Final answer:
By establishing an equation G = k(B/T), where G is the number of girls, B is the number of boys, and T is the number of teachers, we determine the constant of proportionality (k) from the given values. Using this constant, we deduce that there are 10 boys when there are 10 girls and 100 teachers.
Explanation:
The number of girls varies directly as the number of boys (B) and inversely as the number of teachers (T). This can be written as an equation, G = k(B/T), where G is the number of girls, and k is a constant of proportionality. From the given information, when there were 50 girls, there were 20 teachers and 10 boys. Plugging these values into the equation gives us 50 = k(10/20), which simplifies to 50 = k/2. Solving for k gives us k = 100.
Now, to find out how many boys are there when there are 10 girls and 100 teachers, we use the equation with our value for k. We get 10 = 100(B/100). Simplifying this equation gives us 10 = B. Therefore, there are 10 boys when there are 10 girls and 100 teachers.
Sari had 3 times as much money as Raymond. If after she paid Raymond a certain number of dollars, she had $30 and Raymond had $42, which of these statements is correct?
A.
Sari originally had $18.
B.
Sari originally had $24.
C.
Sari paid Raymond $18
D.
Sari paid Raymond $24.
Answer:
D
Step-by-step explanation:
both A and B are false, because no value would allow Sari to pay Raymond and then still have 30 dollars so it has to be C or D
42 - 24 = 18 18 times 3 is 54, so this appears to work
30 + 24 = 54
42 - 18 = 24 24 times 3 is not 48, so C is incorrect
30 + 18 = 48
which of the following is equivalent to 3(2x-5)-4(x-3)=7
Answer:
A
Step-by-step explanation:
When we distribute, we get:
6x - 15 - 4x + 12 = 7
If we combine the like terms, we get:
2x - 3 = 7, which is A in your case. Hope this helps.
The circumference of a circle is 48 pie units. What is the radius of the circle
Answer:
r = 24
Step-by-step explanation:
The formula for circumference is
C = 2*pi*r
48 pi = 2 * pi *r
Divide each side by 2pi
48 pi / 2pi = 2 * pi *r/ 2pi
24 = r
Describe what Pi is and explain how it is used in finding the circumference of a circle
Answer:
Sample response: Pi is a number that is approximated by 3.14, or 22/7. It is the ratio of the circumference to the diameter of any circle. This ratio can be rearranged to find circumference of a circle by multiplying pi times diameter.
Step-by-step explanation:
Lyla made a scale drawing of a city park. She used the scale 1 millimeter = 1 meter. What is the scale factor of the drawing?
Answer:
1ml : 1m
Step-by-step explanation:
The scale factor of the drawing is the ratio of 1 milliliter and 1 meter; that is, 1ml : 1m.
|3x−2|=19 please help quick thanks
Answer:
x=7,-17/3
Step-by-step explanation:
If x = a sec and y = b tan then find b^2x x^2-a^2x y^2
Corey drew a sketch of a paper hat
If a = 4 in and b = 3 in, what is the area of the sketch?
A.
84 in2
B.
60 in2
C.
40 in2
D.
21.5 in
Answer:
Not on there but it is 76in2
Step-by-step explanation:
Starting with the trapezoid. We know that a trapezoid can be split into 2 triangles and 1 rectangle. So the area of the trapezoid will be 4+32+4 which is 40 now that we know the trapezoid's area we can find the rectangle's area. The rectangle's area will be 12x3 which is 36. So, you would add both:40+36= 76in2.
What is the exact distance from (−4, −2) to (4, 6)? (4 points)
A 24
B88
C 100
D 128
I would say it’s B! I know it isn’t A because we can say no to A since it’s such a small number and (-4,-2) to (4,6) isn’t 24 nor bigger then 100 so the only possible answer is B
I hope this helps and makes sense!
Pat's average weekly income from her part time job was 15% more in September than it was in July. her average weekly income in July was 10% less than it was in August. if her average weekly income in September was $207, what was her average weekly income in August?
