Answer:
a. Number of people surveyed were 900.
b. 360 people preferred running.
Step-by-step explanation:
Given:
On a recent survey, 60% of those surveyed indicated that they preferred walking to running.
If 540 people preferred walking.
Now, to find a. number of people were surveyed. b. number of people preferred running.
a.
Number of people preferred walking = 540.
Percentage of people preferred walking = 60%.
Let the total number of people surveyed be [tex]x.[/tex]
Now, to get the number of people surveyed:
60% of x = 540.
[tex]\frac{60}{100} \times x=540[/tex]
[tex]0.60\times x=540[/tex]
[tex]0.60x=540[/tex]
Dividing both sides by 0.60 we get:
[tex]x=900.[/tex]
Thus, number of people surveyed = 900.
b.
Total number of people surveyed = 900.
People preferred walking = 540.
Now, to get the people preferred running we subtract people preferred walking from total number of people surveyed:
[tex]900-540[/tex]
[tex]=360.[/tex]
Thus, people preferred running = 360.
Therefore, a. Number of people surveyed were 900.
b. 360 people preferred running.
Roland has 180 coins in his collection. Approximately 67% of the coins are quarters. About how many quarters does he have?
Answer:
120.6
Step-by-step explanation:
Since we know that 67 percent of coins are quarters.
Total coins = 180
67% of 180= 180 * 67/100
120.6.
So he has about 120.6 quarters.
Answer:
126 quarters
Step-by-step explanation:
67% ≈ 70%
70% = 70/100
70% = 7/10
180 * 7/10 = 126 quarters
4x-4y=0
Y=2x+6
Solve by substitution
Answer: x = -6, and y = -6 (-6, -6)
Step-by-step explanation: What we have here is a pair of simultaneous equations. Since we have been instructed to solve by substitution, we shall begin with the one which has one of the variables as having a coefficient of 1. We shall start with equation 2 which is,
y = 2x + 6
Having taken note of this, we can now go on to the other equation and substitute for the value of y.
Hence, from equation 1,
4x - 4y = 0 (substitute for the value of y)
4x - 4(2x + 6) = 0
4x - 8x - 24 = 0
-4x -24 = 0
Add 24 to both sides of the equation
-4x = 24
Divide both sides of the equation by -4
x = -6
Having calculated the value of x, we can now go on to substitute for the value of x in equation 2.
Therefore,
y = 2x + 6
y = 2(-6) + 6
y = -12 + 6
y = -6.
So, x = -6 and y = -6
Perimeter and area for these 2 please! Give explanation! BIG POINTS
Answer: For the figure on the left {c}, the Area is 30m (squared) and the Perimeter is 46m.
For the figure on the right {d}, the Area is 32cm (squared) and the Perimeter is 34cm
Step-by-step explanation: (Please refers to the attached diagram)
We shall start with the diagram on the left. The first thing is to break it down into regular shapes, such as rectangles, squares, etc. The dotted line that runs from point C to point G divides the figure into two rectangles which are ABCG {or X} and GDEF {or Y}. Line AG measures 10m since it’s the same length as line BC. Similarly line GF measures 2m since it’s the same length as line DE. So rectangle “X” has dimensions;
L = 10, W = 1
Area of a rectangle = L x W
Area = 10 x 1
Area = 10m
Similarly rectangle Y has dimensions L= 10m and W = 2m
Hence area of rectangle “Y” is computed as
Area = L x W
Area = 10 x 2
Area = 20m
Area of the entire figure is derived as
Area of rectangle X + Area of rectangle Y, which is
10m + 20m = 30m {squared)
The perimeter of rectangle X is given as Perimeter = 2(L + W)
Perimeter = 2(10 + 1)
Perimeter = 2(11)
Perimeter = 22m
Also, perimeter of rectangle Y is derived as
Perimeter = 2(L + W)
Perimeter = 2(10+ 2)
Perimeter = 2(12)
Perimeter = 24m
Therefore the perimeter of the entire figure is derived as
Perimeter of rectangle X + perimeter of rectangle Y, which is
22m + 24m and that equals 46m
For the second figure on the right side of the page, we shall also break it down with the dotted lines that runs from point E to point G. That leaves us with rectangle ABGF {or P} and rectangle EGCD {or Q}.
