Answer:
6 different isosceles triangles.
Step-by-step explanation:
This is a AMC 8 2005 question. (You can search up their solution)
There are 6 triangles:
6, 6, 11
7, 7, 9
8, 8, 7
9, 9, 5
10, 10, 3
11, 11, 1
There are only 6 because if there was an isosceles triangle with side lengths such as 5, 5, 13 the triangle would be impossible since the two smaller side lengths must sum up to be greater than the longest side length.
The number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
What is the isosceles triangle?In an isosceles triangle, two sides and angles are equal. The sum of the angle of the triangle is 180 degrees.
Given
Isosceles triangles have integer side lengths and a perimeter of 23.
Let x be the isosceles side and y be the other side. Then
[tex]\rm 2x + y = 23[/tex] ...1
And we know that the sum of the two sides of the triangle must be greater than the third side. Then
[tex]\rm 2x >y[/tex] ...2
From equations 1 and 2, we have
x > 5.75
But the value of x is an integer then x will be 6. Then
All possibilities are
[tex]6 + 6 > 11\\\\7 + 7 > 9\\\\8+8>7\\\\9+9>5\\\\10+10>3\\\\11+11>1[/tex]
Thus, the number of isosceles triangles has integer side lengths and a perimeter of 23 is 6.
More about the Isosceles triangle link is given below.
https://brainly.com/question/7915845
Joey borrows 2000 from his grandfather and pays the money back in monthly payments of 200.
1. Write a lineat function that represents the remaining money owed L(x) after x months.
2. Evaluate L(10) and interpret the meaning in the context of this problem.
A. L(x) - 200x + 2,400; L(10) = 4,400, This represents the amount Joey has paid his grandfather after 10 months.
B. L(x) = 200x + 2,400; L(10) - 4,400, This represents the amount Joey still owes his grandfather after 10 months.
C. L(x) = -200x + 2,400; L(10) = 400, This represents the amount Joey has paid his grandfather after 10 months.
D. L(x) = -200x + 2,400; L(10) = 400, This represents the amount Joey still owes his grandfather after 10 months.
The correct question is;
Joey borrows $2400 from his grandfather and pays the money back in monthly payments of $200.
a. Write a linear function that represents the remaining money owed L(x) after x months.
b. Evaluate L(10) and interpret the meaning in the context of this problem.
A) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey still owes his
grandfather after 10 months.
B) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey has paid his
grandfather after 10 months.
C) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey has paid his
grandfather after 10 months.
D) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey still owes his
grandfather after 10 months.
Answer:
A) L(x) = 2400 - 200x
B) Option D is correct
Step-by-step explanation:
A) We are told that Joey borrowed 2400.
Now he pays back in installments of 200 every month.
Thus for x number of months he would have paid 200x.
Thus,the linear function that represents the remaining money owed is;
L(x) = 2400 - 200x
B) L(10) = 2400 - (200 * 10)
L(10) = 2400 - 2000
L(10) = 400
Thus, after 10 months, Joey is owing 400.
So, looking at the given options, the correct one is option D.
Which of the following pairs consists of equivalent fractions? 12/18 and 10/15 12/20 and 10/25 8/16 and 3/4 5/3 and 3/5
Answer:
12/18 and 10/15
Step-by-step explanation:
12/18 simplifies into 2/3
10/15 simplifies into 2/3
12/20 simplifies into 3/5
10/25 simplifies into 2/5
8/16 simplifies into 1/2
3/4 simplifies into 3/4
5/3 simplifies into 5/3
3/5 simplifies into 3/5
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
What is a fraction number?
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
Let's check all the options, then we have
A) 12/18 and 10/15
12/18 and 10/15
2/3 and 2/3
Yes, they are equivalent fraction numbers.
B) 12/20 and 10/25
12/20 and 10/25
3/5 and 2/5
They are not equivalent fraction numbers.
C) 8/16 and 3/4
8/16 and 3/4
1/2 and 3/4
They are not equivalent fraction numbers.
D) 5/3 and 3/5
5/3 and 3/5
They are not equivalent fraction numbers.
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
More about the fraction number link is given below.
https://brainly.com/question/78672
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There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. b How many ways can we choose a Senator from a chosen state? c How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?
