
Since from Z table
[tex]P(x<3.12)= 0.21186[/tex]
Therefore the proportion of the milk vendors that have prices that were less than $3.12 per gallon is
[tex]P(x<3.12)= 0.21186[/tex]
Find the measure of the missing interior angle of the polygon.
Answer: 224
Step-by-step explanation:
The total degrees of a 7-sided shape is 900. You can find that out using the equation (n-2) times 180. Where n is the number of sides. If you add up all the interior angles they equal 676. Then just subtract 676 from 900. 900-676= 224 degrees. That is the missing interior angle.
Find the measure of angle x, if possible. Round to the nearest tenth. (If not possible, enter IMPOSSIBLE.)
If f(x) = 3x - 2 and g(x) = -x + 4, find (g o f)(x).
Answer:
-3x + 6
Step-by-step explanation:
(gof) = -(3x-2)+4
= -3x + 2 + 4
= -3x + 6
James says hello to every fourth grown every 6 boy he meets how often does James say hello to both the boy and girl together
Answer:
Six multipled by four to get how many girls and boy he will sayhrllo to.
How do your write a feaction with a denominator of 20 as a decimal?
Answer:
Step-by-step explanation:
What is 20 as a decimal? To write 20 as a decimal you have to divide numerator by the denominator of the fraction. 20 is not a fraction so it is a decimal already. And finally we have: 20 as a decimal equals 20
Help me please!!!!!!
What number is the best prediction! Please help :(
Answer:
28
Step-by-step explanation:
the table below shows the distribution of students in Mrs. boxer 6th grade class what is the ratio of the number of girls to the total number of students ? * it is 15 boys and 12 girls. Write each ration as a fraction
Answer:
Ratio is 12:27 ratio as a fraction is 12 over 27
Step-by-step explanation:
no need for explaination lolz
HELP ASAP I WILL MARK BRANLIEST!!!
This probability distribution shows the
number of times a group of people takes
selfies before liking them.
Retakes
o
1
2
3
4
Frequency
27
29
18
14
12
Using this distribution, find the probability that a
person will retake their sexfie exactly 3 times.
p = [?]
Answer:
0.14
Step-by-step explanation:
0.14 is the probability that a person will retake their sexfie exactly 3 times.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
Total frequency = 27+29+18+14+12 = 100
frequency of 3 retakes = 14
p(r) = frequency of 3 retakes/ Total frequency
p(r) = 14/100 = 0.14
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what is the area of the object above
Answer:
62 sq cm
Step-by-step explanation:
if you find the area of the entire shape (12x6) you can then subtract out the cut-out portion (5x2)
72 - 10 = 62
Is it possible to construct a triangle with the given side lengths?
1 ft, 6 ft, 9 ft
Yes or no?
CHECKING YOUR UNDERSTANDING
Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper
1. A dinner plate has a diameter of 10.2 cm. What is the area of the dinner plate?
A. 81.67 cm
C. 93.84 cm
B. 85.12 cm
D. 100.02 cm
2. A dog is tied to a wooden stake in a yard. His leash is 3 m long, and he runs around
in circles pulling the leash as far as it can go. How much area does the dog have
to run around ?
A. 26.28 m2
C. 29.66 m2
B. 28.26 m2
D. 32.28 m²
3. A storm is expected to hit 7 mi in every direction from a small town of Malabon.
What is the area that the storm will affect?
A. 116.68 mi
C. 150.67 mi
B. 124.83 mi
D. 153.86 mi
4. Every December, an amusement park is constructed in Malabon Robinsons Town
mall. A carousel is the most favorite ride of the kids there. The diameter of the
carousel is 20.5 m. What is the area of the carousel?
A. 329.90 m²
C. 392.90 m2
B. 328.90 m2
D. 391.90 m2
5. A lawn sprinkler sprays water 4.5 ft in every direction as it rotates. What is the area
of the sprinkled lawn?
A. 56.885 ft
C. 63.585 ft
B. 60.855 ft
D. 65.385 ft
Answer:
1) 81.67 cm² (Option A)
2) 28.26 m² (Option B)
3) 153.86 mi.² (Option D)
4) 329.90 m² (Option A)
5) 63.585 ft.² (Option C)
Step-by-step explanation:
GENERAL FORMULAES TO BE USED IN THIS QUESTION :-
Diameter of a circle with radius 'r' = 2r
Area of a circle with radius 'r' = πr²
SOLUTION :-
1) Diameter of the dinner plate = 10.2 cm
Radius of the dinner plate = 10.2/2 = 5.1 cm
⇒ Area of the circle = π(5.1)² = 26.01π cm² ≈ 81.67 cm²
2) Length of his leash = 3m
⇒ Area the dog has to run around = π(3)² = 9π m² = 28.26 m²
3) Radius of the circular range of storm = 7 mi.
