Step-by-step explanation:
base = 11
height = 8
so are is 11 x 8 /2
= 44
a racer called the whirlwind. Its poster says that in 1/20 hour it covers 7/10 mile. What is the Whirlwind’s speed in miles per hour?
Answer:
Its speed is 14 mph.
Step-by-step explanation:
Given that regarding racer called The Whirlwind, its poster says that in 1/20 hour it covers 7/10 mile, to determine what is the Whirlwind’s speed in miles per hour the following calculation must be performed:
1/20 x 60 = 0.05 x 60 = 3 minutes
7/10 = 0.7
Therefore, every 3 minutes the Whirlwind travels 0.7 miles.
60/3 = 20
0.7 x 20 = 14
Thus, in an hour it travels 14 miles, with which its speed is 14 mph.
odd number less than 5
Answer:
1 and 3 are the odd numbers that are less than 5. 0, 2 and 4 are the even numbers that are less than 5
Step-by-step explanation:
The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49
1. Find the first term of the progression and the common difference
2. Find the value of n
Answer:
For 1: The first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]
For 2: The value of n is 27
Step-by-step explanation:
The n-th term of the progression is given as:
[tex]a_n=a_1+(n-1)d[/tex]
where,
[tex]a_1[/tex] is the first term, n is the number of terms and d is the common difference
The sum of n-th terms of the progression is given as:
[tex]S_n=\frac{n}{2}[2a_1+(n-1)d][/tex]
where,
[tex]S_n[/tex] is the sum of nth terms
For (1):The 11th term of the progression:
[tex]25=a_1+10d[/tex] .......(1)
Sum of first 4 numbers:
[tex]49=\frac{4}{2}[2a_1+3d[/tex] ......(2)
Forming equations:
[tex]98=8a_1+12d[/tex]
[tex]25=a_1+10d[/tex] ( × 8)
The equations become:
[tex]98=8a_1+12d[/tex]
[tex]200=8a_1+80d[/tex]
Solving above equations, we get:
[tex]102=68d\\\\d=\frac{102}{68}=\frac{3}{2}[/tex]
Putting value in equation (1):
[tex]25=a_1+10\frac{3}{2}\\\\a_1=[25-15]=10[/tex]
Hence, the first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]
For 2:The nth term is given as:
[tex]49=10+(n-1)\frac{3}{2}[/tex]
Solving the above equation:
[tex]39=(n-1)\frac{3}{2}\\\\n-1=26\\\\n=27[/tex]
Hence, the value of n is 27
what is a line passing through the points (1, -1) and (9, 3) in equation form?
Answer:
[tex]x-2y=3[/tex]
Step-by-step explanation:
[tex]We\ are\ given,\\Line\ passes\ through\ the\ points\ (1,-1) and (9,3). Hence,\ this\ means\ that\ the\\ points\ are\ indeed\ solutions\ of\ the\ equation,\ which\ represents\ the\ line.\\Hence,\\We\ know\ that,\\The\ equation\ of\ a\ line\ (Point-Slope)\ is\ given\ by:\\y-y_1=m(x-x_1),\ where\ m\ is\ the\ slope\ of\ the\ graph.[/tex]
[tex]So\ first,\\Lets\ find\ the\ Slope\ of\ the\ Graph.\\Slope(m)=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}\\Hence,\\Here,\\Considering\ (1,-1)\ as\ the\ First\ Point\ and\ (9,3)\ as\ the\ Second\ Point,\ we\ have:x_1=1,x_2=9\ and\ y_1= -1, y_2=3\\Plugging\ the\ values\ in\ the\ Equation\ for\ the\ Slope,\ we\ have:\\[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-1)}{9-1}=\frac{3+1}{9-1}= \frac{4}{8}=\frac{1}{2}\\Hence,\\Coming\ back\ to\ our\ Point-Slope\ Formula\ for\ the\ equation:\\\ We\ already\ have:\\y-y_1=m(x-x_1)\\Substituting\ m=\frac{1}{2} , x_1=1,\ y_1=-1,\ we\ have: \\y+1=\frac{1}{2}(x-1)\\\therefore 2(y+1)=x-1\\\therefore 2y+2=x-1\\\therefore 2y-x=-3\\Multiplying\ with\ (-1)\ on\ both\ sides:\\\therefore x-2y=3\\Hence,\\x-2y=3,\ is\ our\ desired\ equation.[/tex]
Find the GCF of 20 and 95 Using the Euclidean Algorithm. Check your work by using the prime factorization method.
