Answer:
-All integers are whole numbers.
-All rational numbers are natural numbers.
Step-by-step explanation:
The statement which is correct about the sets of numbers is:
All integers are rational numbers.
Option D is the correct answer.
What is a rational number?A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
We have,
Natural number:
Natural numbers are positive integers or non-negative integers which start from 1 and end at infinity.
Integer:
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Whole number:
Whole numbers include all natural numbers and 0.
It does not include fractions, decimals, and negative integers.
Irrational numbers:
An irrational number is a type of real number which cannot be represented as a simple fraction.
It cannot be expressed in the form of a ratio.
Rational number:
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
From the above definition, we can say that,
- Some integers are whole numbers but not all integers are whole numbers.
- No irrational numbers are integers.
-Some rational numbers are natural numbers but not all rational numbers are natural numbers.
- Yes, all integers are rational numbers.
Thus the statement which is correct about the sets of numbers is:
All integers are rational numbers.
Option D is the correct answer.
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Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.
Answer:
Step-by-step explanation:
Given
Garden: [tex]x^2+18x+81[/tex]
One Bag: [tex]x^2 - 81[/tex]
Requires
Determine the number of bags to cover the whole garden
This is calculated as thus;
[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]
Expand the numerator
[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]
[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]
Express 81 as 9²
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]
Evaluate as difference of two squares
[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]
[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
the temperature at which water freezes on the celsius scale is 0 degrees C. It freezes at 32 degrees F on the Fahrenheit scale, write opposites fo these two numbers as integers.
Answer:
If we have an integer number N, the opposite of N will be:
-1*N = -N.
Then, the opposite of 0°C is:
-1*0°C = 0°C.
The number 0 is it's own opposite.
And for 32F, the opposite is:
-1*32F = -32F
So, while the numbers 0°C and 32F physically represent the same thing (the same temperature), mathematically, they behave differently.
A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information. Find the dye amount that represents the 9th percentile of the distribution.
Answer:
4.464 ml
Step-by-step explanation:
Given that:
mean (μ) = 5 mm, standard deviation (σ) = 0.4 ml
The z score is a score in statistics used to determine by how many standard deviation the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if the z score is negative then the raw score is below the mean It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, the 9th percentile (0.09) corresponds to a z score of -1.34
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.34=\frac{x-5}{0.4}\\\\x-5=-0.536\\\\x=5-0.536\\\\x=4.464[/tex]
The dye amount that represents the 9th percentile of the distribution is 4.464 ml
If the mean difference gets larger and sample standard deviation stays the same, what happens to effect size?
Answer:
The effect size of the sample gets larger
Step-by-step explanation:
The effect size of the sample gets larger when the mean difference gets larger and the sample standard deviation stays the same. because the Cohen's effect size is proportional to mean difference and this can be proven below using the Cohen's formula
Cohen's effect size = Mean difference / standard deviation
form the question standard deviation is constant while the mean difference gets larger, hence the effect size will get larger as well
In the diagram, XY bisects ZWXZ.
1
z
2
w
(5x + 3)
(7x - Y
х
mWYZ
type your answer.
In provided diagram angle WXY = angle YXZ
Angle WXY =( 7x-7)°
Angle YXZ = ( 5x +3)°
We have to find out the value of Angle WXZ
→ 7x-7 = 5x +3
→ 7x - 5x = 7+3
→ 2x = 10
→ x = 10/2
→ x = 5 .
Putting the value of x .
→ Angle WXY = 7(2)-7
→ 14-7 = 7°
→ Angle YXZ = 5(2)+3
→ 10+3 = 13°
Angle WXZ = 13° + 7 ° → 20°
So 20° is the required answer .
Answer:
SI
Step-by-step explanation:
What is the area of polygon EFGH?
Nour drove from the Dead Sea up to Amman, and her altitude changed at a constant rate. When she began driving, her altitude was 400400400 meters below sea level. When she arrived in Amman 222 hours later, her altitude was 100010001000 meters above sea level. Let yyy represent Nour's altitude (in meters) relative to sea level after xxx hours.
Answer:
y = 700x - 400
Step-by-step explanation:
A negative number represents an altitude below sea level.
Beginning: -400
y = mx + b
y = mx - 400
In 2 hours the altitude was now 1000 m.
1000 m - (400 m) = 1400 m
The altitude went up 1400 m in 2 hours. The rate of change is
1400/2 m/h = 700 m/h
The rate of change is the slope.
y = 700x - 400
Answer:
The graph answer is below :)
Step-by-step explanation:
Question 7
2 pts
Find the value of x and the length of segment AC if point B is between A and C.
AB = 5x, BC = 9x-2, AC = 11x + 7.6
Value of x=
Length of AC is
Answer: x=3.2 AC= 42.8
Step-by-step explanation:
As point B lies at segment AC AC=AB+BC
Otherwise we can write the equation
5x+9x-2=11x+7.6
14x-2=11x+7.6
14x-2+2=11x+7.6+2
14x=11x+9.6
14x-11x=11x-11x+9.6
3x=9.6
x=9.6:3
x=3.2
AC= 11*x+7.6= 11*3.2+7.6=35.2+7.6=42.8
Karl needs a total of $30 to buy a bike. He has $12. He can earn $6 an hour
babysitting. Which equation can be used to find the number of hours, h, Karl has to
babysit to have the money he needs?