⇒ Area of the circular range of storm = π(7)² = 49π mi.² = 153.86 mi.²
4) Diameter of carousel = 20.5 m
Radius of carousel = 20.5/2 = 10.25 m
⇒ Area of the carousel = π(10.25)² = 105.0625π m² ≈ 329.90 m²
5) Radius of the range of sprinkler = 4.5 ft.
⇒ Area of the range of sprinkler = π(4.5)² = 20.25π ft.² = 63.585 ft.²
(4y − 3)(2y2 + 3y − 5)
Answer:
8y^3+6y^2-29y+15
Step-by-step explanation:
the correct expression is
(4y − 3)(2y^2 + 3y − 5)
Given data
We have the expression
(4y − 3)(2y^2 + 3y − 5)
let us open bracket
8y^3+12y^2-20y-6y^2-9y+15
Collect like terms
8y^3+12y^2-6y^2-20y-9y+15
8y^3+6y^2-29y+15
The universal set is the set of rational numbers. S is the set of integers.
Which represents SC?
{x|x is a real number}
{x|x is a rational number}
{x|x is a rational positive number}
{x|x is a rational non-integer}
Answer:
It's D on EDGE
Step-by-step explanation:
The compliment of the set S is {x|x is a rational non-integer}
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the universal set be represented as U
where the value of U is
U = {x|x is a rational numbers}
And , let the second set be represented as S,
where S = {x|x is an integer}
Now , the compliment of set S is given by = S'
And , S' = 1 - S
On simplifying , we get
S' = 1 - {x|x is an integer} and it belongs to U
So , S' = {x|x is a rational non-integer}
Hence , the set is S' = {x|x is a rational non-integer}
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A person invests 6500 dollars in a bank. The bank pays 6.5% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 22600 dollars?
you made a batch of 24 cookies for school your brother ate 7 of them without asking you. What fraction of your cookies are left?
dau coroana
daca il faceti
Answer:
I give the crown
if you do
Step-by-step explanation:
Answer:
what does that mean?
Step-by-step explanation:
How do we find the perimeter of a shape 20mm 10mm 20mm 60mm 20mm
Answer:
130mm
Step-by-step explanation:
I'm pretty sure you mean each of the sides is this length... so I'll go off of that. 20+10+20+60+20 is the addition for this problem.
20+10+20+60+20=130 is the answer.
Can someone help me with this worksheet? I'm trying to check my daughter's work and I'm not sure how to do this. Showing the work would help me see where and if shes wrong.
Answer:
Step-by-step explanation:
scam . smď
write a function rule for the statement. The output is five times the input.
Answer:
y=5x
Step-by-step explanation:
If the input is x, then the out put is 5x. So y=5x
HELPPPP THXX PLAAAAASSSSSSSS
Answer:
43
Step-by-step explanation:
interior angles add up to 180
Hector used the quadratic formula to solve the polynomial equation
9x^2+ 8x - 2 = 0
Which number did Hector have to square when he used the quadratic formula?
Answer:
STEP
1
:
Equation at the end of step 1
(32x2 - 8x) - 2 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 9x2-8x-2
The first term is, 9x2 its coefficient is 9 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 9 • -2 = -18
Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is -8 .
-18 + 1 = -17
-9 + 2 = -7
-6 + 3 = -3
-3 + 6 = 3
-2 + 9 = 7
-1 + 18 = 17
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
9x2 - 8x - 2 = 0
STEP
3
:
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = 9x2-8x-2
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 9 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 0.4444
Plugging into the parabola formula 0.4444 for x we can calculate the y -coordinate :
y = 9.0 * 0.44 * 0.44 - 8.0 * 0.44 - 2.0
or y = -3.778
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 9x2-8x-2
Axis of Symmetry (dashed) {x}={ 0.44}
Vertex at {x,y} = { 0.44,-3.78}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-0.20, 0.00}
Root 2 at {x,y} = { 1.09, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving 9x2-8x-2 = 0 by Completing The Square .
Divide both sides of the equation by 9 to have 1 as the coefficient of the first term :
x2-(8/9)x-(2/9) = 0
Add 2/9 to both side of the equation :
x2-(8/9)x = 2/9
Now the clever bit: Take the coefficient of x , which is 8/9 , divide by two, giving 4/9 , and finally square it giving 16/81
Add 16/81 to both sides of the equation :
On the right hand side we have :
2/9 + 16/81 The common denominator of the two fractions is 81 Adding (18/81)+(16/81) gives 34/81
So adding to both sides we finally get :
x2-(8/9)x+(16/81) = 34/81
Adding 16/81 has completed the left hand side into a perfect square :
x2-(8/9)x+(16/81) =
(x-(4/9)) • (x-(4/9)) =
(x-(4/9))2
Things which are equal to the same thing are also equal to one another. Since
x2-(8/9)x+(16/81) = 34/81 and
x2-(8/9)x+(16/81) = (x-(4/9))2
then, according to the law of transitivity,
(x-(4/9))2 = 34/81
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(4/9))2 is
(x-(4/9))2/2 =
(x-(4/9))1 =
x-(4/9)
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-(4/9) = √ 34/81
Add 4/9 to both sides to obtain:
x = 4/9 + √ 34/81
Since a square root has two values, one positive and the other negative
x2 - (8/9)x - (2/9) = 0
has two solutions:
x = 4/9 + √ 34/81
or
x = 4/9 - √ 34/81
Note that √ 34/81 can be written as
√ 34 / √ 81 which is √ 34 / 9
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving 9x2-8x-2 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 9
B = -8
C = -2
Accordingly, B2 - 4AC =
64 - (-72) =
136
Applying the quadratic formula :
8 ± √ 136
x = —————
18
Can √ 136 be simplified ?
