There are 152 men, 76 women and 38 children.
Step-by-step explanation:
Total persons = 266
Let,
men = m
women = w
children = c
According to given statement;
m+w+c=266 Eqn 1
m = 4c Eqn 2
w = 2c Eqn 3
Putting value of m and w from Eqn 2 and 3 in Eqn 1
[tex]4c+2c+c=266\\7c=266\\[/tex]
Dividing both sides by 7
[tex]\frac{7c}{7}=\frac{266}{7}\\c=38[/tex]
Putting c=38 in Eqn 2;
[tex]m=4(38)\\m=152[/tex]
Putting c=38 in Eqn 1;
[tex]w=2(38)\\w=76[/tex]
There are 152 men, 76 women and 38 children.
Keywords: linear equations, substitution method
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Which figure shows the correct dimensions of a 1/3 scale drawing of the given figure?
Answer:
10 on top the rectangle and 4 on the left thats the answer , the girl who commented helped me out alot all i did was divide 3 times 30 and 3 times 12
Step-by-step explanation:
Answer:
10 on the top of the square and 4 on the side
Step-by-step explanation:
Please can someone help me answer this question attached.
Answer:
see the explanation
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal angles
step 1
Find the measure of angle BDA
we know that
Triangle ABD is an isosceles triangle
AB=AD ---> given problem
so
m∠ABD=m∠BDA
therefore
m∠BDA=72°
step 2
Find the measure of angle BAD
Remember that the sum of the interior angle in a triangle must be equal to 180 degrees
In the triangle BDA
m∠ABD+m∠BDA+m∠BAD=180°
substitute the given values
72°+72°+m∠BAD=180°
144°+m∠BAD=180°
m∠BAD=180°-144°=36°
step 3
Find the measure of angle BCA
In the triangle ABC
m∠BCA=m∠BAC
we have that
m∠BAC=m∠BAD=36°
therefore
m∠BCA=36°
step 4
Find the measure of angle ABC
In the triangle ABC
m∠BAC+m∠BCA+m∠ABC=180°
substitute the given values
36°+36°+m∠ABC=180°
72°+m∠ABC=180°
m∠ABC=180°-72°=108°
step 5
Find the measure of angle DBC
we know that
m∠DBC+m∠ABD=m∠ABC ----> by addition angle postulate
substitute the given values
m∠DBC+72°=108°
m∠DBC=108°-72°=36°
step 6
Find the measure of angle BDC
we know that
m∠BDC+m∠ADB=180° ----> by supplementary angles
substitute the given value
m∠BDC+72°=180°
m∠BDC=180°-72°=108°
step 7
In the triangle DBC we have
m∠DBC=36°
m∠BCD=m∠BCA=36°
so
The triangle BCD has two equal angles
therefore
Triangle BCD is an isosceles triangle
and
BD=BC
Lines r , s , and t are parallel. That means they have the same slope. Each of these lines has a slope of - 2 . Enter numbers to complete an equation for each line.
Answer:
(a) y = -2 x -2
(b) y = -2 x + 1
(c) y = -2 x + 3
Step-by-step explanation:
The given lines r , s and t are parallel.
⇒ Slope of line r = Slope of line s = Slope of line t = (-2)
The point slope equation for any line is given as
y = m x + C : m = slope pf line, C is y - intercept.
Y intercept is a point on line when x = 0.
Now for the line r, slope = (-2) and y intercept = (-2)
So, the equation is given as y = -2x -2
Now for the line s, slope = (-2) and y intercept = (1)
So, the equation is given as y = -2 x + 1
Now for the line t, slope = (-2) and y intercept = (3)
So, the equation is given as y = -2 x + 3
How many ml of 1:4 solution and how many ml of sterile water are needed to prepare 600 ml of 1:20 solution ?
Answer:
Approximately 143 mL of 1:4 solution and 457 mL of water
Step-by-step explanation:
A 1:4 solution has a concentration of 1/(1+4) = 1/5 or 20%.
Similarly, a 1:20 solution has a concentration of 1/(1+20) = 1/21 or 4.76%.
If x is the mL of 20% solution and y is the mL of water, then:
x + y = 600
1/5 x = 1/21 (600)
Solve:
x = 5/21 (600)
x ≈ 143
y ≈ 457
You need approximately 143 mL of 1:4 solution and 457 mL of water.
A price that is regularly $81 was reduced by 55%.