Her average weekly income in August was $200.
Step-by-step explanation:
To find the income in july :
Given that,
Her average weekly income in September was $207.Her part time job was 15% more in September than it was in July.Let,
'x' be the 100% of income she got in July.
Therefore, the income $207 in September is 115% of x.
⇒ 115% of x = 207
⇒ 1.15 × x = 207
⇒ x = 207 / 1.15
⇒ x = 180
∴ Her average weekly income in July was $180.
To find the income in August :
Given that,
Her average weekly income in July was 10% less than it was in August.We found that, $180 is the average weekly income in July which is 10% less than August.Let,
'y' be the 100% of income she got in August.
Therefore, the income $180 in July is 90% of y.
⇒ 90% of y = 180
⇒ 0.9 × y = 180
⇒ y = 180/0.9
⇒ y = 200
∴ Her average weekly income in August was $200.
her average weekly income in August was $200 .
Step-by-step explanation:
Let in July income was x , So in September :
⇒ [tex]x+\frac{15x}{100}[/tex]
According to question , her average weekly income in September was $207 i.e.
⇒ [tex]x+\frac{15x}{100}=207[/tex]
⇒ [tex]\frac{115x}{100}=207[/tex]
⇒ [tex]x=207(\frac{100}{115})[/tex]
⇒ [tex]x=180[/tex]
Now , average weekly income in July was 10% less than it was in August , let income of august = y, i.e.
Income in august = [tex]180+\frac{August(10)}{100}[/tex]
⇒ [tex]y=180 + \frac{y(10)}{100}[/tex]
⇒ [tex]\frac{9}{10}y=180[/tex]
⇒ [tex]y=\$200[/tex]
Therefore , her average weekly income in August was $200 .
You are a manager at a restaurant. The restaurant’s freezer needs to be kept at a temperature of −5°F. The last reading was −1°F.
How does the temperature need to change to reach the preferred reading?
It needs to decrease by 6°.
It needs to decrease by 5°.
It needs to decrease by 4°.
It needs to increase by 4°.
It needs to increase by 6°.
Answer:
It needs to decrease by 4°
Step-by-step explanation:
-1-4=-5
mark my brainliest? :)
Final answer:
The temperature needs to change by 4°F to reach the preferred reading at -5°F.
Explanation:
The current temperature of the restaurant's freezer is -1°F. To achieve the preferred temperature of -5°F, we need to calculate the difference between the two temperatures The temperature needs to change to reach the preferred reading is 5°. Thus,
Calculating the difference between the preferred temperature (-5°F) and the current reading (-1°F): -5 - (-1) = -5 + 1 = -4°F.Since temperatures are measured in terms of how much they deviate from zero, it needs to decrease, so the change will be positive: 4°F.Therefore, the temperature needs to decrease by 4°F to reach the preferred reading.
Describe one method to calculating the area of the shaded region.
Answer:
Fine the area of the square, then the area of the circle. Subtract the area of the circle from the area of the square and you will get the remaining shaded area.
What is the area of the surface of a cookie was a diameter of 32 feet?
That would be [tex]\pi(32/2)^2\approx804.25\mathrm{ft^2}[/tex].
Hope this helps.
ANSWER!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Total bags = 8
Candies in each bag = 7 candies
So Now
Total candies in the package = 7*8 = 56
What is the next term of the arithmetic sequence?
-6,-8, –10, –12, -14,
Answer:-16 Hope that helps
Step-by-step explanation:
5x2 - 4x – 9 = 0
Master Product:
try
Answer:
Step-by-step explanation:
5×-9=-45
-9+5=-4
5x²-4x-9=0
5x²-9x+5x-9=0
x(5x-9)+1(5x-9)=0
(5x-9)(x+1)=0
x=-1,9/5
4) -8 – 3a = 46 whoever has best answer gets brainliest
Answer:
A= -18
Step-by-step explanation:
-8-3(-18)= 46= -18
Answer:
a=-18
Step-by-step explanation:
Let's break this down step by step.