Answer:
a) rCn = 1176
b) 2352
Step-by-step explanation:
a)Each committee should be formed with 3 members ( no two members could be of the same state) then
Let´s fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then
rCn = n! / (n - r )! *r!
rCn = 49!/ (49 - 2)!*2!
rCn = 49*48*47! / 47!*2!
rCn = 49*48 /2
rCn = 1176
So we can choose in 1176 different ways a senator for a given state
b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.
1176*2 = 2352
2. Write as a complex number.
Answer:
Your answer is correct ✔️
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
2√3 + 3i is the answer
Step-by-step explanation:
The equation of the graphed line is 2x – y = –6. A coordinate plane with a line passing through (negative 3, 0) and (0, 6). What is the x-intercept of the graph? –3 –2 2 6
Answer:
-3
Step-by-step explanation:
-3 is the answer
Answer:
-3
Step-by-step explanation:
The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. The manufacturer claims each tablet has at least 200 milligrams of the active ingredient. The consumer Watchdog Bureau assumes the manufacturer claim is correct, but occasionally tests samples of the tablets to ensure they contain enough of the ingredient. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The sample mean content of the active ingredient is 205.7 milligrams, while the sample standard deviation is 21 milligrams. What is the p-value for this test?
Answer:
The p-value is [tex]p-value = 0.013167[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu[/tex] = 200 milligrams
The sample size is [tex]n = 70[/tex]
The sample mean is [tex]\= x = 205.7[/tex]
The sample standard deviation is [tex]\sigma = 21 \ milligram[/tex]
Generally the Null hypothesis is mathematically represented as
[tex]H_o : \mu = 200[/tex]
The Alternative hypothesis is
[tex]H_a : \mu < 200[/tex]
The test statistics is mathematically represented as
[tex]t_s = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]
substituting values
[tex]t_s = \frac{ 205.7 - 200 }{\frac{21}{\sqrt{70} } }[/tex]
[tex]t_s = 2.270[/tex]
Now the p-value is mathematically represented as
[tex]p-value = P(Z \le t_s )[/tex]
substituting values
[tex]p-value = P(Z \le 2.270 )[/tex]
Using the Excel function[=NORMDIST(2.270)] to calculate the p-value we obtain that
[tex]p-value = 0.013167[/tex]
Answer:
A) 0.012
From CollegeBoard
Ellie bought two planks of wood that were each 4ft 3in long, and two planks of wood that were each 6 ft 5in long. What is the total length of the wood she purchased?
Answer:
21 feet 4 inches
Step-by-step explanation:
Ellie bought two planks of wood that were each 4ft 3in long
Total length of these two planks = 4ft 3in + 4ft 3in = 8 feet 6 inches
she also bought two planks of wood that were each 6 ft 5in long
Total length of these two 6 ft 5in planks = 6 ft 5in + 6 ft 5in = 12 feet10 inches
Thus, total length of all the woods purchased = Total length of 4ft 3in two planks + Total length of the two 6 ft 5in planks
= 8 feet 6 inches + 12 feet 10 inches
adding feet with feet and inches with inches term
= 20 feet 16 inches
we know that 12 inches is equal to 1 feet
thus, 16 inches can be written as 1 feet 4 inches
thus,
20 feet 16 inches will be same as 21 feet 4 inches
The total length of the wood Ellie purchased is 21 feet 4 inches.
The selling price of a car is $15,000. Each year, it loses 12% of its value.
Which function gives the value of the cart years after its purchase?
Select the correct answer below:
f(t) = 15,000(0.12)
f(t) = 15,000(1.12)
f(t) = 15,000(1.88)
f(t) = 15,000(0.88)
f(t) = 15,000 – (0.12)
Answer:
f(t) = 15,000(0.88)Step-by-step explanation:
Applying the formula for the car deprecation we have
[tex]f(t)=P(1-\frac{r}{100} )^n[/tex]
Where,
A is the value of the car after n years,
P is the purchase amount,
R is the percentage rate of depreciation per annum,
n is the number of years after the purchase.
1. The depreciated value of the car after 1 yr is
n=1
[tex]f(t)= 15000(1-\frac{12}{100} )^1\\\f(t)= 15000(1-0.12 )\\\f(t)= 15000(0.88)[/tex]
a survey was done Of 600 shoppers at a grocery store to determine if they like a new flavor Of potato chip. Of the 600 shoppers, 376 of them liked the new flavor. a) What percentage of the 600 shoppers liked the new flavor? Round your answer to the nearest percent. b) If 37.5% of the. 600 shoppers stated they would buy the new flavor, how many of the 600 would buy it?
