Which statement is false?
A. Every irrational number is also real.
B. Every integer is also a rational number.
• C. Every rational number is also an integer.
D. No rational number is irrational.
Answer:
A. false B. true C. false D. true
Whope you all like this answer
3p + 2q = 14
10p + 6q = 44
What is p and what is q
Answer:
p = 2 ; q = 4
Step-by-step explanation:
Given tbe equation :
3p + 2q = 14 - - - (1)
10p + 6q = 44 - - -(2)
What is p and what is q
This is a simultaneous equation ; using elimination method :
Multiply (1) by 6 and (2) by 2
18p + 12q = 84 - - - - (3)
20p + 12q = 88 - - - (4)
Subtract (3) and (4)
-2p = - 4
p = 4/2
p = 2
Put p = 2 in (1)
3p + 2q = 14
3(2) + 2q = 14
6 + 2q = 14
2q = 14 - 6
2q = 8
q = 8/2
q = 4
p = 2 ; q = 4
Suppose that the IQ of a randomly selected student from a university is normal with mean 115 and standard deviation 25. Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Answer:
The interval is [98,132]
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal with mean 115 and standard deviation 25.
This means that [tex]\mu = 115, \sigma = 25[/tex]
Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = -0.675*25[/tex]
[tex]X = 98[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = 0.675*25[/tex]
[tex]X = 132[/tex]
The interval is [98,132]
The farmer is buying fence panels.
He needs a total length of 200 m of fence panels.
Each fence panel is 2.5 m in length.
Work out how many fence panels the farmer will need to buy?
Answer:
80 panels
Step-by-step explanation
convert 23/4 into mixed number
by what number should 2/9 be divided to obtain 8/3
Answer:
[tex] \frac{1}{12} [/tex]
Step-by-step explanation:
[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]
So, if you divide 2/9 by 1/12, you'll get 8/3
Answered by GAUTHMATH
a set of date consists of 225 observations. the lowest value of the data set is 2,403; the highest is
Answer:
8 classes
Step-by-step explanation:
Given
[tex]Least = 2403[/tex]
[tex]Highest = 11998[/tex]
[tex]n = 225[/tex]
Required
The number of class
To calculate the number of class, the following must be true
[tex]2^k > n[/tex]
Where k is the number of classes
So, we have:
[tex]2^k > 225[/tex]
Take logarithm of both sides
[tex]\log(2^k) > \log(225)[/tex]
Apply law of logarithm
[tex]k\log(2) > \log(225)[/tex]
Divide both sides by log(2)
[tex]k > \frac{\log(225)}{\log(2)}[/tex]
[tex]k > 7.8[/tex]
Round up to get the least number of classes
[tex]k = 8[/tex]
CNBC recently reported that the mean annual cost of auto insurance is 1013 dollars. Assume the standard deviation is 284 dollars. You take a simple random sample of 56 auto insurance policies. Find the probability that a single randomly selected value is less than 995 dollars. P(X < 995)
Answer:
P(X < 995) = 0.4761
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
CNBC recently reported that the mean annual cost of auto insurance is 1013 dollars. Assume the standard deviation is 284 dollars.
This means that [tex]\mu = 1013, \sigma = 284[/tex]
Find the probability that a single randomly selected value is less than 995 dollars.
This is the p-value of Z when X = 995. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{995 - 1013}{284}[/tex]
[tex]Z = -0.06[/tex]
[tex]Z = -0.06[/tex] has a p-value of 0.4761. So
P(X < 995) = 0.4761
Convert 0.53 hectograms to centigrams.
53 centigrams
0.000053 centigrams
530 centigrams
5,3000 centigrams
Answer:
As for metric prefixes, "hecto" means hundred and "centi" means hundredth.
So, converting .53 hectograms to centigrams requires multiplying it by 10,000.
So, .53 hectograms * 10,000 equals 5,300 centigrams.