-8-3a=46
Since 3a has a variable, a, we want to get it by itself. So the first step is to do the inverse operation and add 8 on both sides. That leaves this equation:
-3a=54
The 3a is -3a because of the subtraction sign in front. Now we divide on both sides because we want the variable, a, to be by itself. That leaves this simplified expression.
a=-18.
Now, let's work it out in context of the problem.
-8-3x-18=46
3x-18 is -54, and -8-(-54), it would become 46.
What happens to the value of f(x) = log4x as x approaches 0 from the right?
Answer:f(x) approaches negative infinity
Step-by-step explanation:
N/A
Answer:
the 1st one is a (f(x) approaches negative infinity)
the 2nd one is c (f(x) approaches infinity)
Step-by-step explanation:
Can someone please help me with this (thank you)
Answer:
D. ( 3.6 , 2.2)
Step-by-step explanation:
Given
x + y = 5.8....equation 1
y = 2x - 5 ......equation 2
Putting equation 2 in equation 1
x + 2x - 5 = 5.8
3x = 5.8 + 5
3x = 10.8
Therefore x = 3.6
Now
y = 2 * 3.6 - 5
= 7.2 - 5
= 2.2
Hope it will help you.
Answer:
B
Step-by-step explanation:
Joey's cleaning service charges $50 per week to clean a home. Amy's cleaning service charges $50 per week , plus $25 for cleaning supplies.
which equation can be used to express the amount that Amy's cleaning service charges?
A y=50x
B y=50x-25
C y=1/50x
D y=50x + 25
Answer:
D y=50x + 25
Step-by-step explanation:
The number of weeks can vary, so it is placed in front of a variable. The cleaning supplies cost does not, so it does not have a variable, but instead, it is a constant.
Answer:
D
Step-by-step explanation:
y = mx + b is the equation, where m = cost per week and b = cleaning supply cost (constant)
That means the equation is y = 50x + 25
What is the length of the hypotenuse of a right triangle with legs that are 7 and 8 inches long?
Answer:
square root of 113 or 10.63014581
Step-by-step explanation:
Answer:
[tex]\sqrt{113}[/tex]
Step-by-step explanation:
Using pythag theorem:
Length of the hypotenuse is [tex]\sqrt{7^{2}+8^2 }[/tex]
Thus [tex]\sqrt{113}[/tex]
the length of a rectangle is six times it’s width. If the perimeter of the rectangle is 112 yards, find it’s length and width.
The length of rectangle is 48 yards and width of the rectangle is 8 yards, if the perimeter of the rectangle is 112 yards.
Step-by-step explanation:
The given is,
The perimeter of the rectangle is 112 yards
The length of a rectangle is six times it's width
Step:1
Let, p - Perimeter of the rectangle
l - Length of the rectangle
w - Width of the rectangle
Step:2
Formula for perimeter of rectangle,
[tex]Perimeter, p = 2(l+w)[/tex]............................(1)
From given,
p = 112 yards
l = 6w ( ∵ From given)
w = w
Substitute the values,
112 = 2 ( 6w + w )
112 = 2 ( 7w )
112 = 14w
w = 8 yards
From the w value, l becomes
l = 6w
l = 6 × 8
l = 48 yards
Result:
The length of rectangle is 48 yards and width of the rectangle is 8 yards, if the perimeter of the rectangle is 112 yards.
(Angles) What is the measure of angle p, in degrees? *
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Restart to ins
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With new feat
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and we'll do it
Answer:
Third Answer or 62 degrees.
The measure of angle p can be found by subtracting the measures of angles q and r from 180 degrees.
Explanation:The measure of angle p can be determined by subtracting the measures of angles q and r from 180 degrees. Let's say angle q measures 50 degrees and angle r measures 70 degrees. By subtracting these values from 180, we can find that the measure of angle p is 60 degrees.