Answer:
63%
225 buyers
Step-by-step explanation:
To find the percent take the number that liked it over the total
376/600
Change to decimal form
.62666666
Change to percent by multiplying by 100
62.66666666%
The nearest percent is 63%
37.5 % would but it then multiply by the number of shoppers
37.5 % ( 600)
Change to decimal form
.375 * 600
225
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠CAB ≅ ∠SAB ∠CAS ≅ ∠BAS
Answer:
∠CAB ≅ ∠SAB is not true
Step-by-step explanation:
CPCTC means id ABC = XYZ, than A=X, AB=XY, C=Z and so on. Basically the number numbers that come in the same order as the other one is equal.
So ∠CAS ≅ ∠BAS is true but ∠CAB ≅ ∠SAB is not.
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Answer:
sap
Step-by-step explanation:
Write down the first 6 elements of the following sequence (where n ∈ Z +), then give a recursive definition for an. Do not forget the base case. (You do not need to prove it is correct). (a) an = 3n − 10 (b) an = (1 + (−1)n ) n
Step-by-step explanation:
The first six terms for each of the following sequenses are:
(a) a_n = 3n - 10
1. a_1 = -7
2. a_2 = -4
3. a_3 = -1
4. a_4 = 2
5. a_5 = 5
6. a_6 = 8
(b) a_n = (1 + (-1)^n) ^n
1. a_1 = 0
2. a_2 = 4
3. a_3 =0
4. a_4 = 16
5. a_5 = 0
6. a_6 = 32
What is the solution to the following system of equations?
|3x - 2y = 12
[6x - 4y= 24
It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0)
A test was marked out of 80. Aboy scored
60% of the marks on the test. How many
marks did he score?
(A)20
(B)48
(C)60
(D)75
Answer:
B
Step-by-step explanation:
To solve this you do 80/100=.8
You than do .8×60= 48
What is the value of x? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:
10.2 m
Step-by-step explanation:
180 - 81 - 30 = 69
law of sines
x /sin 30 = 19/sin 69
x = 10.2
6th grade math, help me please:)
Answer:
21
Step-by-step explanation:
Just like a dilation you want to find some sort of scale factor. Now when 7/2 is simplified it then becomes 3.5. Now multiply that by 6 since we are trying to find the ratio. when multiplied by 6 it becomes 21 so the ration of wins to losses is 21/6
What is the value of the expression below?
(-8)^4/3
Answer:
16
Step-by-step explanation:
(-8)^4/3
-(8^1/3)⁴
-(∛8)⁴
-(2)⁴
-2⁴
= 16
Answer: the ^^^^ right I check it
Step-by-step explanation:
Combine like terms: 10 + 6y + 2x - 3
Answer:
6y +2x +7
Step-by-step explanation:
10 + 6y + 2x - 3
The only like terms are the constant
6y+2x +10-3
6y +2x +7
Answer:
2x + 6y + 7.
Step-by-step explanation:
10 + 6y + 2x - 3
= 2x + 6y - 3 + 10
= 2x + 6y + 7.
Hope this helps!
In the diagram below, AB is parallel to CD. What is the value of X?
A. 60
В. 100
C.120
D. 80
Question 5(Multiple Choice Worth 4 points) (05.05)Based on the graph, what is the initial value of the linear relationship?
Answer: A) -2
Step-by-step explanation:
The y-intercept (where the graph crosses the y-axis) is the "initial value".
Looking at the given graph, it crosses the y-axis when y = -2
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75
Answer:
x = $0.50
y= $0.75
Step-by-step explanation:
1. Multiply the equations to have the same coefficients
5(6x + 6y = 7.5) → 30x + 30y = 37.5
3(10x + 5y = 8.75) → 30x + 15y = 26.25
2. Subtract the equations
30x + 30y = 37.5
- 30x + 15y = 26.25
15y = 11.25
3. Solve for y by dividing both sides by 15
y = 0.75
4. Plug in 0.75 for y into one of the equations
6x + 6(0.75) = 7.5
5. Simplify
6x + 4.5 = 7.5
6. Solve for x
6x = 3
x = 0.5
Answer:
The cost of one apple is $0.5
The cost of one orange is $0.75
Step-by-step explanation:
Given information
The cost of an apple = [tex]x[/tex]
The cost of an orange = [tex]y[/tex]
Equation to find the values are:
[tex]6x=6y=7.50\\10x+5y=8.75[/tex]
Now, convert the equations to have same coefficient as:
[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]
Now, on solving the above equation by subtracting one from another.
