Answer:
b 18 boys
Step-by-step explanation:
In order to solve this problem we must create a system of equations.
Creating a system of equations
Let x = number of boys and y = # of girls
We are given that in total there are 27 children which means # of boys + # of girls = 27 so we can say x + y = 27
We are also given that there are twice as many boys as girls so we can also say x = 2y ( as # of boys = twice the number of girls )
Solving the system
Now to find the # of boys and girls we must solve the system. To do so we are going to use the substitution method.
What is the substitution method?
The substitution method is where one of your variables ( x in this case ) is defined by an expression in which you can plug in or " substitute " it into the other equation ( we can substitute x = 2y into the other equation and solve for y )
Substitute equation 2 into equation 1
Equation 1 : x + y = 27
==> plug in x = 2y
y + 2y = 27
==> combine like terms
3y = 27
==> divide both sides by 3
y = 9
So there are 9 girls in the classroom
Solving for # of boys
To solve for the number of girls we plug in the # of girls (y=9) into one of the equations and solve for x
equation : x + y = 27
==> plug in y = 9
x + 9 = 27
==> subtract 9 from both sides
x = 18
There are 18 boys in the classroom
Checking our work:
Now that we have found the possible answers we can check our work. To do so we are going to want to plug in the values of x and y into both equations and if both are true our answer is correct
Equation 1 x + y = 27
==> plug in x = 18 and y = 9
18 + 9 = 27
==> simplify
27 = 27 ✓
equation 2 x = 2y
==> plug in x = 18 and y = 9
18 = 2(9)
==> multiply 2 and 9
18 = 18 ✓
Both are correct therefore we can conclude that there are 18 boys and 9 girls.
AYO HELP ME OUT ASAP :(
Answer:
122.7 cm³
Step-by-step explanation:
Volume of composite figure:Square pyramid:
a = 4 cm ; h = 4 cm
[tex]\boxed{\text{Volume of square pyramid = $\dfrac{1}{3}$*base area * height}}[/tex]
[tex]\sf = \dfrac{1}{3}*a^{2}*h\\\\ =\dfrac{1}{3}*4*4*4\\\\ = 21.3 \ cm^3[/tex]
Rectangular prism:
l = 6 cm ; w = 6 cm ; h = 4 cm
[tex]\boxed{\text{Volume of rectangular prism = l*w*h}}[/tex]
= 6 * 6 * 4
= 144 cm³
Volume of composite figure = volume of rectangular prism - volume of pyramid= 144 - 21.3
= 122.7 cm³
Pls help!
Simplify sin θ/√1-sin^2 θ
A) tan Θ
B) tan^2 Θ
C) 1
D) -1
Answer:
hope this will help you ( ◜‿◝ )♡
Step-by-step explanation:
[tex] \frac{ \sin(theta) }{ \sqrt{1 - \sin {}^{2} ( theta) } } \\ \frac{ \sin(theta) }{ \cos(theta) } \\ \tan(theta) [/tex]
Evaluate the expression for the given value.
Answer:
a² = 16
Step-by-step explanation:
substitute a = 4 into the expression
a² = 4² = 4 × 4 = 16
Answer:
16
Step-by-step explanation:
PLEASE HELP!!
Identify an obtuse angle and give its measure.
Answer:
Angle HEF
105*
Step-by-step explanation:
Rob is travelling at a constant speed in a car. He travels 105km in 1 hour and 30 minutes. The speed limit is 80km/h. Is Rob travelling within the speed limit? Show how you decide.
Answer:
Yes.
Step-by-step explanation:
Let's first convert his speed to km/h.
[tex]\frac{105km}{1.5h} = 70\frac{km}{h}[/tex] > [tex]80\frac{km}{h}[/tex]. Therefore, Rob is traveling within the speed limit.
Kelly used the vertical line test to determine whether or not the curve that she
had been given is a function. After conducting the vertical line test, Kelly
determined that the curve is a function. Which of the following choices
represents the result of Kelly's vertical line test?
A. All vertical lines intersected the curve at exactly 2 points.
B. One vertical line intersected the curve at exactly 2 points.
C. One vertical line intersected the curve at exactly 1 point, while
another vertical line intersected the curve at exactly 2 points.
OD. All vertical lines intersected the curve at exactly 1 point.
All vertical lines intersected the curve at exactly 1 point.
===========================================================
Explanation:
If there is a case when a single vertical line crosses 2 or more points on the curve, then it will not be a function. In this situation, it is said that the curve fails the vertical line test.
Passing the vertical line test means that every vertical line passes through exactly one point on the curve. Each x input leads to exactly one output. If such a situation happens, then we have a function.
Since Kelly concluded that the curve is a function, this means the curve passed the vertical line test, and it points us to choice D as the answer.
A company uses paper cups shaped like cones for its water cooler. Each cup has a height of 14cm, and the base has a radius of 3cm . How much water is needed to fill 125 cups?
Please help me find the area of compound shapes?!?!