Source http://www.1728.org/convprfx.htm
Step-by-step explanation:
Which of the following is not true?
Answer:
C. m<c = 140°
Step-by-step explanation:
Let's analyse each of the given options:
A. m<a = 140° is TRUE
Rationale: angle a and 140° are vertical angles. Vertical angles are congruent.
B. m<b = 140° is TRUE.
Rationale: angle a and 140° are alternate interior angles. Alternate interior angles are congruent.
C. m<c = 140° is NOT TRUE.
Rationale: angle c and 140° are same side interior angles. Same side interior angles are supplementary.
D. m<d = 140° is TRUE.
Rationale: angle d and 140° are corresponding angles. Corresponding angles are congruent.
5
12
of the pupils in Year 9 say their favourite colour is red.
There are 240 pupils in Year 9.
How many students said red is their favourite colour?
Answer:
100
Step-by-step explanation:
I assume you mean [tex]\frac{5}{12}[/tex] of the students in Year 9.
Basically, first you need to work out 1/12 of the students, which is just 240 divided by 12, equals 20.
So, we know 1/12 of 240 is 20, therefore, in order to work out 5/12, we must do 20 x 5, which is 100.
From two points on the same level as the base of a tree, the angles of elevation to the top of the tree are found to be 24° and 46°. If the two points are 42 feet apart and on the same side of the tree, how tall is the tree? (Give your answer to the nearest tenth of an inch.)
Answer:
the answer is 32.8in.
Step-by-step explanation:
(sin 22)/42 = (sin 24)/x
x = 45.60
sin 46 = x/45.60
x = 32.80
32.8in.
hope it helped :)
mark me brainliest!
PLEASE EMERGENCY!!!!
Which of the following statements is FALSE?
Answer:
Third one.
BO is not 7.8 cm
Step-by-step explanation:
(6^2)^4 simplify the expression
Answer:
36
Step-by-step explanation:
(6^2)^4
(6)^2+4
6^6
36
simplify the expression : (6²)⁴= (36)⁴= 1679616
Or
[tex]{6}^{2 \times 8} = 1679616[/tex]
Số táo của An, Bình, Chi là như nhau. An cho đi 17 quả , Chi cho đi 19 quả thì lúc này số táo của Chi gấp 5 lần tổng số táo còn lại của An và Bình. Hỏi lúc đầu mỗi bạn có bao nhiêu quả táo? ( Giải bài toán trên bằng phương trình hoặc hệ phương trình )
Answer:
So, the initial number of apples is 7.
Step-by-step explanation:
The number of apples of An, Binh, and Chi are the same. An gave away 17 apples, Chi gave away 19 apples, so now Chi's apples are 5 times higher than the total remaining apples of An and Binh. How many apples did each of you have at first? (Solve the above problem by equation or system of equations)
Let the initial numbers of apples is a.
An gave 17 apples
Chi gave 19 apples
So,
x - 19 = 5 (x - 17 + x)
x - 19 = 5 (2x - 17)
x - 19 = 10 x - 85
9 x = 66
x = 7
Is the distance a baseball travels in the air after being hit a discrete random variable, a continuous random variable, or not a random variable?
Answer: a continuous random variable
Step-by-step explanation:
Can you count the distance it traveled? You can't, so it couldn't be discrete because you can count discrete variables.
Can you measure the distance it traveled? You sure can, that makes it a continuous random variable.
Do you know the exact distance it's going to travel? You won't, therefore it's a random variable since you don't know the value beforehand.
Which of the following statements must be true about this diagram? Check all
that apply.
4 3
1
1
N
A. The degree measure of 23 equals the sum of the degree
measures of 21 and 22.
B. m23 is greater than m 2
C. The degree measure of 24 equals the sum of the degree
measures of 22 and 23.
D. m 4 is greater than m_2.
E. m24 is greater than m 1.
F. The degree measure of 24 equals the sum of the degree measures
of 21 and 22.