30 - 6h + 12 = 0
6+ n = 12
6 + 12 h = 30
6 h + 12 = 30
Answer:
6h + 12 = 30
Step-by-step explanation:
Hence, the equation obtained for number of hours worked is given as 12 + 6h = 30.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
The total money required is given as $30.
Suppose the number of hours for babysitting be h.
Then, the money earned by doing it is $6h.
And, the total money with Karl is 12 + 6h.
As per the question, the following equations can be written as,
12 + 6h = 30
Hence, the equation for finding the number of hours is given as 12 + 6h = 30.
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 7.2 to 4.5
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Given
7.2 : 4.5 ← multiply both parts by 10
= 72 : 45 ← divide both parts by 9
= 8 : 5
= [tex]\frac{8}{5}[/tex]
Find the value of NT
A. 4
B. 14
C. 12
D. 16
Answer:
14
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
12*x = 8 * (x+2)
Distribute
12x = 8x+16
Subtract 8x
12x-8x = 8x+16-8x
4x = 16
Divide by 4
4x/4 = 16/4
x = 4
We want NT
NT = 8+x+2
= 10 +x
= 10 +4
= 14
Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university; however, she must pay in euros. How many euros can Varia expect to pay per month to the university?
Answer: 247.92 euros
Step-by-step explanation:
Given, Varia is required pay $3,500 (in US dollars) per year to the university.
If she must pay in euros , then we convert $3,500 into euros.
Current rate : 1 US dollar = 0.85 euro
Then, $3,500 = ( 0.85 x 3500) euros
= 2975 euros
She can expect 2975 euros to pay per year.
Also, [tex]2975\div 12\approx247.92[/tex] [ 1 years = 12 months]
Hence, She can expect 247.92 euros to pay per month to the university.
A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times. Test this hypothesis (use alpha=.05).
1. What is the appropriate test?
2. State the null hypothesis:
3. State the alternative hypothesis:
4. Find the critical value:
5. Calculate the obtained statistic:
6. Make a decision:
7. What does your decision mean
Answer:
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Step-by-step explanation:
Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as
H0 :p 0.5 against Ha: p ≠ 0.5
The significance level is approximately 0.05
The test statistic to be used is number of heads x.
Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution
Heads (x) Probability (X=x) Cumulative Decumulative
0 1/16384 (1) 0.000061 0.000061
1 1/16384 (14) 0.00085 0.000911
2 1/16384 (91) 0.00555 0.006461
3 1/16384(364) 0.02222
4 1/16384(1001) 0.0611
5 1/16384(2002) 0.122188
6 1/16384(3003) 0.1833
7 1/16384(3432) 0.2095
8 1/16384(3003) 0.1833
9 1/16384(2002) 0.122188
10 1/16384(1001) 0.0611
11 1/16384(364) 0.02222
12 1/16384(91) 0.00555 0.006461
13 1/16384(14) 0.00085 0.000911
14 1/16384(1) 0.000061 0.000061
We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).
We observe that P (X≤2) = 0.006461 > 0.025
and
P ( X≥12 ) = 0.006461 > 0.025
Therefore true significance level is
∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122
Hence critical region is (X≤0) and ( X≥14)
Computation x= 12
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
Mark is buying supplies for his students. He is buying a notebook (n) and a pack of pencils for each of his 25 students. Each pack of pencils costs $1.25. If Mark's total cost is $156.25, which of the following equations can be used to find how much each notebook cost? Select TWO that apply.
Answer:
$5
Step-by-step explanation:
Note. There are no options to select.Let the notebook cost x, then Mark spent:
25x + 25*1.25 = 156.2525x + 31.25 = 156.2525x = 156.25 - 31.2525x = 125x= 125/25x= 5Notebook costs $5
In a zoo there are 6 orang-utans for every 3 baboons. There are 27 orang-utans and baboons altogether. How many are orang-utans?
Answer:
18
Step-by-step explanation:
Okay first we know that for every one baboon there is 2 orang-utans (6 / 3 = 2)
So, I like to play the guess and check:
Lets just use the numbers 12 orang-utans and 6 baboons. We know that those two don't equal 27, so thats not it.
Now we can have 18 orang-utans and 9 baboons. 18 + 9 = 27, which means there are 18 orang-utans.
Hope this helps, and have a good day.
Using the FOIL method, find the product of x - 2 and x - 3 .
Answer:
[tex] \boxed{ {x}^{2} - 5x + 6}[/tex]Step-by-step explanation:
[tex] \mathsf{(x - 2)(x - 3)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )
[tex] \mathsf{x×x - 3x - 2x - 2 × ( - 3 )}[/tex]
Calculate the product
[tex] \mathsf{ {x}^{2} - 3x - 2x - 2 \times (- 3)}[/tex]
Multiply the numbers
[tex] \mathsf{ {x}^{2} - 3x - 2x + 6 }[/tex]
Collect like terms
[tex] \mathsf{ {x}^{2} - 5x + 6}[/tex]
Hope I helped!
