Answer:
B. 3850 m²Step-by-step explanation:
Use the equation of area of circle:
A = πr²Substitute π with 22/7 and r with 35 m as per question.
Find the area:A = 35²*(22/7) = 3850 m²Correct choice is B (with slight difference)
Answer:
B. 3850 m²
Step-by-step explanation:
The area of the base of the lighthouse can be modeled as a circle.
Area of a circle
[tex]\textsf{A}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
Given:
r = 35 mπ = 22/7Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{22}{7} \cdot 35^2[/tex]
[tex]\implies \sf A=\dfrac{22}{7} \cdot 1225[/tex]
[tex]\implies \sf A=\dfrac{26950}{7}[/tex]
[tex]\implies \sf A=3850\:\:m^2[/tex]
Therefore, the area of the circular base of the lighthouse is 3850 m²
Pls helpDetermine the area, in square units, of rectangle ABCD.
Enter the area of rectangle ABCD.
The area of the rectangle, as shown in the image given is calculated as: 48 square units.
What is the Area of a Rectangle?The area of a rectangle = length × width.
Find the length and width of the rectangle:
Length (BC) = 8 unitsWidth (AB) = 6 unitsArea of rectangle ABCD = 8 × 6 = 48 square units.
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Charlotte is buying milk. She can get 64 oz. for $3.00 or 80 oz. for $4.50. Which is the better deal, 64 oz. or 80 oz.?
Answer:
80 oz
Step-by-step explanation:
The following table shows the total number of quizzes taken in high school. how many quizzes are taken per week?
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second. the function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t. what is the max height the pumpkins will reach and what time will it reach that height?
The maximum height of the pumpkin is 3 feet
We have given that,
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second.
The function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t.
We have to determine the maximum height.
What is the maxima?
At the point of maxima f'(x)=0
first, find the maxima
Therefore differentiate the given function with respect to t we get,
[tex]h'(t)=-32t+96[/tex]
h'(t)=0
Then we get,
[tex]0=-32t+96\\-32t=-96\\t=\frac{-96}{-32} \\t=3[/tex]
Therefore the maximum height of the pumpkin is 3 feet.
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Q). Express each of the following recurring decimal as a rational numbers . 1) 0.5 2) 0.13 3) 0.341
The following recurring decimal as a rational number are 1/2, 13/100 and 341 / 1000
What is rational number?A rational number is a number that is expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator such as;
3/4. where,
Numerator = 3Denominator = 4Therefore,
0.5
= 5/10
= 1/2
0.13
= 13/100
0.341
= 341 / 1000
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Write the equation in slope - point form using the following information.
m = [tex]\frac{2}{5}[/tex] and point (-10, 1). Then, convert it to general form.
Answer:
[tex]\sf 2 x-5y +25=0[/tex]
Explanation:
Given points: (-10, 1)slope: 2/5Equation:
[tex]\dashrightarrow \sf y - y_1 =m(x - x_1)[/tex]
[tex]\dashrightarrow \sf y - 1 = \dfrac{2}{5} (x - (-10))[/tex]
[tex]\dashrightarrow \sf y = \dfrac{2}{5} x +4 + 1[/tex]
[tex]\dashrightarrow \sf y = \dfrac{2}{5} x +5[/tex]
[tex]\dashrightarrow \sf 5y = 2 x +25[/tex]
[tex]\dashrightarrow \sf 2 x-5y +25=0[/tex] General form: ax + by + c = 0The mean percent of childhood asthma prevalence in 43 cities is 2.16%. A random sample of 31 of these cities is selected. What is the
probability that the mean childhood asthma prevalence for the sample is greater than 2.6% ? Interpret this probability. Assume that o=1.36%.
The probability is:
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.
What is Probability ?
Probability is the measure of likelihood of an event.
For a Normal Distribution ,
the z-score formula is given by
[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]
Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .
It is the measure of the deviation of the data from its central tendency.
Each z-score has a probability value.
It is given in the question that
Mean of 2.16% = [tex]\rm \mu\\[/tex] = 2.16
Standard deviation of 1.36% means that [tex]\rm \sigma\\[/tex] = 1.36
For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]
s = 1.36/√31
s = 0.2442
Substituting the values
Z = (2.6 -2.16)/0.2442
Z =1.8
the p value from the graph of z and p , 0.9643
To determine value of probability more than X is 1 - 0.9643= 0.0357
the
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.
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What is a factor of X2–9 X +14
The factors of the expression x^2 - 9x + 14 are (x - 7) and (x - 2)
How to factor the expression?The expression is given as:
x^2 - 9x + 14
Expand
x^2 - 2x - 7x + 14
Factorize the expression
x(x - 2) - 7(x - 2)
Factor out x - 2 from the expression
(x - 7)(x - 2)'
Hence, the factorized expression of x^2 - 9x + 14 is (x - 7)(x - 2)'
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Fill out the chart please!