Learn more about Angle measurement here:https://brainly.com/question/33833061
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What’s the value of x in degrees
Answer:
92⁰
Step-by-step explanation:
a = 35⁰ ( vertically opposite )
b = 53⁰ (vertically opposite )
a + b + x = 180⁰ (Angle sum property of triangle)
35⁰ + 53⁰ + x = 180⁰
x = 180⁰ - 88⁰
x = 92⁰
Answer:
[tex]x = 97 \: \: degrees[/tex]
Step-by-step explanation:
[tex]a = 35 \\ b = 53 \\ (vertically \: \: opposite \: \: angles)[/tex]
[tex]35 + 53 + x = 180 \\ 86 + x = 180 \\ x = 180 - 83 \\ x =9 7 \: \: degrees[/tex]
sum of the angles in a triangle is 180 degrees.
hope this helps
brainliest appreciated
good luck! have a nice day!
Which of the following is a dilation?
O (x, y)----(x, 3y)
O (x,y)--(3x, 3y)
O (x, y)--(x,y-3)
O (x, y)---(.5x, .4y)
O Both 2 & 4
¿Cuál dígito debe ir en el recuadro para
que el siguiente número sea divisible
entre 2, 3 y 9? 8,? 48
Answer:
7
Step-by-step explanation:
English:
Which digit should go in the box to
make the next number divisible
between 2, 3 and 9? 8 ,? 48
Let x be the number, then the number will look like this:
8x48
This number is already divisible by 2, because it ends with an even number.
Now we need to check for divsibility by 3.
For this to be divisible by 3, the sum of the digit should be a multiple of 3.
[tex]8 + x + 4 + 8 = x +20[/tex]
We know if a number is divsible by 9, it is also divsible by 3.
So
[tex]x + 20=9,18,27,....[/tex]
The least positive solution is
[tex]x + 20 = 27[/tex]
[tex]x = 27 - 20[/tex]
[tex]x = 7[/tex]
Therefore 8748 is divsible by 2,3, and 9.
What’s the area and the perimeter
Area formula: a = l * w
a = 8 * 4.5
a = 36
Perimeter formula: p = 2l * 2w
p = 2(8) + 2(4.5)
p = 16 + 9
p = 25
Best of Luck!
A wheelbarrow weighs 55 pounds. It can carry a load up to 1/2 ton. How many pounds does the wheelbarrow weigh when it is filled to capacity?
Answer:
1055 lbs.
Step-by-step explanation:
Since 1 ton is 2000 pounds, half a ton is 1000 pounds. The wheelbarrow weights 55 pounds in itself, so the total weight will be 1000 + 55 = 1055 lbs.
Let ABCD be a convex quadrilateral. Let P and Q be points on side AB such that AP = PQ = QB. Similarly, BR = RS = SC, CT = TU = UD, and DV = VW = WA.
The area of quadrilateral ABCD is 180. Find the area of hexagon AWTCSP.
Answer:
Isn't this an AoPS Problem?
Step-by-step explanation:
Question 1
4 pts
Which set of line segments could create a right triangle? (4 points)
O 15,30,35
O 15,36,39
O 15, 20, 29
O 5,15,30
Answer:
(B)15,36,39
Step-by-step explanation:
To determine which of the line segments could create a Right Triangle, we check if it satisfies the Pythagoras Theorem, taking the longest part to be the Hypotenuse in all cases.
By Pythagoras Theorem: [tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
In 15,30,35
[tex]35^2\neq 15^2+30^2\\1225\neq 1125[/tex]
In 15,36,39
[tex]39^2=36^2+15^2\\1521=1521[/tex]
In 15, 20, 29
[tex]29^2\neq 15^2+20^2\\841\neq 625[/tex]
In 5,15,30
[tex]30^2\neq 15^2+5^2\\900\neq 250[/tex]
We can see that only 15,36,39 satisfies the required condition and thus it could be used to create a right triangle.