Answer:
$36.45
Step-by-step explanation:
81 - 55%
Convert percentage to decimals
55% = 0.55
81 - 55%
= 81 - 0.55(81) <= 81 reduced by 55% of 81
= 81 - 44.55 <= simplify and solve
= 36.45
i’m confused can someone get me the answer
mr wood's monthly expenses was $2.125 after he had reduced it by 15 %the oroginal monthoy expenses was 80% of his monthly income
find the original monthly expenses
Answer:
$2.50
Step-by-step explanation:
Let the original monthly expenses be 'x'.
Given:
Reduced monthly expenses = $2.125
Reduction in monthly expenses = 15%
Therefore, remaining percentage of monthly expenses = 100 - 15 = 85%
Now, as per question:
[tex]85\%\ of\ x=2.125\\\frac{85}{100}\times x=2.125\\0.85x=2.125\\x=\frac{2.125}{0.85}=\$2.50[/tex]
Therefore, the original monthly expenses of Mr. Wood was $2.50.
Also, we can find his monthly income using the value of 'x'.
As per question, his monthly expenses is 80% of his income.
So, 80% of income = 2.5
Income = [tex]\frac{2.5}{0.80}=\$3.125[/tex]
So, his monthly income is $ 3.125
If P(x)=6x^3=13x^2+x-2, and P(-2)=0, then the factorization of P(x) is
Answer:
Factorization of [tex]P(x)=(x+2)(2x+1)(3x-1)[/tex]
Step-by-step explanation:
Given:
The given polynomial is [tex]P(x)=6x^3+13x^2+x-2[/tex]
Also, [tex]P(-2)=0[/tex]
Since, for [tex]x=-2[/tex], [tex]P(x)[/tex] is 0, therefore, [tex]x+2[/tex] is a factor of the polynomial.
Now, let us divide the given polynomial by [tex]x+2[/tex] using long division method. Therefore,
[tex]\frac{6x^3+13x^2+x-2}{x+2}=6x^2+x-1[/tex]
The process of long division is shown below.
Now, factoring the quotient [tex]6x^2+x-1[/tex], we get
[tex]6x^2+x-1=6x^2+3x-2x-1=3x(2x+1)-1(2x+1)=(3x-1)(2x+1)[/tex]
Therefore, the factors of polynomial [tex]P(x)[/tex] are [tex](x+2),(2x+1),\ and\ (3x-1)[/tex]
Hence, the factorization of [tex]P(x)[/tex] is:
[tex]P(x)=(x+2)(2x+1)(3x-1)[/tex]
A description of what Derek did wrong and what he should have done instead the correct solution graphed on a number line
Answer:
Derek did it wrong that he did not change the inequality sign while dividing both side terms of the inequality by - 3.
Step-by-step explanation:
We are going to solve an equation of inequality of single variable x.
We will start with, -3x + 5 > 20
⇒ -3x + 5 - 5 > 20 - 5
⇒ - 3x > 15
⇒ [tex]\frac{-3x}{-3} < \frac{15}{-3}[/tex]
⇒ x < - 5
Therefore, while dividing both side terms by -3, the inequality sign will change from > to < sign.
So, Derek did it wrong that he did not change the inequality sign while dividing both side terms of the inequality by a negative number. (Answer)
Bill wants to make 22 small pizzas for a party. He has 16 cups of flour. Each pizza crust takes 3/4 cup of flour
he have enough flour?
The solution is 16.5 cups
The number of cups of flour for 22 small pizzas is 16.5 cups and Bill does not have enough flour for the party
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of cups of flour required be = A
Now , the equation will be
The number of pizza's Bill has for the party = 22 pizzas
The number of cups of flour Bill has = 16 cups
The number of cups of flour required for 1 pizza = 3/4 cups of flour
So , The total number of cups of flour for 22 pizzas = 22 x number of cups of flour required for 1 pizza
Substituting the values in the equation , we get
The total number of cups of flour for 22 pizzas = 22 x ( 3/4 )
The total number of cups of flour for 22 pizzas = 16.5 cups of flour
So , the number of cups of flour required > number of cups of flour Bill has
Therefore , the value of A is 16.5 cups
Hence , Bill does not have enough flour for the party
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1. You have two cards with a sum of (-12) in your hand.
a. What two cards could you have?
Answer:
The required cards can be -6 and -6.
Step-by-step explanation:
Consider the provided integer -12.
We need to find the two cards whose sum is -12.
There are lots of choices for the two cards whose sum is -12.
Few choices are:
If we first card is -6 and the second card is also -6 then the sum will be -12:
[tex]-6-6=-12[/tex]
If we first card is -4 and the second card is -8 then the sum will be -12:
[tex]-4-8=-12[/tex]
If we first card is -10 and the second card is -2 then the sum will be -12:
[tex]-10-2=-12[/tex]
Thus, the required cards can be -6 and -6.