Rectangle “P” has dimensions L= 4 and W = 2
Area of rectangle P = 4 x 2
Area of rectangle P = 8cm
Similarly area of rectangle Q is given as Area of Q = 8 x 3
Area of Q = 24cm
Area of the entire figure is derived as
Area of P + Area of Q,
8cm + 24cm
= 32cm {squared}
To compute the perimeter of rectangle P
Perimeter of a rectangle = 2(L + W)
Perimeter of rectangle P = 2(4 + 2)
Perimeter of rectangle P = 2(6)
Perimeter of rectangle P= 12cm
Similarly Perimeter of rectangle Q = 2(L + W)
Perimeter of rectangle Q = 2(8 + 3)
Perimeter of rectangle Q = 2(11)
Perimeter of rectangle Q = 22cm
Hence, perimeter of the entire figure is derived as perimeter of rectangle P + perimeter of rectangle Q which equals
12cm + 22cm and that equals
34cm.
The sum of two numbers is 50. The first number is 43 less than twice the second number. Write and solve a system of equations to find the two numbers.
Answer: 19 and 31
Step-by-step explanation: Make the first number x, the second number y.
The sum of x and y is 50: x+y=50
x is 43 less than 2y: x=2y-43
replace x in equation x+y=50 with x=2y-43: 2y-43+y=50
combine like terms: 3y-43=50
add 43 to both sides: 3y=93
divide both sides by 3: y=31
replace y in equation x+y=50 with y=31: x+31=50
subtract 43 31 from both sides: x=19
the solution to the question is the first number is 19, the second number is 31
The two numbers that sum up to 50 with one being 43 less than twice the other, we set up a system of equations, solve for one variable, and then substitute it back into the other equation, resulting in the numbers 19 and 31.
The question asks us to find two numbers whose sum is 50 and where the first number is 43 less than twice the second number. To solve this, we can create a system of equations to represent the given conditions. Let the first number be x and the second number be y.
According to the question, the sum of the two numbers is 50, which gives us our first equation:
x + y = 50 (Equation 1)
The first number x is 43 less than twice the second number y. This provides the second equation:
x = 2y - 43 (Equation 2)
We now have a simple system of two linear equations:
x + y = 50
x = 2y - 43
We can substitute the second equation into the first to solve for y:
(2y - 43) + y = 50
3y - 43 = 50
Add 43 to both sides:
3y = 93
Divide both sides by 3:
y = 31
We can now substitute y = 31 back into Equation 2 to find x:
x = 2(31) - 43
x = 62 - 43
x = 19
Therefore, the two numbers are 19 and 31.
What number decreased by 77 equals negative 18
Answer:
59
Step-by-step explanation:
77+(-18)=59
Check:
59-77=(-18)
Hoped this helped !
Cheers, Z.
Answer:
59
Step-by-step explanation:
59-77=-18
77+-18=59
PLEASE HELP
Examine the system of equations.
-3x + y = 4,
-9x + 5y = -1
What is the solution?
Answer:
x= - 3.5
y= - 6.5
Step-by-step explanation:
-3x+y = 4 equation 1
-9x + 5y = -1 equation 2
and
equation 1 can be written as
y = 4+ 3x
so put this in equation 2
-9x + 5 ( 4+ 3x) = -1
-9x +20 +15x = -1
6x = -21
X= -21 ÷ 6
X = - 3.5
so put this value of x in equation 1 to find value of y
-3 ( -3.5) + y = 4
10.5 + y = 4
y = 4 - 10.5
Y = - 6.5
Answer:
x= - 3.5
y= - 6.5-
write the fraction as a sum of fractions three different ways 7/10
Which value is an output of the function? -6,-2,4,7
Without knowing the function itself, it's impossible to definitively say which of the values (-6,-2,4,7) is an output. Any of these numbers could potentially be an output depending on the function.
