The correct option is B.
The equation is B. 4c + 70 = 7c + 160, where c represents the number of candles sold by each girl.
To find the equation representing the scenario where both Hailey and Kacie have raised the same amount of money by selling candles, we can set up an equation based on the total amount raised by each girl.
Let's represent:
- Hailey's total amount raised as H
- Kacie's total amount raised as K
- The number of candles each girl sells as c
Given:
- Hailey's total amount raised, H = $160
- Kacie's total amount raised, K = $70
The equation representing the scenario where both Hailey and Kacie have raised the same amount of money by selling candles is:
4c (Hailey's selling price per candle) = 7c (Kacie's selling price per candle)
So, we have:
4c = 7c
To solve for c, we need to make the total amounts equal on both sides. We already have the total amounts raised by each girl:
Total amount raised by Hailey = $160
Total amount raised by Kacie = $70
Now, let's set up the equation:
4c (for Hailey) = 7c (for Kacie)
4c - 7c = 160 - 70
-3c = 90
Now, divide both sides by -3 to solve for c:
c = -90 / -3
c = 30
So, each girl needs to sell 30 candles to raise the same amount of money.
Therefore, the correct equation representing the scenario is:
B. 4c + 70 = 7c + 160
The complete question is here:
Hailey and Kacie are selling candles to raise money.
• Hailey is selling candles for $4 each and has already raised $160.
• Kacie is selling candles for $7 each and has already raised $70
Which equation can be used to find c, the number of candles each girl needs to sell so that the total amount raised is the same for both Hailey and Kacie?
A. 4c+7c=160+70
B. 4c+70=7c+160
C. 4c+160=7c+70
D. 4+160=7c+70c
In one day, Peter cleaned 17.5 rooms in 8.75 hours while working for a house cleaning business. Approximately how many rooms did he clean per hour?
2 rooms
5 rooms
8 rooms
9 rooms
The answer is 2 rooms because you do 17.5 divided by 8.75 and you get 2
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
Number of rooms = 17.5
Time taken to clean = 8.75 hours
We need to find the number of rooms he clean per hour.
So, the number of rooms per hour is given by
[tex]\dfrac{17.5}{8.75}\\\\=2[/tex]
Hence, there are 2 rooms that he clean per hour.
Therefore, First option is correct.
Given the diagram below what is the length of segment EF
Answer:5.5
Step-by-step explanation:
A. P. E. X.
The length of the line segment EF will be 55 units. Then the correct option is B.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
In the diagram, the line segment EF is the given as the half of the sum of the line segment BC and the line segment AD.
EF = (BC + AD) / 2
From the diagram, the length of the line segment AD is 7.6 units and the length of the line segment BC is 3.4 units.
Put these values in equation. Then the length of the line segment EF will be
EF = (3.4+ 7.6) / 2
EF = 11 / 2
EF = 5.5 units
Thus, the length of the line segment EF will be 55 units.
Then the correct option is B.
More about the trapezium link is given below.
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How do you solve this ? Check for extraneous solutions
ANSWER
[tex]x = 6[/tex]
EXPLANATION
The given equation is
[tex] \sqrt{3x + 7} = x - 1[/tex]
We square both sides of the equation to obtain,
[tex](\sqrt{3x + 7} ) ^{2} =( x - 1)^{2} [/tex]
This implies that,
[tex]3x + 7 = {x}^{2} - 2x + 1[/tex]
Rewrite in standard quadratic equation form.
[tex] {x}^{2} - 2x - 3x+ 1 - 7 = 0[/tex]
[tex]{x}^{2} -5x - 6= 0[/tex]
Factor
[tex](x - 6)(x + 1) = 0[/tex]
This implies that,
[tex]x = 6 \: x = - 1[/tex]
We check for extraneous solution by substituting each x-value into the original equation.
When x=-1,
[tex]\sqrt{3( - 1)+ 7} = - 1- 1[/tex]
[tex]\sqrt{4} = - 2[/tex]
2=-2....False
Hence x=-1 is an extraneous solution.
When x=6,
[tex]\sqrt{3( 6)+ 7} = 6- 1[/tex]
[tex]\sqrt{25} = 5[/tex]
5=5 is True.
Hence x=6 is the only solution.
What is the value of x?
Enter your answer in the box.
x =
The two angles shown ( 134 and X) make a straight line.
A straight line equals 180 degrees.
To find X subtract 134 from 180.
X = 180 - 134
x = 46
2. The triangles are similar. Show how they are similar and justify your answer.
They are similar because they are both the same type of triangles and are just rotated and shrunk.
They are similar because they have equal corresponding angles and proportional sides.
What is the value of d?
Answer options: 70,85, 55, 42.5
Answer:
85°
Step-by-step explanation:
Opposite angles in a cyclic quadrilateral add up to 180°.in the figure provided, angle d is opposite the angle whose value is 95° while angle c is opposite the angle marked 110°. there fore its value can be calculated as follows:
angle d= 180-95
angle d=85°
What are the two equations that need to be solved to find the solutions for the absolute value equation |3x+5|=x-1
the 2 equations that need to be solved are [3x+5] and x-1. If you need the answer to what x is you'd solve it by evening out the problems. so first add one to both so you'd have 3x+6=x then you'd take the 3x and subtract it from both sides making it 6=-2x. Then divide 6 by negative 2 making it -3=x.
Answer:i think the answer was 3=x but i'm not sure i really do think it is
Step-by-step explanation:
What is the total length of all the seeds that the students measured?
what's the volume of a cylinder if the height is 5mm and diameter is 24 mm
Answer:
V = 2,260.8
Step-by-step explanation:
To find the volume of a cylinder, you must use the equation: V = pi*r^2*h.
V = pi*12^2*5
V = pi*144*5
V = pi*720
V = 2,260.8
The following graph represents the possible areas of a rectangle with a perimeter of 40 feet. Select all the statements that accurately describe the area of the rectangle based on the graph shown. Question 5 options: The maximum area is 10 square feet. The minimum area is 100 square feet. The maximum area is 100 square feet. The area will be less than or equal to 100 square feet.
Answer:
Statements of Max Area as 100 sqft and area of less or equal to 100 sqft are true
Step-by-step explanation:
P=40
P=2L+2w
A=L•w
If L=10, w=10, A=100
If L=1, w=19, A=19
If L=0.5, w=19.5, A=9.75
If L=10.5, w=9.5, A=99.75
×Max area is NOT 10
✓Max Area is 100
×Minimum area is NOT 100
✓Area ≤100
What is the initial value of the equation shown? y = −4x − 3 −4 −3 3 4
The initial value is when Y equals when x is 0.
Replace x with 0 in the equation and solve for y.
Y = -4x -3
y = -4(0) - 3
y = 0-3
y = -3
Answer:
-3
Step-by-step explanation:
The initial value of an equation is when x=0
y = −4x − 3
Let x =0
y = -4(0) -3
y = 0-3
y=-3
The initial value is -3
Find the radius of a circle with a circumference of 21.99 feet
Answer:
Radius ≈ 3.5 ftStep-by-step explanation:
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
r - radius
We have C = 21.99 ft. Substitute and solve for r:
[tex]21.99=2\pi r[/tex] divide both sides by 2π
[tex]r=\dfrac{21.99}{2\pi}[/tex]
Use [tex]\pi\approx3.14[/tex]
[tex]r\approx\dfrac{21.99}{2(3.14)}=\dfrac{21.99}{6.28}\approx3.5[/tex]
The radius of a circle with a circumference of 21.99 feet is 3.50 ft
Circumference of a circle:circumference = 2πrwhere
r = radius
Therefore,
circumference = 21.99 ft
circumference = 2πr
circumference = 2 × 3.14 × r
21.99 = 6.28r
divide both sides by 6.28
r = 21.99 / 6.28
r = 3.50159235669
r = 3.50 ft
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when a ladder is rested against a tree, the foot of the ladder is 1 m from the base of the tree and forms an angle of 64° with the group. How far up the tree does the ladder reach.
Answer:
2.05 meters
Step-by-step explanation:
Superimpose a triangle when drawing out the situation. The distance the ladder reaches up the tree is the side of the triangle opposite of the angle. The distance the ladder is from the tree is side adjacent to the triangle. We can use tangent to solve this.
Tan X = (opposite side)/(adjacent side)
Tan 64 = a/1
Tan 64 = a (anything over 1 is just itself)
2.050303842 = a (use tan on your calculator)
The table shows the height of a ball that was dropped from a 380-foot tower. What was the ball's rate of fall during the first 3 seconds?
0s-380ft
1-s-350ft
2s-290ft
3s-200ft
Answer:
60ft/s
Step-by-step explanation:
To find the rate
rate = f(3) - f(0)
-------------
3-0
rate = 200-380
---------------
3-0
rate = -180/3 = -60 ft/s
The negative tells us it is falling
The fall falls 60ft/s
Answer:
The correct answer is 60 feet / second.
Step-by-step explanation:
We are given the height of a ball which is falling from a height of 280 feet for 3 seconds.
We are to find the ball's rate of fall during the first 3 seconds.
For that, we will take the difference between the heights and divide it by the time.
Ball's rate = [tex] \frac { 3 8 0 - 2 0 0 } { 3 } [/tex] = 60 feet / second
What is the value of x so that the line segment with endpoints W(x, −2) and X(5, −4) is parallel to the line segment with endpoints Y(2, 2) and Z(5, 6)?
x equals six start fraction one over two end fraction
x = 6 x
equals three start fraction one over two end fraction
x = 7
Answer:
x equals six start fraction one over two end fraction
Step-by-step explanation:
Segments which are parallel have the same slope. Find the slope of of YZ. Then using that value, find the slope WX and solve for the value of x.
Slope of YZ is:
[tex]m = \frac{y_2-y_1}{x_2-x_1}=\frac{2-6}{2-5}=\frac{-4}{-3}=\frac{4}{3}[/tex]
Since they are parallel, then WX has a slope of 4/3 too.
Slope of WX is:
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\\frac{4}{3}=\frac{-2--4}{x-5}\\\\\frac{4}{3}=\frac{2}{x-5}\\\\\frac{4}{3} (x-5) = 2\\\\4x -20=6\\\\4x = 26\\\\x = 6\frac{1}{2}[/tex]
What is 9.05 rounded off to the nearest whole number
Answer:
9
Step-by-step explanation:
9.05= 9.0=9
0 isn't greater than five, so you leave it as 9
Write the equation of a circle
Answer:
[tex]\large\boxed{(x-9)^2+(y+5)^2=4}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (9, -5) and the radius r = 2. Substitute:
[tex](x-9)^2+(y-(-5))^2=2^2\\\\(x-9)^2+(y+5)^2=4[/tex]
A football team stood in a circle before a game to plan their strategy. The circle they formed had a radius of 1 yard. What is the circle's diameter?
yards
Answer:
The circle diameter is 2 yards because half of 2 is 1 which makes the radius 1 yard.
The diameter is 2
Hope this helps
if sin theta = 2/3 and tan theta <0 what is the value of cos theta?
a) (sqrt5)/2
b) -sqrt5
c) (sqrt5)/3
d) -(sqrt5)/3
Answer:
d) [tex]\cos(\theta)=-\frac{\sqrt{5}}{3}[/tex]
Step-by-step explanation:
If [tex]\sin(\theta)=\frac{2}{3}[/tex] and [tex]\tan(\theta)\:<\:0[/tex], then
[tex]\theta[/tex] is in quadrant 2.
Recall that;
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
We substitute the given sine ratio to obtain;
[tex](\frac{2}{3})^2+\cos^2(\theta)=1[/tex]
[tex]\frac{4}{9}+\cos^2(\theta)=1[/tex]
[tex]\cos^2(\theta)=1-\frac{4}{9}[/tex]
[tex]\cos^2(\theta)=\frac{5}{9}[/tex]
[tex]\cos(\theta)=\pm \sqrt{\frac{5}{9}}[/tex]
[tex]\cos(\theta)=\pm \frac{\sqrt{5}}{3}[/tex]
We are in the second quadrant, therefore
[tex]\cos(\theta)=-\frac{\sqrt{5}}{3}[/tex]
whats the answer for this?
Answer:
15+c-d
Step-by-step explanation:
4(3+1/4c-1/2d) or in decimals 4(3+0.25c-0.5d)
distribute the 4 (in other words use the distributive property)
4 · 3 = 12
4 · 0.25 = 1
4 · 0.5 = 2
12 + 1 + 2 = 15
15 + c-d is your answer
hope I helped <3
Graph the line y=-2x-3
To graph the equation y = -2x - 3, start by plotting the y-intercept at (0, -3) and then use the slope to find more points. Connect these points to form the line.
Explanation:The given equation is y = -2x - 3. To graph this equation, we can start by plotting the y-intercept, which is -3. This means that the line intersects the y-axis at the point (0, -3). From there, we can use the slope, which is -2, to find more points on the line. For example, when x = 1, y = -2(1) - 3 = -5. So, we can plot another point at (1, -5). By connecting these points, we can draw a straight line that represents the equation y = -2x - 3.
HELP PLEASE I NEED THIS DONE
Answer:
138.3ft^3
Step-by-step explanation:
Volume for cylinders : V = pi*r^2*h
Volume for cones : V = pi*r^2*(h/3)
Since we know the radius (r) is 2 and the height is 10 and 3 for the cylinder and cone respectively, all we do is plug in.
Volume for cylinder is about 125.7ft^3
Volume for cone is about 12.6ft^3
Then just add them together for a total of 138.3ft^3
The parabola y=x^2 is scaled vertically by a factor of 1/10
What is the equation of the new parabola?
Answer:
Step-by-step explanation:
We want to scale by a factor of 1/10 so |a| = 1/10. This means that the graph is compressed vertically.
We do not reflect across the x axis so a = 1/10.
The new parabola is: y = 1/10 x^2
The new equation of the parabola will be [tex]y=\frac{x^{2} }{10}[/tex].
The given parabola is:
[tex]y=x^{2}[/tex]
What is a parabola?A parabola is a plane curve that is mirror-symmetrical and is approximately U-shaped.
When the parabola y=x² is scaled vertically by a factor of 1/10.
The new equation of parabola will be = [tex]y=\frac{x^{2} }{10}[/tex].
This means the graph of a new parabola will look similar to the previous parabola(symmetric about the origin) but outputs(function values) will be different.
Hence, the new equation of the parabola will be [tex]y=\frac{x^{2} }{10}[/tex].
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What is the equation of the following graph in vertex form?
The right answer is y=(x+3)^2 -1
A train travels 20 miles in 15 minutes. How far will it travel in a hour and a half?
Step-by-step explanation:
An hour and a half is 90 minutes.
Knowing this, set up a proportion.
20 over 15 is equal to x over 90.
x is equal to: 120 miles
What is the complete factorization of the polynomial below? x^3+2x^2+ x + 2
The complete factorization of the given polynomial is (x² + 1)(x + 2).
Explanation:To factorize the polynomial [tex]x^3 + 2x^2 + x + 2[/tex], we first look for any common factors. In this case, we don't have any common factors, so we move on to factoring by grouping.
Unfortunately, this cubic polynomial does not factorize nicely into simpler terms using rational numbers. It would involve using heavy algebra and complex numbers to factor. Usually, for a cubic polynomial of this nature, a numerical method will be employed to find its roots.
We can group the terms as [tex]x^3 + 2x^2 + x + 2[/tex]). Taking out the common factors from each group, we get:
[tex]x^2[/tex](x + 2) + 1(x + 2).
Now, notice that we have a common binomial term (x + 2), so we can factor that out as well:
([tex]x^2[/tex] + 1)(x + 2).
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Dina has a number cube that she uses for a game. The number cube has the shape of a triangular pyramid, with 4 faces numbered 1 through 4.
Dina rolls the number cube 100 times and records the results. She calculates the relative frequency of each outcome
Outcome: 1 2 3 4
Relative Frequency : 0.23 0.24 0.26 0.27
Which statements about Dina's experiment are true?
Select EACH correct answer.
A) The relative frequencies in the table are reasonably close.
B) The theoretical probability of rolling an even number is 0.51.
C) The relative frequency of rolling an even number is 0.51.
D) The number cube is not likely to be fair.
Answer:
A) The relative frequencies in the table are reasonably close; C) The relative frequency of rolling an even number is 0.51.
Step-by-step explanation:
The relative frequencies given are at most 0.02 apart. This means they are reasonably close.
The theoretical probability for each outcome would be 1/4, or 0.25; this means the theoretical probability of rolling an even number would be 0.50, not 0.51.
However, the relative frequency of rolling an even number would be 0.24+0.27 = 0.51.
Since the relative frequencies are reasonably close, the number cube is likely to be fair.
Answer:
Option A and C are true.
Step-by-step explanation:
Given : Dina has a number cube that she uses for a game. The number cube has the shape of a triangular pyramid, with 4 faces numbered 1 through 4.
Dina rolls the number cube 100 times and records the results. She calculates the relative frequency of each outcome
Outcome : 1 2 3 4
Relative Frequency : 0.23 0.24 0.26 0.27
To find : Which statements about Dina's experiment are true?
Solution :
Option A - The relative frequencies in the table are reasonably close.
This statement is true, as we see that the relative frequency are all between 0.23 to 0.27 that are reasonably close.
Option B - The theoretical probability of rolling an even number is 0.51.
This statement is not true, as the theoretical probability of rolling even numbers is
2 even numbers from 4, so probability is
[tex]P=\frac{2}{4}=\frac{1}{2}=0.5[/tex]
Option C - The relative probability of rolling an even number is 0.51.
This statement is true, as the relative frequency of an even number is 0.24+0.27=0.51
Option D - The number cube is not likely to be fair.
The statement is not true, as the relative frequency are reasonably close which implies that the number cube is likely to be fair and sum of the relative frequency is 1.
Therefore, Option A and C are correct.
Find the area of figure B
Answer: tithe area of figure b is 315.
Step-by-step explanation:
Simplify each expression
Answer:
[tex]\frac{2y+3}{7y-1}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{10y^2+15y}{35y^2-5y}[/tex]
Factor both the numerator and the denominator.
[tex]=\frac{5y(2y+3)}{5y(7y-1)}[/tex]
Cancel out the common factors.
[tex]=\frac{2y+3}{7y-1}[/tex]
Answer:
The correct answer is,
(10y² + 15y)/(35y² - 5y) = (2y + 3 )/( 7y - 1)
Step-by-step explanation:
It is given an expression,
(10y² + 15y)/(35y² - 5y)
To simplify the given expression
Taking 5y as common from both numerator and denominator,
(10y² + 15y )/( 35y² - 5y) = 5y( 2y + 3)/5y( 7y - 1)
= (2y + 3 )/( 7y - 1)
Therefore the simplified form of given expression is given by,
(10y² + 15y)/(35y² - 5y) = (2y + 3 )/( 7y - 1)
PLEASE HELP!! Drag the tiles to the boxes to form correct pairs.
A school district conducted a survey to find out which games students in different schools enjoy watching the most. The table contains the survey results. (Some values have been rounded off to the nearest whole number.) Match the descriptions to their correct values.
the relative frequency of elementary
school students who prefer watching
football to the total number of
elementary school students, as a
percentage rounded to the nearest
whole number
10
the relative frequency of middle
school students who prefer watching
basketball to the total number of
students, as a percentage rounded
to the nearest whole number
19
the difference of the number of
students who like watching baseball
and the number of students who like
watching soccer
25
the difference of the number of high
school students who like watching
soccer and the number of high
school students who like watching
tennis
43
Answer:
Step-by-step explanation:
the relative frequency of elementary
school students who prefer watching
football to the total number of
elementary school students, as a
percentage rounded to the nearest
whole number
.[tex]\frac{(26)}{137} \\=0.1897\\=19%[/tex]
the relative frequency of middle
school students who prefer watching
basketball to the total number of
students, as a percentage rounded
to the nearest whole number
=[tex]\frac{50}{502} =0.0996\\\\=9.96%\\=10%[/tex]
the difference of the number of
students who like watching baseball
and the number of students who like
watching soccer
=102-59=43
the difference of the number of high
school students who like watching
soccer and the number of high
school students who like watching
tennis ..
=36-11=25