Answer:
[tex]27cm^{2}[/tex]
Step-by-step explanation:
Area of compound shapes = Area of shape A + Area of shape B
Area of this shape = (L x B) + (L x B)
= (5 x 3) + (6 x 2)
= 15 + 12
= [tex]27cm^{2}[/tex]
Answer:
A = 27 cm²
Step-by-step explanation:
the figure consists of 2 rectangles
the one on the right with dimensions 2 cm by 6 cm and
the one on the left with dimensions 5 cm by 3 cm
the total area (A) is then calculated as
A = (2 × 6) + (5 × 3) = 12 + 15 = 27 cm²
A portion of the Quadratic Formula proof is shown. Fill in the missing statement
Find all sets of four consecutive even integers whose sum is between 155 and 165
Answer:
36 38 40 42
and
38 40 42 44.
Step-by-step explanation:
160 / 4 = 40 so the numbers are close to 40.
38 + 40 + 42 + 44 = 164
36 + 38 + 40 + 42 = 156.
( multiplying matrixes please help) Find the product of the following two
matrices.
[tex]\left[\begin{array}{cc}1&3\\0&-2& \end{array}\right] \begin{bmatrix} 3& 1&-1& 0 \\ -1& 0&3&-1\end{bmatrix}\\\\\\=\begin{bmatrix} 3-3& 1+0&-1+9&0-3\\ 0+2&0-0&0-6&0+2\end{bmatrix}\\\\\\=\begin{bmatrix} 0&1&8&-3\\2&0&-6&2\end{bmatrix}[/tex]
I will gove you 100 points
To find side given angle and two sides:
a² = b² + c² − 2bc cos(A)
Here given:
a = AC cmb = 10 cmc = 7 cmangle A = 120°Solve for AC (a):
a² = (10)² + (7)² − 2(10)(7) cos(120)a² = 219a = √219a = 14.7986 cma = 14.8 cmAnswer:
AC = 14.8 cm (1 dp)
Step-by-step explanation:
Cosine rule
[tex]\sf b^2=a^2+c^2-2ac \cos B[/tex]
(where a, b and c are the sides, and B is the angle opposite side b)
Given:
a = 10 cmc = 7 cmB = 120°b = ACSubstituting the given values into the formula and solving for b:
[tex]\implies \sf AC^2=10^2+7^2-2(10)(7) \cos 120^{\circ}[/tex]
[tex]\implies \sf AC^2=100+49+70[/tex]
[tex]\implies \sf AC^2=219[/tex]
[tex]\implies \sf AC=\pm\sqrt{219}[/tex]
As length is positive,
[tex]\implies \sf AC=\sqrt{219}\:cm[/tex]
[tex]\implies \sf AC=14.8\:cm\:(1\:dp)[/tex]
A rectangular courtyard has a length of 16 m and a width of 10 m. Find the perimeter of the rectangle defined by this courtyard. In other words, what is the length of the fence required to encompass the courtyard?
Answer:
26^2 meters
Step-by-step explanation:
l + b
16 + 10
= 26m×2
The art club raised \$248$248dollar sign, 248 through fundraisers. Then they spent \$206$206dollar sign, 206 to set up an art show. They raised another \$316$316dollar sign, 316 at the art show. How much money did the art club have after the show
Considering the amount they raised and the amount they spent, it is found that the art club had $358 after the show.
How to find the net amount of the art club?The net amount is found by the subtraction of the amount raised by the amount spent.
In this problem:
The amount raised, in dollars, is of 248 + 316 = 564.The amount spent is of $206.Then:
A = 564 - 206 = $358.
The art club had $358 after the show.
More can be learned about net amount had https://brainly.com/question/12371230
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Describe and correct the error in finding the distance between the points (−3,−2) and (7,4).
I tried 2\sqrt{34} adn 11.6619 but they didn't work as correct answers
Please help!
Step-by-step explanation:
Hope you'll understand
Answer:
the answer is the numbers in the expressions inside the bracket should be added not subtracted
Step-by-step explanation:
hope it helps
Evaluate the function 2/3t , when t = 30.
Question 2 options:
10
15
20
25
Answer:
20
Step-by-step explanation:
2/3(30)
=20
Find the measures of the missing angles. The triangle is not drawn to scale.
108°
A=
B= 31
Answer:
B=41
Step-by-step explanation:
Triangle = 180 degrees.
108+31=139
180-139=41\
B = 41 degrees
Find the value of X.
Answer:
x=4
Step-by-step explanation:
We know that in a parallelogram opposite sides are equal
Hence on equating we get,
[tex]6x - 20 = 4[/tex]
[tex]6x = 4 + 20[/tex]
[tex]6x = 24[/tex]
[tex]x = 4[/tex]
Please help! Will give Brainliest!!!!!!!!!!!!
Answer:
for the first answer the second option is correct and 8 will go in the box and for the second question the second option is correct and 40 will go in the box.
Examine the tree diagram. What is the theoretical probability of spinning AT LEAST one blue out of two spins?
Answer:
5/9.
Step-by-step explanation:
Theoretical probability = number of outcomes with1 or 2 blues
-------------------------------------------------------
number of all possible outcomes
= 5/9
Which of the following is the shape of a cross-section of the figure shown
below?