Answer:
D, E, and F
Step-by-step explanation:
✔️Statement D is true:
Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2
✔️Statement E is true:
Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1
✔️Statement F is true:
Rationale:
m<4 is an external angle of the triangle.
m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,
m<4 = m<1 + m<2
Please help!!!!
I’m using Plato
1 by 4 ^ 256 is equal to 4 and 1 by 4 ^ 64 will be root 4 so here the answer will be 4 into 4 root 4
there option 4 will be correct
if 18 : 6 = x : 3 then what is 5 + 3x
Answer:
32
Step-by-step explanation:
18 : 6 = 3
therefore, x : 3 has to equal 3.
X : 3 = 3
X = 3 × 3
X = 9
To verify:
18 : 6 = 9 : 3
3 = 3
It's true that X = 9, so now just replace the X with 9 in the next equation
5 + 3(9) = 32
Answer:
32
Step-by-step explanation:
18 : 6 = x : 3
Product of means = Product of extremes
6 * x = 3*18
x = [tex]\frac{3*18}{6}[/tex]
x = 3*3
x = 9
Now plugin x = 9 in the expression
5 + 3x = 5 + 3*9
= 5 + 27
= 32
7/3a - 8/5 +4/15a
Simplified
Answer:
13/5a - 8/5
Step-by-step explanation:
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,7/3a - 8/5 +4/15a.
We have to simplify the expression.
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
=7/3a - 8/5 +4/15a
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
Learn more about the expression here:
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A cyclist rides at an average speed of 25 miles per hour. If she wants to bike 195 km, how long (in hours) must she ride
1km = 0.621371miles
195 km= ?
cross multiplication
= 121.167 miles
25 miles= 1hour
121.167miles = ?hours
121.167=25x
divide by 25x both sides
=4.84 hours
approx 5hours
She must ride for 5 hours if she wants to bike 195 km.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Given that cyclist rides at an average speed of 25 miles per hour.
Since 1 km = 0.621371 miles
So 195 km = 121.167 miles
The speed of the cyclist (s) = 24 miles per hour.
Distance covered by the rider = 195 km
Distance covered by the rider (d) = 121.167 miles
By using the formula, time taken by a body, we calculate the time,
⇒ t = d/s
Substitute the value of d and s in above the equation
⇒ t = 121.167/ 24
Apply the division operation,
⇒ t = 5
Hence, she must ride for 5 hours if she wants to bike 195 km.
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Simplify the following expression.
3^{0}
Answer:
Anything to the power of zero (with the exception of zero itself) is equal to one.
So 3⁰ = 1
A.For a group of individuals, the random variable x denotes the number of credit cards per individual with the following distribution. x: 0 1 2 3 4 5 P(x): .27 .28 .20 .15 .08 .02 a. find the mean, variance and standard deviation of x b. find the probability that a randomly selected individual holds at least 1 card.
Answer:
1.55
2.66
1.631
Step-by-step explanation:
Given :
x: 0 1 2 3 4 5
P(x): .27 .28 .20 .15 .08 .02
The expected mean, E(X) = Σ(x*p(x))
E(X) = (0*0.27)+(1*0.28)+(2*0.20)+(3*0.15)+(4*0.08)+(5*0.02)
E(X) = 1.55
The expected variance :
Σx²*p(x) - E(X)
(0^2*0.27)+(1^2*0.28)+(2^2*0.20)+(3^2*0.15)+(4^2*0.08)+(5^2*0.02) - 1.55
4.21 - 1.55 = 2.66
The standard deviation :
√variance = √2.66 = 1.631
identify the system by type
Answer:
Inconsistent system
Step-by-step explanation:
Given
The attached graph
Required
The type of system
When two lines are parallel, it means they have the same slope and as such, the system has no solution.
Equations with the same slope are:
[tex]y = 2x + 6[/tex]
[tex]y = 2x- 8[/tex]
Both have a slope of 2
Such system are referred to inconsistent system.