Explanation:In the context of this question, an output of a function refers to the result you get after substituting an input (or value from the domain) into the function. For example, if we have a function f(x) = x+2, and we input the value 3 (from our domain), our output (or range) will be 5. Unless we know the actual function, it's difficult to determine which of the listed values (-6,-2,4,7) is an output because any of these could potentially be an output depending on the function. Thus, without additional context, the statement 'Which value is an output of the function?' cannot be definitively answered.
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The output of a function is -6.
The output of a function is the value that the function produces when a certain input is given. In the table above, the function is f(x). We are given that x can be any of the values -6, -2, 4, or 7. We want to know which of the values -6, -2, 4, 7, or 12 is an output of the function.
To find out, we can look at the table. We see that the only value in the table that is an output of the function is -6. This is because when we plug in x = -6 into the function, we get f(x) = -6.
Therefore, the answer is -6.
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solve for x. step by step please show the work
x+(-4) =10
x + (-4) = 10.
We can use the positive - negative rule.
x + (-4) = 10.
x - 4 = 10.
x = 10 + 4
x = 14.
What is 1/4 * 4x + 8
Answer:
2
Step-by-step explanation:
do like terms
1/4 x 8 = 2
divide un-like terms
4x ÷ 8 = 2
What is 50/400 simplified
Step-by-step explanation:
[tex] \frac{50}{400} = \frac{5}{40} = \frac{1}{8} = 0.125[/tex]
please answer this if you can thank you :))
Answer:
The variable that has the highest power is considered to be the degree of polynomials in an algebraic equation.
A column:
1) [tex]4x^3[/tex] .
The degree is 3.
2)[tex]x^2+4[/tex].
The degree is 2.
3) [tex]x-2[/tex]
The degree is 1.
B column:
1) [tex]2x^2+1[/tex]
The degree is 2.
2) [tex]x^2-x[/tex]
The degree is 2.
3) [tex]x^3-5x^2+1[/tex]
The degree is 3.
A×B columns:
While Multiplying two terms in a equation, if the variables are same then multiply the constant value and sum the exponent value.
1) [tex](4x^3)(2x^2+1)[/tex].
=[tex]8x^5+4x^3.[/tex]
The degree is 5.
2) [tex](x^2+4)(x^2-x)[/tex].
=[tex]x^4-x^3+4x^2-4x[/tex].
The degree is 4.
3) [tex](x-2)(x^3-5x^2+1)[/tex].
[tex]=x^4-5x^3+x-2x^3+15x^2-3.\\=x^4-7x^3+15x^2+x-3.[/tex]
The degree is 4.
What are the terms in the expression, 2 + 6 + 10b – 8a?
The terms in the expression 2 + 6 + 10b - 8a are 2, 6, 10b, and -8a, where 2 and 6 are constants, and 10b and -8a are variable terms.
Explanation:The terms in the expression 2 + 6 + 10b – 8a are 2, 6, 10b, and –8a. A term is a single mathematical expression which can be a number, a variable, or numbers and variables multiplied together. Here, the numbers 2 and 6 are called constant terms because they don’t change, 10b is a variable term which means it has a number (coefficient) and a variable (b), and similarly, –8a is a variable term with a negative coefficient and the variable a.
Shane spends 48% of her income on cruises.if she makes $68,000 per year,how much does she spend on cruises?
Answer:
She spend $32,640 on cruises.
Step-by-step explanation:
Given:
Shane spends 48% of her income on cruises.
If she makes $68,000 per year.
Now, to find the money she spend on cruises.
Shane makes income per year = $68,000.
Percent Shane spends of her income on cruises = 48%.
Now, to get the income she spends on cruises:
48% of $68,000.
[tex]=\frac{48}{100} \times 68000[/tex]
[tex]=0.48\times 68000[/tex]
[tex]=\$32,640.[/tex]
Therefore, she spend $32,640 on cruises.
Every Halloween, trick-or-treaters love going to Erica's house to see her spooky decorations and get some of her delicious caramel chews.