Yes! The prime factorization of 136 is
2•2•2•17
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 136 = √ 2•2•2•17 =
± 2 • √ 34
√ 34 , rounded to 4 decimal digits, is 5.8310
So now we are looking at:
x = ( 8 ± 2 • 5.831 ) / 18
Two real solutions:
x =(8+√136)/18=(4+√ 34 )/9= 1.092
or:
x =(8-√136)/18=(4-√ 34 )/9= -0.203
Two solutions were found :
x =(8-√136)/18=(4-√ 34 )/9= -0.203
x =(8+√136)/18=(4+√ 34 )/9= 1.092
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
ax² + bx + c = 0
In the quadratic formula the "b" coefficent gets sqaured
bx = 8x
b = 8
Answer choices)
A. (2/3x, 2/3y)
B. (3/2x, 3/2y)
C. (1/2x, 1/2y)
D. (2x, 2y)
Please help me :((
9514 1404 393
Answer:
B. (3/2x, 3/2y)
Step-by-step explanation:
It is perhaps easiest to see that B' is 3 grid squares from the origin while B is 2 grid squares from the origin. The scale factor is the ratio of these distances:
3/2
Dilation about the origin multiplies each coordinate value by the scale factor:
(x, y) ⇒ (3/2x, 3/2y)
A researcher is testing a hypothesis of a single mean. The critical z value for a = .05 and a two‑tailed test is +1.96. The observed z value from sample data is ‑2.05. The decision made by the researcher based on this information is to _____ the null hypothesis.
Answer:
The decision made by the researcher based on this information is to reject the null hypothesis.
Step-by-step explanation:
Two-tailed hypothesis test:
Critical value: [tex]z_c[/tex]
Test statistic: z
If [tex]|z| < |z_c|[/tex], we do not reject the null hypothesis.
If [tex]|z| > |z_c|[/tex], we reject the null hypothesis.
In this question:
[tex]z_c = 1.96, z = -2.05, |z| = 2.05[/tex]
Since [tex]|z| > |z_c|[/tex], we reject the null hypothesis.
The decision made by the researcher based on this information is to reject the null hypothesis.
A right triangle has legs with lenghts of 7 units and 12 units. What is the area of the triangle?
Answer:
area of triangle =1/2 x b x h
Step-by-step explanation:
=1/2 x 7 x 12
= 1/2 x 84
= 42 units
Factorize this fully 20x² +500x+3000
Answer:
20(x+15)(x+10)
Step-by-step explanation:
Hi there!
As your question states, we need to fully factor the polynomial: 20x²+500x+3000
These are pretty big numbers; let's pull out the GCF, as that will make it easier to factor
the GCF is 20
so factoring 20 out of the polynomial will get:
20(x²+25x+150)
As you can see, the polynomial inside the parenthesis is a lot easier to factor than the original with really big numbers.
Now use FOIL to factor x²+25x+150 into 2 binomials
25 is the sum of the last terms
150 is the product of the last terms
think: which two numbers add up to 25 but multiply to get 150?
those two numbers are 15 and 10
x²+25x+150 factored is (x+15)(x+10)
but remember we have the 20 in front of x²+25x+150 (or now, (x+15)(x+10))
therefore the fully factored binomial is 20(x+15)(x+10)
Hope this helps! :)
A company has machinery calibrated for a certain widget to manufacture the product so that all of the products will average out to a mean weight of 7 grams and a standard deviation of 2 grams. What would you expect as a sampling distribution if you were to take repeated samples of 100 widgets?
Answer:
By the Central Limit Theorem, the sampling distribution of repeated samples of 100 widgets would be approximately normal with mean 7 grams and standard deviation 0.2 grams.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean weight of 7 grams and a standard deviation of 2 grams.
This means that [tex]\mu = 7, \sigma = 2[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]
What would you expect as a sampling distribution if you were to take repeated samples of 100 widgets?
By the Central Limit Theorem, the sampling distribution of repeated samples of 100 widgets would be approximately normal with mean 7 grams and standard deviation 0.2 grams.