Emily took 39 minutes to bike the biking section of a race. It then took her 9 minutes per mile to run the running section of the race. She represented this with the equation t= 39+9m, where t represents the total time she was racing in minutes and m represents the number of miles she ran in the running section. What is the slope and the y-intercept of this data
Answer:
Slope=9, y-intercept= 39
Step-by-step explanation:
The equation is already in y=mx+b form, where m is the slope and b is the y-intercept
(rearrange positions of 9m and 39 to get t=9m + 39)
So, the slope is 9 and the y-intercept is 39
negative 8 minus the product of three and a number is 19
Answer:
The number is -9.
Step-by-step explanation:
I set it up like this:
(-8) - 3x = 19
Then you add 8 to both sides of the equation in order to get rid of the negative 8.
(-8) + 8 - 3x = 19 + 8
After solving you would end up with this:
- 3x = 27
Then, you need to get the x by itself, so you divide by -3. In order to keep the equation equal though, you need to also divide the right side of the equation by -3.
- 3x ÷ -3 = 27 ÷ -3
Your final answer after solving would be:
x = -9
Chang is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $86 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.60 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Answer:
35
Step-by-step explanation:
86-65=21$ (initial fee diffrence)
21/0.6= 35
for 35 m company B charge less than A unless if renter want to drive further 35m so company A present a better offer.
Find the solution(s) to 9x2 - 54x = 0. Check all that apply.
The solutions to the equation 9x^2 - 54x = 0 are x = 0 and x = 6, found by factoring and setting each factor equal to zero.
To find the solution(s) to the equation 9x2 - 54x = 0, we can start by factoring out the greatest common factor, which is 9x. This gives us:
9x(x - 6) = 0
Now, we set each factor equal to zero:
9x = 0x - 6 = 0From the first equation, we divide by 9 to isolate x:
x = 0
From the second equation, we add 6 to both sides:
x = 6
Thus, the solutions to the equation are:
x = 0x = 6644 divide by 32 pls help
The answer would be 20.125 or 161/8, because to divide numbers, it is like the fraction 644/32. For example, if you have 644 mcord.weebly.com sites or bananas and you need to equally divide them into 34 groups, their would be 20.125 mcord.weebly.com sites or bananas in each group.
A college has 9 more english instructors than math instructors. if the total number of English and math instructors is 57, find the number of english instructors and the number of math instructors.
Answer:
There are 24 math instructors and 33 english instructors.
Step-by-step explanation:
Let x be the number of math instructors and y be the english instructors. Since the college has 9 more English instructors than math instructors, set up the equation like this: x+(x+9)=57 where x+y=57, you can see that y=x+9.
Now, it's time to solve for x and y.
x+(x+9)=57
2x+9=57
2x=57-9
2x=48
x=48/2=24
y=24+9=33
x=24, y=33
Answer:
24 math instructors & 33 english instructors
Step-by-step explanation:
x+(x+9)=57
2x+9=57
2x=57-9
2x=48
x=48/2=24
y=24+9=33
x=24, y=33
estimate the line of best fit using two points on the line.
Answer:
A. y = [tex]-\frac{2}{3}[/tex] x + 12
Step-by-step explanation:
Given the two points:
A = (x1, y1) = (6, 8)
B = (x2, y2) = (9. 6)
From the photo, we can see that the line of fest fit is a straight line (linear) that go through the two points above.
We have the standard form of a linear equation is:
y = mx + bwhere m is the slope and b is the y-intercept
To find the slope, we use the following formula:
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
<=> m = [tex]\frac{6-8}{9-6}[/tex] = [tex]-\frac{2}{3}[/tex]
Substitute m into the standard equation, we have:
y = [tex]-\frac{2}{3}[/tex] + b (1)Because the line go through point A, so we substitute A into (1), we have:
8 = [tex]-\frac{2}{3}[/tex] *6 + b
<=> b = 12
So our equation is: y = [tex]-\frac{2}{3}[/tex] x + 12
Answer: y=-2/3x+12
Step-by-step explanation:
Scott drove 871 miles in 13 hours. At the same rate, how long would it take him to drive 469 miles?