Best regards!
Simplify 10 - [14 = (3 + 4) · 2]+3
Answer:
There is a typo near the equal sign.
There can be two different answers if we think that = sign as + or -.
First way: Making = as +
=> 10 - [14 + (3+4) x 2] +3
=> 10 - [14 + 7 x 2] + 3
=> 10 - [14 + 14] + 3
=> 10 - 28 + 3
=> 10 + 3 - 28
=> 13 - 28
=> -15
=> So, -15 is the answer if we consider "=" sign as "+" sign.
Second way: Making = as -
=> 10 - [14 - (3+4) x 2] + 3
=> 10 - [14 - 7 x 2] + 3
=> 10 - [14 - 14] + 3
=> 10 - 0 + 3
=> 10 + 3
=> 13
=> So, 13 is the answer if we consider "=" sign as "-" sign.
PLEASE ANSWER ASAP!!!!
Question refers to Table in the picture
Use a proportional reasoning statement like the one in the picture to determine how many feet are in 3 miles. Notice that the conversion fact 1 mile = 5,280 feet is written as a ratio in the picture.
A. x = 15,840 feet
B. x = 10,560 feet
C. x = 21,120 feet
D. x = 26,400 feet
any unrelated answer will be reported
Answer:
The answer is A 15,840, because 5,280 x 3 is equivalent to A
Answer:
A. x = 15,840 feet.
Step-by-step explanation:
[tex]\frac{5280 feet}{1 mile} =\frac{x feet}{3 miles}[/tex]
[tex]\frac{5280}{1} =\frac{x}{3}[/tex]
1 * x = 5,280 * 3
x = 15,840 feet
So, your answer is A. x = 15,840 feet.
Hope this helps!
If the errors produced by a forecasting method for 3 observations are +3, +3, and −3, then what is the mean squared error?
Answer:
9
Step-by-step explanation:
The mean squared error (MSE)of a set of observations can be calculated using the formula :
(1/n)Σ(Actual values - predicted values)^2
Where n = number of observations
Steps :
Error values of each observation (difference between actual and predicted values) is squared.
Step 2:
The squared values are summed
Step 3:
The summation is the divided by the number of observations
The difference between the actual and predicted values is known as the ERROR.
(1/n)Σ(ERROR)^2
n = 3
Error = +3, +3, - 3
MSE = (1/3)Σ[(3)^2 + (3)^2 + (-3)^2]
MSE = (1/3) × [9 + 9 + 9]
MSE = (1/3) × 27
MSE = 9
f(x) = -3x + 7
What is f (0)?
Answer:
f(0) = 7
Step-by-step explanation:
f(x) = -3x + 7
Let x =0
f(0) = -3*0 + 7
f(0) = 7
PLEASE HELP ! (2/4) - 50 POINTS -
Answer:
The correct answer would be 15.5 or C.
Let A and B be any two sets. Show that:
Show that (
AUB)', (BUA)' = 0
Step-by-step explanation:
(AUB)' means they are all outside the set A and B so thats 0. Hope it helps
g A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. a. How many simple events are in the sample space
Answer:
64
Step-by-step explanation:
Let us consider E_abc to be the event that a, b and c appear on the first, second and third slot of the spin machine.
Now, we are told that each slot has 4 possibilities which are a cherry, a lemon, a star, or a bar when spun.
Thus, from mn rule in probability, the total number of simple events in the sample space is = 4³ = 64
One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
which of the following greatest
6+(-2)
6-(-2)
6×(-2)
6+(-2)
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
in the factory 25 men working 26 hour can produce 1300 radios . how manny hours must the same group of men work to produce 450 radios
Answer:
9 hours
Step-by-step explanation:
Since the group of men remains the same, number of hours is proportional to number of radios.
1300/26 = 450/h
h = 26 * 450 / 1300 = 9 hours
I need help with this question
Answer:
a. 2
b. x^2 + 10x + 26
c. x^2 + 2x + 2
Step-by-step explanation:
For each part, replace x with the value you are given and simplify.
f(x) = x^2 - 2x + 2
a.
f(2) = 2^2 - 2(2) + 2 = 2
b.
f(x + 6) = (x + 6)^2 - 2(x + 6) + 2
= x^2 + 12x + 36 - 2x - 12 + 2
= x^2 + 10x + 26
c.
f(-x) = (-x)^2 - 2(-x) + 2
= x^2 + 2x + 2
plz someone help me with this question
Answer:
(x+3)^2=-4(y-3)
Step-by-step explanation:
(x-h)^2 = 4p(y-k)
P is the distance between the focus and vertex
P = 1 --> used distance formula for the points of -3,2 -3,3
Vertex is -3,3 --> according to picture
(x+3)^2=-4(y-3)
P is negative since it goes downwards in the picture.