There is a proportional relationship between the number of kids in a group, x, and the total number of caramel chews Erica gives to that group, y.
x (kids) y (caramel chews)
2 6
4 12
5 15
6 18
Write an equation for the relationship between x and y.
y=
Answer:
[tex]y=3x[/tex]
Step-by-step explanation:
Let
x ----> the number of kids in a group
y ----> the total number of caramel chews Erica gives to that group
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
Find the value of the constant of proportionality k
take a ordered pair from the data in the table and determine the value of k
For x=2, y=6 ----> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{6}{2}=3\ caramels/kid[/tex]
therefore
[tex]y=3x[/tex]
Subtract. Express your answer in lowest terms 10 2/5 - 3 4/5
6 3/11 that well be the answer
Answer:6 3/5
Step-by-step explanation: 10 2/5 - 3 4/5 = 33
5
= 63
5
= 6.6
Simplify the expression: 2/3 divided by - {1/6 - 8/6}
Answer:
4/7
Step-by-step explanation:
1/6-8/6=-7/6
-[1/6-8/6]=7/6
---------------------
(2/3)/(7/6)=(2/3)(6/7)=12/21=4/7
In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28. During the next 20 years, the price increased an average of 6% each year. Write a model giving the annual price p (in dollars) of a ticket t in years after 2000.
[tex]y = 48.28(1.06)^t[/tex] is the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found
Solution:
Given that,
In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28
During the next 20 years, the price increased an average of 6% each year
The increasing function is given by:
[tex]y = a(1+r)^t[/tex]
Where,
y is the value after t years
t is the number of years
a is the initial value
r is rate of increase in decimal
From given,
a = 48.28
[tex]r = 6 \% = \frac{6}{100} = 0.06[/tex]
Substituting the values we get,
[tex]y = 48.28(1+0.06)^t\\\\y = 48.28(1.06)^t[/tex]
Thus the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found
PLEASE HURRY WILL GIVE YOU MY ACCOUNT AND BRAINLIEST IF YOU ANSWER CORRECTLY
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Which is true of the data in the box plots? Select three choices.
1 The median weight for shelter A is greater than that for shelter B.
2 The median weight for shelter B is greater than that for shelter A.
3 The data for shelter A are a symmetric data set.
4 The data for shelter B are a symmetric data set.
5 The interquartile range of shelter A is greater than the interquartile range of shelter B
WILL REPORT IF WRONG
Answer:
A, D, E
Step-by-step explanation:
The sales tax for an item was $29.60 and it cost $370 before tax. Find the sales tax rate. Write your answer as a percentage
Answer: 8%
Step-by-step explanation: 370 * 8% = 29.60
Answer: 8% sales tax rate
Step-by-step explanation:
First, you need to find what percentage 29.60 is from 370, so you divide 29.60 by 370 and you get 0.08 then you multiply that by 100 to get your answer in percent. 100 multiplied by 0.08 would be 8%.
Triangle LAQ has side lengths of 9, 20, and 15. Classify the triangle by its sides.
scalene triangle
equilateral triangle
isosceles triangle
scalar triangle
Answer:
Scalene triangle
Step-by-step explanation:
It is a scalene triangle because none of the sides are equal .equilateral triangle have the three sides equal. isosceles triangle have only two equal sides
36x - 8y2 when x=3 an y= -6
Hey there!
First off, I’m going to assume that the 2 in the second term is an exponent. If it isn’t, let me know and I’ll fix the answer.
Anyways, let’s start by plugging the values for the variables into the equation.
36(3)-8(-6)^2
Square -6
108-8(36)
Multiply.
108-288
Subtract.
-180
Your answer is -180.
Hope this helps!
H E L P
Factor -6m + 9.
a. -6( m - 3)
b. -6( m + 9)
c. -3(2 m - 3)
d. -3(2 m + 3)
Answer:
c
Step-by-step explanation:
-6m + 9
-3(2m - 3)
Answer:
I think it's c sorry if I am wrong.
Step-by-step explanation:
Lin's father is paying for a $20 meal. He has a 15%-off for the meal. After the discount, a 7% sales tax is applied. What does Lin's father pay for the meal?
Answer:
18.19
Step-by-step explanation:
$20-15%=$17
$17+7%=18.19
Lin's father pays $18.19 for the meal after the 15% discount and 7% sales tax.