871 miles ........... 13 hours
469 miles ............x hours
x = 469×13/871 = 7 hours
patrick had 1\6 package of cookies he split it with his two how much of the package did each brother get
Step-by-step explanation:
Answer:
2/6
Step-by-step explanation:
solve 5(x/2+3)=35 what is the answer
Answer:
x=8
Step-by-step explanation:
5(x/2+3)=35
x/2+3=35/5
x/2+3=7
x/2=7-3
x/2=4
x=4*2
x=8
Answer:
x=8
Step-by-step explanation:
Divide both sides of the equation by 5 to get (x/2) + 3 = 7, then subtract 3 from each side to get x/2 = 4; finally multiply both sides by 2 to get x = 8
30 POINTS 7TH GRADE MATH! There are 15 girls in your class this year. That is a 15% increase from last year.
a. Write a proportion to solve for the number of girls in the class last year.
Solve the proportion in part (a).
Answer:
13 grls in ur class
Step-by-step explanation:
15*115%=17
17-15=2
25-2=13
Hope tht this helps :)
a)The proportion to solve for the number of girls in the class last year will be (15-x)/x = 0.15.
b)The value of x obtained after solving the proportion is 13.043.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
It is given that there are 15 girls in your class this year and there is a 15% increment from last year.
Suppose x is the number of girls in the class last year,
⇒15 = 15 % of x + x
⇒(15-x)/x = 0.15
Solving the above equation for finding the value of x,
15 - x = 0.15 x
15 = 0.15 x + x
15 = 1.15 x
x =15 / 1.15
x=13.043
Thus, the proportion to solve for the number of girls in the class last year will be (15-x)/x = 0.15, and the value of x obtained after solving the proportion is 13.043.
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What is the slope of y = -1+ 3.x?
Answer:
The slope is 3.
Step-by-step explanation:
y=-1+3x
y=3x-1
y=mx+b where m=slope and b=y-intercept
Write the percent as a decimal. 122%
Answer:
1.22
its obvious, lets say 100% of 1 is 1. 22% of 1 is 0.22. 1+0.22=1.22
The percent 122% as a decimal will be 1.22.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.
The expression is given below.
⇒ 122%
Then the percent 122% as a decimal will be
⇒ 122 / 100
⇒ 1.22
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Michelle's heart rate is 12 beats every 10 seconds. What is her heart rate in beats per MINUTE (bpm)?
A
22 bpm
B
62 bpm
C
72 bpm
D
120 bpm
Answer: 72
Step-by-step explanation: Simple, how many seconds are in a minute? 60. How do you get from 10 to 60? Multiply by 6. Then you take the beats every 10 seconds (12) and multiply by 6 (What it took to get from 10 to 60) to get 72.
A grocery store sells sliced turkey. the graph show shows the relationship between the weight of the sliced turkey and the total cost of the sliced turkey
Answer:
I think it is option C :>
The square below represents one whole what percent is represented by the shaded area
Answer:
Step-by-step explanation:
The square has 100 smaller parts.
92 of them are shaded, that means 92% of the square is shaded.
Steven has 9 gold coins that are identical in appearance. However, one coin is counterfeit and weighs slightly less than the others. Using a balance scale, how can he find the counterfeit coin in just two weighings?
Answer:
Split the coins into three groups, A, B and C consisting of 3 coins in each group.
Weigh: A--B
1. If A=B, the the counterfeit is in group C
Weigh any two coins in group C and figure out the rest.
2. If A≠B, then the counterfeit is in the lighter group.
Weigh any two coins in the lighter group and figure out the rest.
Steven can find the counterfeit coin in just two weighings by dividing the 9 coins into 3 groups and using the balance scale.
Explanation:Steven can find the counterfeit coin in two weighing by following these steps:
Divide the 9 coins into 3 groups of 3 coins each. Weigh the two groups of 3 coins on the balance scale. If the two groups balance, the counterfeit coin is in the third group. Weigh two of the coins from this group on the scale.If one of the coins is lighter, it is a counterfeit coin. If the scale balances, the remaining coin is the counterfeit.By dividing the coins into three groups, Steven eliminates two-thirds of the coins after the first weighing and then narrows it down to just two coins in the second weighing.
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What is another way to write the ratio 13:6
Answer:
13/6
Step-by-step explanation:
it can also be written as a fraction
3) The equation 41.44=k7 shows that buying 7 bags of apples
would cost 41.44 dollars. How much is it for one bag?
Answer:
k = $41.44/7 bags = $5.92/bag
The cost of one bag of apples is 5.92 dollars.
To find the cost of one bag of apples, we can divide the total cost by the number of bags.
Given the equation [tex]\(41.44 = 7k\)[/tex], where [tex]\(k\)[/tex] represents the cost of one bag, we can solve for [tex]\(k\)[/tex] by dividing both sides of the equation by 7:
[tex]\[ k = \frac{41.44}{7} \][/tex]
Calculating:
[tex]\[ k = \frac{41.44}{7} = 5.92 \][/tex]