The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
What is the Mean, Median, and Interquartile Range of a Data?Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
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period of f(x)=cos(x)+2
Answer:
The period is 2π
Explanation:
The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.
A piece of card, 1200 cm² in area, will make a tube 13 cm long. How long is a similar
tube made from a similar piece of card with an area of 500 cm³?
The length of the similar tube will be 5041 cm.
What is the area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Given that:-
A piece of card, 1200 cm² in area, will make a tube 13 cm long. How long is a similar?Tube made from a similar piece of card with an area of 500square centimetres.The radius of the first tube will be calculated as:-
1200 = 2πr ( 13 )
r = 12 / 2π x 113
r = 14.7 cm
Now the length of the second tube will be:-
500 = 2π x 14.7 x L
L = 500 / 2π x 14.7
L = 5.41 cm.
Therefore the length of a similar tube will be 5041 cm.
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In a city park, three walking paths form triangle ABC. The length AB is 800 meters, the length BC is 900 meters, and the length AC is 850 meters. Which angle of this triangle has the greatest measure?
Answer:
Step-by-step explanation:
angle c
The angle of the triangle with the greatest measure is ∠A
What is a triangle?A triangle is a polygon with three sides and three angles.
Analysis:
For the triangle, ABC the angle facing the side with the greatest measure is the angle with the greatest measure. From the given information side BC is the side with the greatest measure and the angle facing it is ∠A.
In conclusion, the angle with the greatest measure is ∠A
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what is 15/56 in simplest form
Answer:
15/56
Step-by-step explanation:
15 and 56 have a GCF of 1.
The roots of the quadratic equation x²+bx+c = 0 are a and ß a) Evaluate i) a² + ß², ii) (a − ß)² b) Find the quadratic equation whose roots are (a² +ß²) and (a - 3)²
If ɑ and β are the roots of x² + bx + c = 0, then we can write
x² + bx + c = (x - ɑ) (x - β)
Expanding the right side gives
x² + bx + c = x² - (ɑ + β) x + ɑβ
so that ɑ + β = -b and ɑβ = c.
Recall that for all real numbers m and n,
(m + n)² = m² + 2mn + n²
a) It follows that
(i) ɑ² + β² = (ɑ + β)² - 2ɑβ = (-b)² + c = b² + c
(ii) (ɑ - β)² = ɑ² - 2ɑβ + β² = b² + c - 2c = b² - c
b) I assume you mean to find the quadratic whose roots are ɑ² + β² and (ɑ - β)² (and not (ɑ - 3)²). The simplest quadratic of this form is
(x - (ɑ² + β²)) (x - (ɑ - β)²)
Using the results from part (a), this becomes
(x - (b² + c)) (x - (b² - c))
and expanding, we get
x² - (b² + c + b² - c) x + (b² + c) (b² - c)
= x² - 2b² x + b⁴ - c²
14 + w is the same as which expression?
A
14w
B
14 - w
C
w + 14
D
w - 14
Answer:
C
Step-by-step explanation:
14 + w is the same as w + 14
Answer:
C. w + 14.
Step-by-step explanation:
The order does not matter when you are adding terms.
this is called the Commutative Property of Addition.
the first container of milk has twice as many gallons as the second if john uses 2 gallons from the second and 3 gallons from the first if the first one has 4.5 times more than the second how much did they each have originally
Answer:
SORRY I DONOT KNOW THE ANSWER
Step-by-step explanation:
i am sorry i do not know the amswer
4. What is the slope of a line that is parallel to the line shown?
Answer:
0.2÷3.0=15.0
Step-by-step explanation:
Which inequality does the graph
represent?
y
−2 O 2 x
2
−2
Answer:
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the diagonal of the rectangular solid with the given measures. (Part of the answer is provided for you.)
l = 18, w = 10, h = 2
Answer:
Step-by-step explanation:
Length=18
Width/Breadth =10
Height=2
The formula for a diagonal face of a cuboid is=√(l²+ b²)
Face diagonal=√(18²+10²)
= 20.59 to 2.d.p
The formula for the body diagonal of a cuboid is=√(l² + b² + h²)
Body diagonal=√(18² + 10² + 2²)
=20.69 to 2.d.p
find the distance between the two points in simplest radical form.
(3,-8) and (8,4)
Answer:
13
Step-by-step explanation:
The way to find the distance between two points on the coordinate plane is to use the distance formula, which is basically a way of applying the Pythagorean Theorem.
The distance formula is [tex]\sqrt{(x_{1}- x_{2} )^2 + (y_{1}- y_{2})^2}[/tex]. Let's say the coordinate (3, -8) is (x1, y1) and the coordinate (8, 4) is (x2, y2). We can plug these values into the formula:
[tex]\sqrt{(3- 8 )^2 + (-8 - 4)^2}\\\sqrt{(-5)^{2} + (-12)^{2}} \\\sqrt{25+144} \\\sqrt{169} \\13[/tex]
So, the distance between the two points is 13.