A. Rectangle
B. Square
C. Prism
D. Pentagon
Answer:rectangle
Step-by-step explanation:
please solve quickly
Answer:
75.36
hope this helps :)
Image for last question look at my last
Answer:
Part A: 12.5 cm
Part B: 0.8 km
Step-by-step explanation:
Map scale problems can be solved with proportions.
Part A
5 cm / 2 km = x cm / 5 km
5/2 = x/5
2x = 25
x = 12.5
Answer: 12.5 cm
Part B
5 cm / 2 km = 2 cm / x km
5/2 = 2/x
5x = 4
x = 4/5
x = 0.8
Answer: 0.8 km
For a certain population of penguins, the distribution of weight is approximately normal with mean 15.1 kilograms (kg) and standard deviation 2.2 kg. Approximately what percent of the penguins from the population have a weight between 13.0 kg and 16.5 kg
Using the normal distribution, it is found that 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 15.1, \sigma = 2.2[/tex].
The proportion of penguins from the population have a weight between 13.0 kg and 16.5 kg is the p-value of Z when X = 16.5 subtracted by the p-value of Z when X = 13.
X = 16.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16.5 - 15.1}{2.2}[/tex]
Z = 0.64
Z = 0.64 has a p-value of 0.7389.
X = 13:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13 - 15.1}{2.2}[/tex]
Z = -0.95
Z = -0.95 has a p-value of 0.1711.
0.7389 - 0.1711 = 0.5678.
0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
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PLEASE HELP ILL MARK BRAINEST!!!!
Answer:
-3 -2 -1 = -6 0 times 1 times 2 times 3 = 0 -12 -7 -4 = -23
Step-by-step explanation:
In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio. What is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election?
0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio
We need to find the probability of that the democratic candidate wins both Michigan and Ohio in the next presidential election
As 6 wons from Michigan out of 10, so it 6/10
4 wons from Ohio out of 10, so it 4/10
The probability is 6/10/×4/10
24/100=0.24
In the next year also democratic candidate wons then the probabiltiy will be same 0.24
Hence 0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election
To learn more on probability click:
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helphelphelphrlpherlphelphelp
Answer: 1725
Step-by-step explanation: A= A+B/2 h= 50+65/2x30=1725
The volume of a cone is 108 pi cubic inches. Its height is 4 inches. What is the radius of the cone? Round the answer to the nearest tenth if necessary. 5. 2 in. 9 in. 34. 7 in. 81 in.
Answer:
im gonna say it would be around 9 inches, because the actual answer, a decimal, isnt an option so the closest would be around 9 in.
Help me , it is 50 point
Answer:
a) 52.0 cm
b) 62.8 cm
c) 114.8 cm
Conversion:
120° = 2π/3 radians
(a) Find Length of chord PR;
⇒ 2(radius)sin(θ/2)
⇒ 2(30)sin((2π/3)/2)
⇒ 2(30)sin((2(3.142)/3)/2)
⇒ 30√3
⇒ 52.0 cm
(b) Find Length of arc PQR;
⇒ radius(θ)
⇒ 30(2π/3)
⇒ 30(2(3.142)/3)
⇒ 62.8 cm
(c) The perimeter of shaded region;
⇒ Length of chord + Length of arc
⇒ 62.84 + 51.965
⇒ 114.8 cm
Answer:
(a) 52.0 cm
(b) 62.8 cm
(c) 115 cm
Step-by-step explanation:
Part (a)
[tex]\textsf{Chord length}=2r \sin \left(\dfrac{\theta}{2}\right)[/tex]
where:
r = radius[tex]\theta[/tex] = central angle (measured in degrees)Given:
r = 30 cm[tex]\theta[/tex] = 120°chord = PRSubstitute the given values into the formula:
[tex]\begin{aligned}\implies PR & =2(30)\sin \left(\dfrac{120^{\circ}}{2}\right)\\\\& = 30\sqrt{3}\\\\ & = 52.0\:\sf cm\:(3\:sf)\end{aligned}[/tex]
Part (b)
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad[/tex]
where:
r = radius[tex]\theta[/tex] = central angle (measured in degrees)Given:
r = 30 cm[tex]\theta[/tex] = 120°arc = PQR[tex]\pi[/tex] = 3.142Substitute the given values into the formula:
[tex]\begin{aligned}\implies PQR & =2 (3.142)(30)\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \quad\\\\ & = \dfrac{1571}{25}\\\\ & = 62.8 \sf \:\:cm \:(3 \:sf)\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}\textsf{Perimeter of shaded portion} & = \textsf{chord length} + \textsf{arc length}\\\\ & = 30\sqrt{3}+\dfrac{1571}{25}\\\\ & = 114.80152...\\\\ & = 115\:\: \sf cm\:(3\:sf)\end{aligned}[/tex]
There are 15 boys in school base ball team , they represent 5% of grace Christian school , In all how many are there in school
Answer:
300
Step-by-step explanation:
[tex]5\% \: of \: x = 15 \\ x = 1500 \div 5 = 300[/tex]