Answer:
5
Step-by-step explanation:
To start, you use the formula a/b=c, in which a is bigger than b. In this case, that's 95/20=c. The greatest common factor is 5.
In a math class, 9 pupils receive a grade of 90. If 18% of the class got 90, how many pupils are there in a class?
Answer:
Let the total number of pupil be x.
Given that,
Number of pupils that received a grade of 90=9
Percentage of pupil that receive a grade of 90=18%
So,
18% of x=9
18x/100=9
x=50
Hence, there are 50 pupils in the class.
reduce 1/2 × 16/9 is to lowest form
Answer:
The correct answer will be "[tex]\frac{8}{9}[/tex]".
Step-by-step explanation:
The given expression is:
= [tex]\frac{1}{2}\times \frac{16}{9}[/tex]
By applying multiplication, we get
= [tex]\frac{16}{18}[/tex]
= [tex]\frac{8}{9}[/tex]
Thus, the above is the lowest form.
What is the value of log Subscript 5 Baseline 125?
Answer:
[tex]log_5 \ 125 = 3[/tex]
Step-by-step explanation:
[tex]log_5 \ 125 = log_2 \ 5^3 = 3 \times log_5 \ 5 = 3 \times 1 = 3[/tex]
The value of [tex]$\log _{5} 125$[/tex] can be estimated utilizing the logarithm rule. The value of [tex]$\log _{5} 125$[/tex] exists 3.
What is a logarithm?The logarithm stands for the inverse function of exponentiation. In logarithm base must be raised to yield a given number for an exponent.
Given:
[tex]$\log _{5} 125$[/tex]
Estimate the value of the given logarithm, we get
[tex]$\log _{5} 125=\log _{5}(5)^{3}$[/tex]
[tex]$\log _{5} 125=3 \log _{5} 5$[/tex]
From logarithm rule [tex]$\log m^{n}=n \log m$[/tex], we get
[tex]$\log _{5} 125=3 \times 1$[/tex]
[tex]$\log _{5} 125=3$[/tex]
Therefore, the value of [tex]$\log _{5} 125$[/tex] is 3.
To learn more about logarithm
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If AABC= A DEF, which congruences are true by CPCTC? Check all that
apply.
APEC correct answer is:
AB =DE
AC= DF
See photo.
Answer:
Options A, B and D
Step-by-step explanation:
If the two triangles are congruent, their corresponding parts will be congruent.
If ΔABC ≅ ΔDEF
By the property of CPCTC,
AB ≅ DE
AC ≅ DF
BC ≅ EF
∠A ≅ ∠D
∠C ≅ ∠F
∠B ≅ ∠E
Therefore, Options A, B and D are the correct options.
Karen purchased 3 gallons of yellow paint and 4 gallons on blue paint from the hardware store. The total cost was $105. Yellow
paint and blue paint sell for the same price per gallon. Which THREE statements are correct?
Answer:
In order to answer this properly, I would need to see the choices. However, I can tell you that:
-Each gallon of paint cost $15
-Karen spent $45 on yellow paint
-Karen spent $60 on blue paint
Step-by-step explanation:
Karen bought a total of 7 cans of paint, all the same price.
105/7=15.
15*3=45 (yellow paint)
15*3=60 (blue paint)
Hope this helps.
24×63_64
help me sll
Answer:
1448
Step-by-step explanation:
24 × 63-64
Multiply 24 and 63 to get 1512.
1512-64
Subtract 64 from 1512 to get 1448.
answer
1448
The dot plots below show the ages of students belonging to two groups of painting classes: Based on visual inspection, which group most likely has a lower mean age of painting students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.