Determine the value of "a" for which g(h(a)) = 13
Answer:
a = 6
Step-by-step explanation:
g(x) = 5x - 2
h(x) = √(x + 3)
g(h(x)) = 5[tex]\sqrt{x+3}[/tex] - 2
g(h(a)) = 5[tex]\sqrt{a+3}[/tex] - 2
5[tex]\sqrt{a+3}[/tex] - 2 = 13
5[tex]\sqrt{a+3}[/tex] = 15
[tex]\sqrt{a+3}[/tex] = 3
( [tex]\sqrt{a+3}[/tex] )² = 3²
a + 3 = 9
a = 6
Brad took 5 kicks and made 4 goals: 4/5
Sydney will take 10 shots and she wants to make an equivalent fraction of the goals. How many goals must She make?
4/5 x ?/? = ?/10
Answer: 8/10
Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10
True or false: f(x) represents a function.
A. True
B. False
Answer:
A.) True
Step-by-step explanation:
A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.
5. What is the measurement of each angle?
Answer:
x=14
Step-by-step explanation:
The sum of a interior angle is 180°
(7x-11)+(2x-3)+(5x-2)°=180°
7x+2x+5x=180+11+3+2
14x/14=196/14
x= 14
Hope this answers your question!! :)
What is the area of the shape
The area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively, option (a) is correct.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.
We know the area of the kite = pq/2
Where p and q are the length of the diagonals
p = 10+10 = 20 ft
q = 7+11 = 18 ft
Area = (20×18)/2
Area = 180 square feet
Thus, the area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively option (a) is correct.
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The Algebra Club has decided to rent a convention center for their annual Algebra Gala. The cost for the rental will be split evenly among the attendees, which means that the price per person varies inversely with the number of people attending.
If 25 people attend, the cost will be $30 per person.
How many people would need to attend to get the cost under $20 per person?
A) 28
B) 38
C) 48
D) 58
The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The archway of the main entrance of a university is modeled by the quadratic equation
y = -x² + 6x ....1
The university is hanging a banner at the main entrance at an angle defined by the equation
4y = 21 − x ....2
Then the banner attached to the archway will be
From equations 1 and 2, we have
4(-x² + 6x) = 21 - x
-4x² + 24x = 21 - x
4x² - 25x + 21 = 0
4x² - 21x - 4x + 21 = 0
x(4x - 21) - 1(4x - 21) = 0
(4x - 21)(x - 1) = 0
x = 5.25, 1
Then the value of y will be
When x = 5.25, then we have
y = -(5.25)² + 6(5.25)
y = 3.938
When x = 1, then we have
y = -(1)² + 6(1)
y = 5
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
The graph is given below.
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4X+8<28
ayudenme por favor
Answer:
x < 5.
Step-by-step explanation:
Creo que esto es correcto. :')
Find the value of y in the solution to the system of equations shown.
3y = 18x + 6
y = 2x + 14
A. y = 3
B. y = 4
C. y = 20
D. y = 26
Divide by 3
y=6x+2--(1)y=2x+14--(2)Equating
6x+2=2x+144x=12x=3Now
y=6(3)+2y=18+2y=20C
Answer:
C. y = 20
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}3y = 18x + 6\\y = 2x + 14\end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies (3)y=(3)2x+(3)14[/tex]
[tex]\implies 3y=6x+42[/tex]
Subtract this from the first equation to eliminate 3y:
[tex]\begin{array}{r l}3y & = 18x+6\\-\quad3y&=6x+42\\\cline{1-2}0&=12x-36\end{array}[/tex]
Solve the resulting equation for x:
[tex]\implies 12x-36=0[/tex]
[tex]\implies 12x=36[/tex]
[tex]\implies x=3[/tex]
Substitute the found value of x into the original second equation and solve for y:
[tex]\implies y=2(3)+14[/tex]
[tex]\implies y=6+14[/tex]
[tex]\implies y=20[/tex]
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
(32)4
3-3
3243 2-1
(34)²
3-3 2-3 63 24 35
(40)2
(23)
1
112122
2
23.3
The simplified value is shown below:
What is exponents and powers?Exponent refers to the number of times a number is used in a multiplication. Power can be defined as a number being multiplied by itself a specific number of times.
First,
3²*4³*[tex]2^{-1}[/tex]/(3*4)²
=9*64/144*2
= 576/288
=2
Second,
(3*2)^4 *[tex]3^{-3}[/tex]/2³*3
=1296/8*81
=1296/648
=2
Third,
[tex]3^{-3} *2^{-3} *6^{3} /(4^{0} )^{2}[/tex]
= [tex]6^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]
= [tex]2^{3}* 3^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]
=1
Fourth,
[tex]2^{4}* 3^{5} /(2*3)^{5}\\=2^{4}* 3^{5} /2^{5}*3^{5}[/tex]
= 1/2
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