Explanation:To find out what Lin's father pays for the meal after the discount and sales tax, we need to follow these steps:
Calculate the amount of the discount by multiplying the original price by the discount rate.Subtract the discount amount from the original price to find the discounted price.Calculate the amount of the sales tax by multiplying the discounted price by the sales tax rate.Add the sales tax amount to the discounted price to find the total amount paid for the meal.Let's apply these steps to the given information:
Discount rate: 15%Sales tax rate: 7%Original price: $20Step 1: Discount amount = $20 x 15% = $3
Step 2: Discounted price = $20 - $3 = $17
Step 3: Sales tax amount = $17 x 7% = $1.19
Step 4: Total amount paid = $17 + $1.19 = $18.19
Therefore, Lin's father pays $18.19 for the meal after the discount and sales tax.
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What is the binomial expansion of (x + 2y)7?
2x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + 2y7
x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + y7
x7 + 7x6y + 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7
Step-by-step explanation:
We find,
[tex](x+2y)^7[/tex]
To find, the binomial expansion of of [tex](x+2y)^7[/tex] = ?
We know that,
[tex](x+y)^{n} =^nC_0x^n+^nC_1x^{n-1}y+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+...+^nC_ny^n[/tex]
∴ [tex](x+2y)^7[/tex]
Here, n = 7, x = x and y = 2y
[tex](x+2y)^7[/tex]= [tex]^7C_0x^7+^7C_1x^{7-1}(2y)+^7C_2x^{7-2}(2y)^2+^7C_3x^{7-3}(2y)^3+^7C_4x^{7-4}(2y)^4+^7C_5x^{7-5}(2y)^5+^7C_6x(2y)^6+(2y)^7[/tex][tex]=x^7+7x^{6(2y)+21x^{5}4y^2+35x^{4}8y^3+^35x^{3}16y^4+21x^{2}32y^5+7x64y^6+128y^7[/tex]
[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]
∴ The binomial expansion of of [tex](x+2y)^7[/tex]
[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]
Thus, the required "option 4)" is correct.
Answer:
D. x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7
Step-by-step explanation:
Is y=-3x^2 +10 a function
Answer:
YES
Step-by-step explanation:
how many triangles can be drawn with side lengths of 3 inches, 5 inches, and 6 inches
Answer:
One triangle
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Verify the length sides of triangle
Applying the triangle inequality theorem
1) 3+5 > 6 ---> is true
2) 3+6 > 5 ---> is true
3) 5+6> 3----> is true
therefore
One triangle can be drawn with the given lengths
With side lengths of 3 inches, 5 inches, and 6 inches, only one triangle can be drawn as these dimensions meet the triangle inequality theorem, allowing for the creation of one unique triangle.
Explanation:The question is about determining if a triangle can be constructed with given side lengths. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the third side. In this case, the side lengths are 3 inches, 5 inches, and 6 inches.
Adding the lengths of the two shorter sides, 3 inches + 5 inches = 8 inches, which is greater than the length of the longest side, 6 inches. This means a triangle with these side lengths can be drawn. However, it is important to note that the lengths provided can only create one unique triangle, since the lengths are fixed and there can't be another triangle with different angles with the same side lengths.
Therefore, with side lengths of 3 inches, 5 inches, and 6 inches, exactly one triangle can be drawn.
what is 67,456 divided by 32 and tell me how
Answer:
2108
Step-by-step explanation:
Divide 67,456 by 32, using long division.
1) How many times 32 go into 67? (2 times, with a remainder of 3)
2) Bring down the 4.
3) How many times does 32 go into 34? (1 time, with a remainder of 2)
4) Bring down the 5
5) How many times does 32 go into 25? (0 times, so write 0)
6) Bring down the 6.
7) How many times does 32 go into 256? ( 8 times, no remainder)
8) Your answer is 2108
What is -4 divided by -0.2?
Answer:
20
Step-by-step explanation:
-4/-0.2
When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.
Explanation:When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.
jake rode his bike from 2:30 to 3:30. then he took a shower.he finished his shower 30 minutes after the bike ride ended what time was it when he finished his shower? how would you show this time on a clock face
Answer:
4
Step-by-step explanation: