Answer:
Approx. 5.3 miles
Step-by-step explanation:
Select and place the symbol that will make the statement true.
6 ? 8
Answer:
6<8
Step-by-step explanation:
This is actually simple since the 6 is less than 8 the thing will face away from the 6 and towards the 8.
I NEED HELP ASAP The base of a triangle is 21 in. The height is 14 in. What is the area of the triangle?
A) 35 in2
B) 98 in2
C) 147 in2
D) 294 in2
Answer:
C 147in2
Step-by-step explanation:
Formula: [tex]\frac{bh}{2}[/tex]
b=base
h=height
21*14=294
294/2=147
A snowboard is on sale for $476. If the
original price was $560, what is the
percent discount?
Answer:
15%
Step-by-step explanation:
we call the original price 100% and to find the discount amount :
Multiply 100 by $476 then divide by $560
100 × $476 ÷ $560 = 85
$476 is 85% of the original price therefore the amount of discount as in percentage is 100 - 85 = 15%
You invest $15,000 to start a hot dog stand at the local sports complex. It costs you $.65 to produce each hot dog. How many hot dogs must you sell before your average cost per hot dog is $1.15?
The answer should be 30,000. I just do not understand how to get to it.
Thank you in advance!
Answer:
Below is the procedure to find the answer: 30,000 hot dogs.
Explanation:
The average cost is found dividing the total cost by the number of hot dogs:
[tex]Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs[/tex]
The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:
[tex]Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog[/tex]
Substitute the values:[tex]Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15[/tex]
Where x is the number of hot dogs.
Solve for x from the equation:[tex](15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000[/tex]
Which shows you how you can find that the answer is 30,000 hot dogs.
Final answer:
To find the number of hot dogs needed to achieve an average cost of $1.15, including a fixed investment of $15,000 and a variable cost of $.65 per hot dog, the calculation reveals that 30,000 hot dogs must be sold to reach this target.
Explanation:
The question asks how many hot dogs must be sold before the average cost per hot dog is $1.15, given an initial investment of $15,000 and a production cost of $.65 per hot dog. To find the break-even point in terms of units sold to reach the target average cost, we use the formula to calculate average cost: Average Cost = (Fixed Costs + Variable Costs) / Quantity. Here, the fixed cost is the initial investment of $15,000, and the variable cost is $.65 per hot dog.
To find the number of hot dogs needed to achieve an average cost of $1.15, we set up the equation: $1.15 = ($15,000 + $.65Q) / Q. Solving for Q gives us 30,000 hot dogs as the break-even point where the average cost per hot dog would be $1.15.
This calculation allows the business owner to understand how many units need to be sold to overcome the initial investment and start making a profit on each hot dog sold at or above $1.15.
enter the explicit rule for the geometric sequence.
3/2, 3/4, 3/8, 3/16, 3/32, . . .
an=
The width of a rectangular painting is 3in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting
Question:
A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting
a. write an expression for the combined area of the painting and frame.
b. use the expression to find the combined area when the height of the painting is 12 in.
c. use the expression to find the combined area when the height of the the painting is 15 in.
Answer:
a) (h + 5)(2h + 8) is the expression for the combined area of the painting and frame
b) The combined area when h = 12 is 544 square inches
c) The combined area when h = 15 is 760 square inches
Solution:
Given that,
A frame that is 2.5 inches wide goes around the painting
The frame will go around all 4 sides of the painting.
That means that the length of each side of the painting will increase by 2.5 inches
Therefore,
The height of painting and frame is:
h = h + 2.5 + 2.5
h = h + 5
(2.5 inches on the top and the bottom)
Also given that,
Width of a rectangular painting is 3 inches more than twice the height
w = 3 + 2h
Now the width of painting and frame is:
w = 3 + 2h + 2.5 + 2.5
(Again, 2.5 inches on the top and the bottom)
w = 2h + 8
Thus the combined area of the painting and frame is:
[tex]Combined\ area = (h+5)(2h+8)[/tex]
B) Substitute h = 12 inches
[tex]Combined\ area = (12+5)(2(12)+8)\\\\Combined\ area = 17 \times (24+8) = 17 \times 32\\\\Combined\ area = 544[/tex]
Thus the combined area when h = 12 is 544 square inches
C) Substitute h = 15 inches
[tex]Combined\ area = (15+5)(2(15)+8)\\\\Combined\ area = 20 \times (30+8) = 20 \times 38\\\\Combined\ area = 760[/tex]
Thus combined area when h = 15 is 760 square inches
Find the circumference of this figure. Show your calculations.
Answer:
Circumference of circle= 37.68 units
Circumference of sector= 6.28 units
Step-by-step explanation:
The given figure is a circle with given radius OB= 6 units.
The circumference of a circle is the total length of its boundary.
For the complete circle its circumference can be calculated by;
Circumference= [tex]2\pi r[/tex]
[tex]=2*3.14*6\\=37.68[/tex] units
For the circumference of the Sector with 60° in the figure, the circumference can be calculate by:
[tex]=\frac{60}{360}* 2*\pi*6\\\\=\frac{1}{6}*12*3.14\\\\ =2*3.14\\\\=6.28[/tex] units
So, the circumference of the full circle is 37.68 units and the circumference of the sector is 6.28 units.
in rectangle PQRS, shown below, the diagonal PR is 15 meters. if the sine of angle SPR is 7/10, what is the value of RS?
Answer:sin =perpendicular/hypotenuse
Step-by-step explanation:
Sin angle is given use tan theta or cos theta to find the RS
A blue rope is three times as long as the red rope. A green rope is five times as long as the blue rope. If the total length is 508.25 meters, what is the length of the blue rope?
Answer:
The length of the blue rope is 80.25 meters.
Step-by-step explanation:
B = Blue Rope
G = Green Rope
R = Red Rope
B=3R (Blue is 3 x as long as Red)
G=5B (Green is 5 x as long as Blue)
B+G+R = 508.25 (The three ropes together are 508.25 meters)
Since B=3R, I will rewrite the equation above
3R + G + R = 508.25
Now, I will write G in terms of R:
G=5B
B=3R, so 5B = 15R (multiply both sides by 5) which means that G=5B=15R, so G=15R.
Rewrite the equation again in terms of R:
3R + 15R + R = 508.25
19R = 508.25 (combine like terms)
R = 26.75 (divide both sides by 19 to solve for R)
Now, use the value 26.75 (R, which is the length of the red rope) to solve for B (the length of the blue rope):
B=3R
B=3(26.75)
B=80.25 meters
Which number line represents the solutions to x + 4 = 2?
A
+
-7
-6
+
-5
+
-4
+
-3
-2
+
-1
0
1
2
+
3
+
4
+
5
+
6
+
7
A
+
-7
+
-6
+
-5
+
-4
+
-3
+
-2
+
-1
+
0
+
1
+
3
2
+
5
4
+
6
+
+
7
+
I
+
+
+
+
-7
+
-6
+
-5
+ + + +
-4 -3 -2 -1
+
1
2
+
3
+
4
+
5
6
+
7
to to
+
+
-7
-6
-5
-4
-3
-2 -1
1
2
3
+ +
4
5
6
7
Answer:
-2
Step-by-step explanation:
The solution of the expression x + 4 = 2 is shown in image.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
Expression is,
⇒ x + 4 = 2
Now, We can simplify as;
⇒ x + 4 = 2
Subtract 4 both side,
⇒ x + 4 - 4 = 2 - 4
⇒ x = - 2
Thus, The solution of the expression is,
\⇒ x = - 2
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Of the 40 students in Ms. Carr's class, 87.5% live less than 10 miles from school. How many of the students in Ms. Carr's class live less than 10 miles from school.
Answer:
35
Step-by-step explanation:
Total number of students in class is 40
87.5% of the class = 87.5/100 *40 =35
The students in Ms. Carr's class that live less than 10 miles from school are 35 students.
To find out how many students in Ms. Carr's class live less than 10 miles from school, we can use the percentage provided in the question.
1. Identify the total number of students in the class:
Ms. Carr has a total of 40 students in her class.
2. Determine the percentage of students living less than 10 miles from school:
We know that 87.5% of these students live less than 10 miles from school.
3. Convert the percentage to a decimal for calculation:
To convert 87.5% to a decimal, we divide by 100:
[tex]\[ 87.5\% = \frac{87.5}{100} = 0.875 \][/tex]
4. Calculate the number of students:
Now, multiply the total number of students by the decimal:
Number of students = 0.875 × 40 = 35
5. Conclusion:
Therefore, 35 students in Ms. Carr's class live less than 10 miles from school.
the amount in a savings account increased from $200 to $216. what was the percent increase?
Answer:
7.41%
Step-by-step explanation:
16/216 =
16 ÷ 216 =
0.074074074074074 =
0.074074074074074 × 100/100 =
0.074074074074074 × 100% =
(0.074074074074074 × 100)% ≈
7.407407407407% ≈
7.41%;
A line passes through the origin and through points A(−2, b−14) and B(14−b, 72). What is the greatest possible value of b?
Answer:
The greatest possible value for b is 26.
Step-by-step explanation:
Given that the line passes through the Origin O(0, 0); A(-2, b - 14) &
B(14 - b, 72).
Let us assume the points are in the order: AOB.
Since the line passes through all these points the slope of the line segment AO = The slope of the line segment AB.
Slope of a line with two points: [tex]$ \frac{y_2 - y_1}{x_2 - x_1} $[/tex] where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the points given.
[tex]$ (x_1, y_1) = (0,0) $[/tex]
[tex]$ (x_2, y_2) = (-2, b - 14) $[/tex]
Therefore, the slope of the line segment AO = [tex]$ \frac{b - 14}{-2} $[/tex]
Similarly, for the slope of the line segment OB.
The two points are [tex]$ (x_1, y_1) = (0, 0) $[/tex] and [tex]$ (x_2, y_2) = (14 - b, 72) $[/tex].
The slope is: [tex]$ \frac{72}{14 - b } $[/tex]
Since, the slopes are equal we can equate:
[tex]$ \frac{b - 14}{-2} = \frac{72}{14 - b} $[/tex]
[tex]$ \implies \frac{b - 14}{-2} = \frac{72}{-(b - 14)} $[/tex]
[tex]$ \implies (b - 14)^2 = 72 \times 2 = 144 $[/tex]
[tex]$ \implies (b - 14)^2 = 12^2 $[/tex]
Taking square root on both sides we get:
[tex]$ \implies (b - 14) = \pm 12 $[/tex]
[tex]$ \implies b = 2 \hspace{2mm} or \hspace{2mm} 26 $[/tex]
Therefore, the maximum value of b = 26.
Hence, the answer.
What is the value of x?
Answer: x = 15
Step-by-step explanation: The first thing to note is that what we have here are two similar triangles. First we have triangle ABC and secondly we have triangle EDC. Line BD is a transversal that cuts line AE at point C. Hence we can deduce that angle ACB is equal in measurement to angle ECD (opposite angles). Next we also observe that the other two angles are right angles, that is, 90° in size. Therefore we can conclude that the other two angles (angle ABC and angle EDC) are also of the same measurement.
We can now establish the ratio of the similar sides.
Line AB = Line ED
Line AC = Line EC
AB/ED = AC/EC
24/40 = 2x/3x + 5
3/5 = 2x/3x + 5 {the left hand side has been reduced to it's simplest form}
Next we cross multiply and that gives us
3(3x + 5) = 5(2x)
9x + 15 = 10x
Subtract 9x from both sides of the equation
15 = 10x - 9x
15 = x
Boyle’s law states that the volume of gas varies inversely with applied pressure. Suppose the pressure on 60 cubic meters of gas is raised from 1 atomsphere to 3 atmospheres. What new volume does the gas occupy?
Answer: 20m³
Step-by-step explanation:
From the statement
V <> 1/p --------------------- 1
V = k/p --------------------- 2
K. = VP ---------------------- 3
V = 60 , p = 1
To find k which is a constant, we put those values in equation 3
K = 60 x 1
= 60.
Now from the second statement
V = k/p where p is 3
Therefore,
V = 60/3
= 20m³
identify the terms, coefficients, and constants in the expression.
1. 3 + c + e
2. 5m + 9
3. 3p2 + 7
Answer:
1. 3 is a constant term of the expression.
2. 9 is constant term of the expression.
3.7 is a constant term of the expression.
Step-by-step explanation:
1. 3+c+e
Here 3 is a constant term of the expression.
c and e are the variables.
The coefficient of c is 1.
The coefficient of e is 1.
It is a trinomial expression.
2.
5m +9
9 is constant term of the expression.
m is a variable of the expression.
The coefficient of m is 5.
It is a binomial expression.
3.
3p²+7
7 is a constant term of the expression.
p is the variable.
The coefficient of p² is 3.
It is a binomial expression.
You have 8 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
You will need 119 cups to sell all of the lemonade.
Step-by-step explanation:
Given,
Diameter of cups = 9 cm
Radius of cup = [tex]\frac{Diameter}{2}=\frac{9}{2}=4.5\ cm[/tex]
Height of cups = 12 cm
We will find volume of cup.
[tex]Volume = \frac{1}{3}\pi r^2h\\[/tex]
Putting all the values
[tex]Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3[/tex]
Therefore;
Each cup can hold 254.34 cubed centimeter of lemonade.
Number of gallons = 8
1 gallon = 3785 cm³
8 gallons = 3785*8 = 30280 cm³
Let,
x = Number of cups
Volume of lemonade in one cup * Number of cups = Volume of 8 gallons
254.34x=30280
Dividing both sides by 254.34
[tex]\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05[/tex]
Rounding off to nearest whole number
x = 119
You will need 119 cups to sell all of the lemonade.
Keywords: volume, division
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The diagonals of a rhombus are 14 and 48 cm Find the length of a side of the rhombus
what does 6x +2(5x -6)
Answer:
Step-by-step explanation:
Is you simplify, you get 16x-12
6x+2(5x-6)
6x+10x-12
16x-12
Answer:
Assuming you just want it simplified, the answer would be 16x - 12
Step-by-step explanation:
6x + 2(5x - 6)
6x + 10x - 12
16x - 12
The perimeter of a rectangle must be less than 172 feet. If the length is known to be 53 feet, find the range of possible widths for the rectangle. (Note: The formula for the perimeter of a rectangle is P=2l+2w , where l is the length and w is the width).
Express your answer in interval notation. Use decimal form for numerical values.
Answer:
1 - 32.5
Step-by-step explanation:
If the perimider is less then 172, that the limit is 171. 171 - (53)2 = 65. divide that by the two sides that are the width it equals 32.5
Perimeter is the sum of the length of the sides used to make the given figure. The range of the width of the rectangle is (0,33).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given that the perimeter of a rectangle must be less than 172 feet. Also, given that the length of the rectangle is 53 feet. Therefore, we can write inequality of the width of the rectangle as,
2(Length) + 2(Width) < Perimeter
2(53 feet) + 2(Width) < 172 feet
106 feet + 2(Width) < 172 feet
2(Width) < 172 feet - 106 feet
2(Width) < 66 feet
Width < 66feet / 2
Width < 33 feet
Hence, the range of the width of the rectangle is (0,33).
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Find the minimum value of the
parabola
y = x2 − 4x − 5 .
Answer:
-2x-5
Step-by-step explanation:
Given that (3,-8) is on the graph of f(x), find the
corresponding point for the function
f(x+4).
If I remember correctly, the x-coordinate 3 goes 4 left and the new ordered pair is (-1,-8). Don't take my word for it unless I'm actually right.
A park has a 333 meter (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis tall tether ball pole and a 6.8\,\text{m}6.8m6, point, 8, start text, m, end text tall flagpole. The lengths of their shadows are proportional to their heights.
Which of the following could be the lengths of the shadows?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Tether ball pole shadow: 1.35\,\text{m}1.35m1, point, 35, start text, m, end text
Flagpole shadow: 3.4\,\text{m}3.4m3, point, 4, start text, m, end text
(Choice B)
B
Tether ball pole shadow: 1.8\,\text{m}1.8m1, point, 8, start text, m, end text
Flagpole shadow: 4.08\,\text{m}4.08m4, point, 08, start text, m, end text
(Choice C)
C
Tether ball pole shadow: 3.75\,\text{m}3.75m3, point, 75, start text, m, end text
Flagpole shadow: 8.35\,\text{m}8.35m8, point, 35, start text, m, end text
(Choice D)
D
Tether ball pole shadow: 0.6\,\text{m}0.6m0, point, 6, start text, m, end text
Flagpole shadow: 1.36\,\text{m}1.36m1, point, 36, start text, m, end text
(Choice E, Checked)
E
Tether ball pole shadow: 2\,\text{m}2m2, start text, m, end text
Flagpole shadow: 4.8\,\text{m}4.8m
Answer:
b and d
Step-by-step explanation:
The following D Tether ball pole shadow: 0.6\,\text{m}0.6m0, point, 6, start text, m, end text Flagpole shadow: 1.36\,\text{m}1.36m1, point, 36, start text, m, end text and E Tether ball pole shadow: 2\,\text{m}2m2, start text, m, end text Flagpole shadow: 4.8\,\text{m}4.8m could be the lengths of the shadows. Correct Option is 4 and 5.
Let's assume "x" is the length of the tether ball pole shadow, and "y" is the length of the flagpole shadow.
According to the information given, the proportional relationship can be expressed as:
Tether ball pole height / Tether ball pole shadow length = Flagpole height / Flagpole shadow length
The height of the tether ball pole is 333 meters, and the height of the flagpole is 6.8 meters.
So, we have the following equation:
333 meters / x = 6.8 meters / y
Now, let's solve for "y" in each choice and check which choices satisfy the proportional relationship:
Choice A:
333 / 1.35 = 6.8 / 3.4
246.67 ≈ 2
Choice B:
333 / 1.8 = 6.8 / 4.08
185 ≈ 1.67
Choice C:
333 / 3.75 = 6.8 / 8.35
88.8 ≈ 0.81
Choice D:
333 / 0.6 = 6.8 / 1.36
555 ≈ 5
Choice E:
333 / 2 = 6.8 / 4.8
166.5 ≈ 1.42
The two choices that satisfy the proportional relationship are:
(Choice D) Tether ball pole shadow: 0.6 m, Flagpole shadow: 1.36 m
(Choice E) Tether ball pole shadow: 2 m, Flagpole shadow: 4.8 m
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Please help!! question is in the picture
Answer:
C
Step-by-step explanation:
Total number of rolls = 96
There are three even numbers: 2, 4 and 6.
Number 2 was rolled 13 times
Number 4 was rolled 17 times
Number 6 was rolled 20 times
Hence, even number was rolled [tex]13+17+20=50[/tex] times.
The experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.
Therefore,
[tex]P=\dfrac{50}{96}=\dfrac{25}{48}[/tex]
How to do 2(x+1.25)=3.5 by dividing both sides first.
Answer:
1/2
Step-by-step explanation:
2(x+1.25)=3.5
2x+2.5=3.5
2x=3.5-2.5
2x=1
x=1/2
Does anyone know this?
Use this formula to get the total angle measurement of the figure:
T=180(n-2)
Since there are 7 sides, the total measurement must be:
180(7-2)
180(5)
900 degrees
Set up an equation and solve for x:
123+121+127+128+139+125+x=900
763+x=900
x=137
So the missing angle is 137 degrees.
Hope this helped!
Need help ASAP please
If the function f(x) = (2x - 3)^3is transformed to g(x) = (-2x - 3)^3, which type of transformation occurred?
A. vertical shift
B. horizontal reflection
C. horizontal shift
D.vertical reflection
A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours
Answer:
d
Step-by-step explanation:
Answer:
24 hours
24 hours is the solution to 300=10(2)^t/15
Which equation has the solutions x = StartFraction 5 plus-or-minus 2 StartRoot 7 EndRoot Over 3 EndFraction?
3x2 – 5x + 7 = 0
3x2 – 5x – 1 = 0
3x2 – 10x + 6 = 0
3x2 – 10x – 1 = 0
Answer:
3x^2 - 10x - 1 = 0 $OPTION D ON EDGE$
Step-by-step explanation:
Answer:
3x2 – 10x + 6 = 0
Step-by-step explanation:
Givena general quadratic equation
ax²+bx+c = 0
The general formula for finding x is;
x = -b±√b²-4ac/2a
Where a,b and c are the coefficient of x², x and x° respectively
Given the solution in question to be;
x = 5±2√7/3
The quadratic equation that has thw above general solution will be;
3x²-10x+6 = 0
From the equation, a = 3, b= -10 and c = 6
Substituting this value in the general formula to get x we have;
x = -(-10)±√(-10)²-4(3)(6)/2(3)
x = 10±√100-72/6
x = 10±√28/6
x = 10±√7×4/6
x = 10±2√7/6
Dividing through by 2 gave;
x = 2(5±2√7)/6
x = 5±2√7/3 (which gives the solution in question)