Hence, (c) is correct.
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. text({)1, 1/4, 1/16, 1/64, 1/256, ... text(})
Answer:
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
Step-by-step explanation:
Given
[tex]({)1, 1/4, 1/16, 1/64, 1/256, ... (})[/tex]
Required
The general term
The given sequence is geometric.
So first, we calculate the common ratio (r)
[tex]r = T_2/T_1[/tex]
So, we have:
[tex]r = 1/4 \div 1[/tex]
[tex]r = 1/4[/tex]
The function is then calculated using:
[tex]T_n =T_1 * r^{n-1}[/tex]
This gives
[tex]T_n =1 * 1/4^{n-1}[/tex]
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
Yuki bought a drop–leaf kitchen table. The rectangular part of the table is a 2–by–3–foot rectangle with a semicircle at each end, as shown.
Answer:
[tex](a)\ Area = 13.0695[/tex]
[tex](b)\ Area = 26.139[/tex]
Step-by-step explanation:
Given
The attached image
Solving (a): The area (one side up)
This is calculated as:
Area= Area of semicircle + Area of rectangle
So, we have:
[tex]Area = \pi r^2 + l *w[/tex]
Where:
[tex]l,w =2,3[/tex] --- the rectangle dimension
[tex]d = 3[/tex] --- the diameter of the semicircle
So, we have:
[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]
[tex]Area = \pi * 2.25 + 6[/tex]
[tex]Area = 2.25\pi + 6[/tex]
[tex]Area = 2.25*3.142 + 6[/tex]
[tex]Area = 13.0695[/tex]
Solving (b): Area when both leaves are up.
Simply multiply the area in (a) by 2
[tex]Area = 2 * 13.0695[/tex]
[tex]Area = 26.139[/tex]
what is the sum of the geometric series 4∑ t=1 6t-1
Answer:
Hello friend kya in snap and p to Trisha
Four times a number is 88 less than 6 times the number. Find the number.
Answer:
44
Step-by-step explanation:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
The number is 44.
To find the number.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).
Given that:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
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Find the standard normal area for each of the following (Round your answers to 4 decimal places.): Standard normal area a.P(1.26 < Z < 2.16) b.P(2.05 < Z < 3.05) c.P(-2.05 < Z < 2.05) d.P(Z > .55)
Answer:
The correct answer is:
(a) 0.0884
(b) 0.0190
(c) 0.9596
(d) 0.2921
Step-by-step explanation:
(a)
= [tex]P(1.26<Z<2.16)[/tex]
= [tex]P(Z<2.16)-P(Z<1.26)[/tex]
= [tex]0.9846-0.8962[/tex]
= [tex]0.0884[/tex]
(b)
= [tex]P(2.05<Z<3.05)[/tex]
= [tex]P(Z<3.05)-P(Z<2.05)[/tex]
= [tex]0.9989-0.9798[/tex]
= [tex]0.0190[/tex]
(c)
= [tex]P(-2.05<Z<2.05)[/tex]
= [tex]P(Z<2.05)-P(Z<-2.05)[/tex]
= [tex]0.9798-0.0202[/tex]
= [tex]0.9596[/tex]
(d)
= [tex]P(Z>0.55)[/tex]
= [tex]1-P(Z<0.55)[/tex]
= [tex]1-0.7088[/tex]
= [tex]0.2912[/tex]
AC if TC = 20q + 10q^2?
Answer:
AC = (20+ 10q)
Step-by-step explanation:
Given that,
Total cost, TC = 20q + 10q²
We need to find AC i.e. average cost.
It can be solved as follows :
[tex]AC=\dfrac{TC}{q}\\\\AC=\dfrac{20q + 10q^2}{q}\\\\AC=\dfrac{q(20+ 10q)}{q}\\\\AC={(20+ 10q)}[/tex]
So, the value of AC is (20+ 10q).