Answer:
it's group A because they have more reliable sources
please help me please
Answer:
30,000
Step-by-step explanation:
Can someone please answer this
18- 3 x 2/5 - 12
Could someone help me with this?
Answer:
I hope it helps u.......
I NEEED HELPPPPP PLEASEEEE UM BEGGING SOMEONE PLEASEEEEEEEEEEEE
Answer:
p = 28.56
Step-by-step explanation:
Circumference of circle
c = 2πr
Since this is a semicircle the perimeter is half the circumference
p = πr
p = 3.14 * 4
p = 12.56
---------------------------
Triangle
the outer perineter is just the two outer sides
p = 6 + 10
p = 16
-------------------------
total outer perimeter
p = 12.56 + 16
p = 28.56
Rewrite the following subtraction problem as an addition problem.
Answer:
x+129=592
Step-by-step explanation:
add 129 to each side
I’ll give u brainlest please
Answer:
315
Step-by-step explanation:
the formula is V = B * h
B is the area of the base
V = (1/2)(10)(7) * 9
A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the
orange.
By what percentage is the grapefruit heavier than the apple?
pls answer
Grapefruit=108
Orange=100
Apple=90
a) (108-90)/90*100 = 18/90*100=20%
b) (108-90)/108= 18/108*100=16 2/3%
Answer:
The grapefruit is 20% heavier than the orange:)
Step-by-step explanation:
Let the weight of orange be x.
This means that the weight of grapefruit is:
1.08x
( Since grapefruit is: 8% heavier than orange )
Also, the weight of apple is 10% lighter than apple.
This means that the weight of apple is: 0.90 x
Beth corbin's regular hourly wage are is $16,and she receives an hourly rate of $24 for work in excess of 40 hours. During a January pay period,Beth works 45 hours. Beth's federal income tax withholding is $95, she has no voluntary deductions, and the FICA tax rate is 7.65%. Compute Beth corbi's gross earnings and net pay for the pay period
Answer:
$760 gross
$614.13 is net
Step-by-step explanation:
Beth earns $16 x 40 for the first 40 hours she works.
Then she earns overtime--> 5 hours at $24 per hour
Her "gross" earnings are before any deductions or taxes.
So 16x40 = 640 and 5x24= 120 so her January gross earnings are 640+120=
$760 gross
Her "net" pay is what is left over after taxes.
So take the $760 and subtract the $95 withholding = $665
Taxes are 7.65% so multiply 665 x 0.0765 = 50.8725 and subtract that also.
614.1275 rounded to $614.13 is net.
10x-3(x-6)=x+30 please help me
Step-by-step explanation:
10x-3(x-6)=x+30
10x-3x+18=x+30
7x+18=x+30
6x=12
x=2
Answer:
x=2
Step-by-step explanation:
10x-3(x-6)=x+30
Distribute
10x -3x+18 = x+30
Combine like terms
7x +18 = x+30
Subtract x from each side
7x-x +18 = x+30-x
6x +18 = 30
Subtract 18
6x+18-18 = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x=2
3. Write the ones digit in the square of each of the following numbers
a.13
b. 27
c.46
d.20
e.75
f.31
g.42
h.64
i.38
j.79
Answer:
a.9
b.9
c.6
d.0
e.5
f. 1
g.4
h.6
i.4
j.1
99 students at a college were asked whether they had completed their required English 101 course, and 71 students said "yes". Find the best point estimate for the proportion of students at the college who have completed their required English 101 course. Round to four decimal places.
Answer: 0.070
Step-by-step explanation:
The question is asking you to estimate how many students completed the English 101 course.
1. Round 99 and 71 to 100 and 70
2. I am not completely sure but I believe the answer is 0.070?
3. Hope it helps! :)
a container has 16 1/2 cups of lemonade. Asher gives each of his classmates 3/4 of a cup if lemonade. if asher gives away all of the lemonade how many classmates does asher give lemonade to
how did you find the standard deviation?