We get,
[tex]15y=11.25\\y=0.75[/tex]
Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].
As,
[tex]6x+4.5=7.5\\x=0.5[/tex]
Hence,
The cost of one apple is $0.5
The cost of one orange is $0.75
For more information visit
https://brainly.com/question/11897796?referrer=searchResults
What is the reciprocal of (17h)/(46j)?
Answer:
I dont give the answer right away so you read what i write and fully understand :D
Step-by-step explanation:
The reciprocal of something is basically when you flip something over. Since 17h/46j is a fraction, the reciprocal is 46j/17h. Remember, a number times the reciprocal is always equal to one.
Answer:
46j over 17h
Step-by-step explanation:
a reciprocal fraction is formed by flipping the fraction around
for example:
2/3
reciprocal= 3/2 or 1.5
HOPE THIS HELPS!!! :)
8.43 An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 45 minutes. a. What sample size is needed if the executive wants to be 90% confident of being correct to within {5 minutes
Answer:
a
The sample size is [tex]n = 219.2[/tex]
b
The sample size is [tex]n = 537.5[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 45 \minutes[/tex]
The Margin of Error is [tex]E = \pm 5 \ minutes[/tex]
Generally the margin of error is mathematically represented as
[tex]E = z * \frac{\sigma }{\sqrt{n} }[/tex]
Where n is the sample size
So
[tex]n = [\frac{z * \sigma }{E} ]^2[/tex]
Now at 90% confidence level the z value for the z-table is
z = 1.645
So
[tex]n = [\frac{1.645 * 45 }{5} ]^2[/tex]
[tex]n = 219.2[/tex]
The z-value at 99% confidence level is
[tex]z = 2.576[/tex]
This is obtained from the z-table
So the sample size is
[tex]n = [\frac{2.576 * 45 }{5} ]^2[/tex]
[tex]n = 537.5[/tex]
For the 90% confidence interval, the sample size is 219.2 and for the 99% confidence interval, the sample size is 537.5 and this can be determined by using the formula of margin of error.
Given :
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily.From past studies, the standard deviation is estimated as 45 minutes.The formula of the margin of error can be used in order to determine the sample size is needed if the executive wants to be 90% confident of being correct to within 5 minutes.
[tex]\rm ME = z\times \dfrac{\sigma}{\sqrt{n} }[/tex]
For the 90% confidence interval, the value of z is 1.645.
Now, substitute the values of all the known terms in the above formula.
[tex]\rm n=\left(\dfrac{z\times \sigma}{ME}\right)^2[/tex] --- (1)
[tex]\rm n=\left(\dfrac{1.645\times 45}{5}\right)^2[/tex]
n = 219.2
Now, for 99% confidence interval, the value of z is 2.576.
Again, substitute the values of all the known terms in the expression (1).
[tex]\rm n=\left(\dfrac{2.576\times 45}{5}\right)^2[/tex]
n = 537.5
For more information, refer to the link given below:
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Marcus made a sail for his toy boat. If the sail is 5 inches long and the top angle of the sail is 40°, what is the width of the bottom of the sail (w) to the nearest tenths place?
Answer:
4.2 in
Step-by-step explanation:
let us first visualize the sail as a triangular shape
the angle of the triangle from top is 40°
the height of the triangle is give as 5 in
we can apply SOH CAH TOA to solve for the base of the sail
the opposite = the base of the sail
the adjacent = the height of the sail= 5 in
therefore
Tan∅= Opp/Adj
Tan(40)= Opp/5
Opp= Tan(40)*5
Opp= 0.8390*5
Opp= 4.195 in
Hence the width of the sail is 4.2 in to the nearest tenths
Answer:
4.2
Step-by-step explanation:
Please answer this correctly without making mistakes.Please simplify the correct answer
Answer:
19/70 of NASA shuttle missions were carried out by Discovery.
9/140 of NASA shuttle missions were carried out by Challenger.
17/70 of NASA shuttle missions were carried out by Endeavour.
Step-by-step explanation:
Adding the number of missions carried out by NASA gives us 140 in total.
Discovery's total amount of missions simplified is 19/70.
Challenger's total amount of missions is already in the simplest form.
Endeavour's total amount of missions simplified is 17/70.
Answer:
81/140
Step-by-step explanation:
Well to find the fraction we first need to total amount of NASA missions.
38 + 32 = 70
70 + 34 = 104
104 + 27 = 131
131 + 9 = 140
Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.
38 + 9 + 34 = 81
Now we can make the following fraction,
81/140
This is already in simplest form.
Thus,
the answer is 81/140.
Hope this helps :)
Which of the following statement is incorrect?
4
A.3/4<4/5
B.5/6>0.83
C.2/3>0.66
D.1/3>0.3
درا
Answer:
None,
they are all correct.
Step-by-step explanation:
A)
3/4 - 75%
4/5 - 80%
3/4 < 4/5
B)
5 ÷ 6 = .83333333333
5/6 > .83
C)
2 ÷ 3 = .666666666
2/3 > .66
D)
1 ÷ 3 = .33333333333
1/3 > .3
Thus,
all of the given statements are correct.
Hope this helps :)
Brainliest for correct awnser! What is the domain of f(x)?
Answer:
[tex]\mathrm{B.}[/tex] All real numbers except x = 2, x = 5
Step-by-step explanation:
If the denominator is equal to 0 then the function would be undefined.
Set the denominator equal to 0.
x² - 7x + 10 = 0
Factor the left side of the equation.
(x - 5)(x - 2) = 0
Set the factors equal to 0.
x - 5 = 0
x = 5
x - 2 = 0
x = 2
The domain is all real numbers except x = 2 and x = 5.
Which ordered pair is a solution of this equation 6x-y=-4 . -2,0 -1,-2 -2,-1 0, -2
Answer:
(-1,-2)
Step-by-step explanation:
[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]
so the only one is (-1,-2)
Find the angle between (u= sqrt 5i) -8j and (v= sqrt 5i) +j. Round to the nearnest tenth of a degree.
Answer:
98.5
Step-by-step explanation:
The dude above do be wrong doh
this graph shows the solution to which inequality?
Answer:
B. y > 2/3x + 1
Step-by-step explanation:
To find slope we'll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
(-3,-1) (3,3)
3 - -1 = 4
3 - -3 = 6
2/3x
The y intercept is 1,
we know this because that's the point the line touches the y axis.
Thus,
the answer is B. y > 1/3x + 1.
Hope this helps :)
The graph of the solution of an inequality is given .
The graph represents the inequality is [tex]y>\frac{2}{3} x+1[/tex]
Option B
Given :
The graph of an inequality. To find the inequality for the given graph we use linear equation [tex]y=mx+b[/tex]
where m is the slope and b is the y intercept
To find out slope , pick two points from the graph
(-3,-1) and (3,3)
[tex]slope =\frac{y_2-y_2}{x_2-x_1} =\frac{3+1}{3+3} =\frac{2}{3} \\m=\frac{2}{3}[/tex]
Now we find out y intercept b
The point where the graph crosses y axis is the y intercept
The graph crosses y axis at 1
so y intercept b=1
The linear equation for the given graph is
[tex]y=\frac{2}{3} x+1[/tex]
Now we frame the inequality . we use test point that lies inside shaded region
Lets take (4,5)
[tex]y=\frac{2}{3} x+1\\5=\frac{2}{3} (4)+1\\5=3.6\\5>3.6\\y>\frac{2}{3} x+1[/tex]
The inequality for the given graph is
[tex]y>\frac{2}{3} x+1[/tex]
Learn more : brainly.com/question/24649632
For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the new equation, find x if the point P(x, 4) lies on the new line. y=3x-1 y=1/4 x+2
Answer:
The answer is below
Step-by-step explanation:
a) y=3x-1
The standard equation of a line is given by:
y = mx + c
Where m is the slope of the line and c is the intercept on the y axis.
Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:
3 × d = -1
d = -1/3
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]
b) y=1/4 x+2
Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:
1/4 × f = -1
f = -4
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]