Answer:
Step-by-step explanation:
It's the square root of the variance
The variance is just the second moment minus the first moment squared
Determine which data are qualitative and which data are quantitative. Explain your reasoning
a. The yearly salaries of the employees at a school district. (9)
b. The employee numbers of the employees at an accounting firm.
c. The area codes of a sample of 350 residents of nursing homes. (2)
d. The ages of a sample of 350 residents of nursing home. (eta)
e. The answers to a survey of 5000 people about how likely is it that the US will enter a 1930s-like depression. The answers are: Very likely, somewhat likely, not very likely, not at all likely. (20)
f. The IQ index of the students in a statistics class.
What are the levels of measurement of data in question 4? Justify
a. Yearly salaries: (20)
b. Employee numbers: (ca)
c. Area codes: (eca)
d. The ages:
e. Survey answers: (ca)
f. IQ index: (en)
Answer:
1. A. Quantitative data
B. Quantitative data
C. Qualitative data
D. Quantitative data
E. Qualitative data
F. Quantitative data
2.a. Yearly salaries: interval or ratio data
b. Employee numbers: interval or ratio data
c. Area codes : nominal data
d. The ages: interval or ratio data
e. Survey answers: ordinal data
f. IQ index: interval or ratio data
Explanation:
Qualitative data is data in the form of a quality such as a characteristic. It is usually a noun, such as whether a person is fair or dark in complexion. Quantitative data is data in form of quantity such as the amount in dollars of one's salary.
There are four levels of data measurement. They are: nominal data, ordinal data, interval data, and ratio data. Nominal and ordinal data are qualitative data while interval and ratio data are quantitative data.
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
An inverse function is y = k/x
replace x and y with the given values:
6 = k/18
Solve for k by multiplying both sides by 18:
k = 108
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
Solution:-[tex]\sf{The \: relation \: y \: varies \: inversely \: as \: x \: translates \: to \: y = \frac{k}{x}.}[/tex]
Substitute the values to find k:
[tex]\sf\rightarrow{y= \frac{k}{x} }[/tex]
[tex]\sf\rightarrow{6= \frac{k}{18} }[/tex]
[tex]\sf\rightarrow{k=(6)(18)}[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{108}}}[/tex]
Answer:-[tex]\sf{The \: equation \: of \: variations \: is \: y={ \color{red}{ \frac{108}{x} }}}[/tex]
[tex]{\huge{\color{blue}{━━━━━━━━━━━━}}}[/tex]
#CarryOnMath⸙
1. If f(x)=4*, then which of the following is the value of f(-2)?
Answer:
what is the following
Step-by-step explanation:
Which of the following is the general term for the sequence? -a, a^2, -a^3, a^4,...
-a(-a)^ n-1
(-a)^n + 1
(-1)a^n + 1
a(-1)^n - 1
Answer:
The answer would be [tex]-a(-a)^{n-1}[/tex].
Step-by-step explanation:
We can simply substitute the terms into this equation. Checking the 1st term, [tex]-a(-a)^{1-1} = -a(-a)^{0} = -a(1) = -a[/tex]. Moving on to the second term, we see [tex]-a(-a)^{2-1} = -a(-a)^{1} = -a(-a) = a^{2}[/tex]. And so on and so forth. We can see how the answer fluctuates between negative and positive, while gaining one more exponent every term, which fits with the sequence given. Therefore, the answer would be [tex]-a(-a)^{n-1}[/tex].
Hope this helped!
Prove the following statement by contradiction.
If a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational.
Proof by contradiction: Select an appropriate statement to start the proof.
A. Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational.
B. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is irrational.
C. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is rational.
D. Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is rational.
E. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is a rational number, and a + br is irrational.
Then by definition of rational,
a = c/d, b = i/j , and a + br = m/n
where c, d, i, j, m, and n are___and____. Since b ≠ 0, we also have that i ≠ 0. By substitution,
c/d + i/j r = m/n
Solving this equation for r and representing the result as a single quotient in terms of c, d, i, j, m, and n gives that
r = c - a/b
Answer:
spongebob at the bottom of the sea
Step-by-step explanation:
In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.
The step would be, "Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational." Option A is correct.
Given that,
a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational. the first step of the proof with contradiction is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
For the statement,
a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational.
Contradiction will be "suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational."
Thus, the step would suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational.
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