Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:
Step 1: 89 pupils out of a possible 200 answered with joy, as shown in the table.Step 2 - It is also stated that there were a total of 28 students in the age range of 6 to 8 years who answered positively.Step 3 - Accordingly, the likelihood that the pupil belongs to the 6 to 8-year-old age range is:P = 28/89
Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
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The complete question is given below:
Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?
PLEASE HELP ASAP!!
1. Use the space provide to respond to each statement concerning the given graph of a radical function.
a.) State the domain of the function.
b.) State the range of the function.
c.) Identify the end behavior of the function.
d.) Identify the x – intercept. Write as an ordered pair.
e.) Determine the absolute minimum of this function.
Part a
The domain is the set of x-values, which is [tex][1, \infty)[/tex].
Part b
The range is the set of y-values, which is [tex][-3, \infty)[/tex].
Part c
As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex].
Part d
The x-intercept is when y=0, which is [tex](2, 0)[/tex].
Part e
The absolute minimum is the lowest point, which has a y-coordinate of [tex]-3[/tex].
Part a
The domain is the set of x-values, which is .
Part b
The range is the set of y-values, which is .
Part c
As , .
Part d
The x-intercept is when y=0, which is .
Part e
The absolute minimum is the lowest point, which has a y-coordinate of
Triangles FAD and DCE are translations of triangle ABC.
Select all the statements that must be true. (Lesson 1-21)
A. Points B, A, and F are collinear.
PERIOD
E
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
D. The measure of angle CED is the same as the measure of angle FAD.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
F. Triangle ADC is a reflection of triangle FAD.
The statements about triangles FAD and DCE which are translations of triangle ABC include the following:
A. Points B, A, and F are collinear.
(B.) The measure of angle BCA is the same as the measure of angle CED.
C. Line AD is parallel to line BC.
(E.) The measure of angle DAC is the same as the measure of angle BCA.
The types of transformation.Generally, there are four (4) main types of transformation and these include the following:
ReflectionDilationRotationTranslationWhat is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since triangles FAD and DCE both represent the translations of triangle ABC (see attachment), we can logically deduce the following information:
Points B, A, and F all lie on the same line BF, which makes point B, A, and F collinear.All of the sides and angles of triangle ABC (ΔABC) are equal to triangle DCE (ΔDCE), which makes angle BCA (m∠BCA) equal to angle CED (m∠CED).Line AD and line BC are parallel lines because they can never meet.The measure of angle DAC (m∠DAC) is the same as the measure of angle BCA (m∠BCA).Read more on translation here: https://brainly.com/question/19880883
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Which expression is equivalent to (m^−5n^−3)^−3?
Answer:
[tex]m^{15} n^{9}[/tex]
Step-by-step explanation:
Given: ZADB = ZCBD ZABDZCDB m ZA= 3x + 15 mZC=8x-20 Find: x and m ZA A4 D B
Answer:
x = 7 , ∠ A = 36°
Step-by-step explanation:
since ∠ ADB ≅ ∠ CBD ( alternate angles )
and ∠ ABD ≅ ∠ CDB ( alternate angles )
then ABCD is a parallelogram
the opposite angles of a parallelogram are congruent , so
∠ C = ∠ A , that is
8x - 20 = 3x + 15 ( subtract 3x from both sides )
5x - 20 = 15 ( add 20 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Then
∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°
Answer: x = 7 and m∠A = 36
Step-by-step explanation:
Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB
This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C
⇒3x +15 = 8x - 20
⇒3x + 15 - 3x = 8x - 3x -20
⇒5x = 20 + 15
⇒x = 7
Now m∠A = (3X7) +15 = 36
Thanks to whoever helps
Answer:
Step-by-step explanation:
erm
A triangle is 180 degrees
Add both angles then subtract by 180
Hari's weekly allowance varies depending on the number of chores he does. He received $18 in allowance the week he did 20 chores, and $12 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.
The equation of his allowance in slope-intercept form is y = 0.5x + 8
He received $18 in allowance the week he did 20 chores.
He received $12 in allowance the week he did 8 chores.
The ordered pairs will be (8,12) and (20,18)
The slope intercept form is
y = mx + b
Where m is the slope
b is the y intercept
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
m = (18-12)/(20-8)
m = 6/12
= $0.5 per chores
Now we have to find b,
Substitute the value of any ordered pair in the slope intercept form
12 = 0.5×8+b
12 = 4+b
b = 12-4
b = 8
Hence, the equation of his allowance in slope-intercept form is y = 0.5x + 8
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Which number is the greatest?
-8
-10
-7
Answer:
-7
Step-by-step explanation:
-7 is the greatest because it is closer to 0 on the number line.
←
Mattie Evans drove 140 miles in the same amount of time that it took a turbopropeller plane to travel 540 miles. The speed of the plane was 200 mph faster than the speed of the car
Find the speed of the plane.
The speed of the plane was
(Simplify your answer.)
mph.
Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.
How to determine the speed of this plane?In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:
Let d₁ represent the distance covered by Mattie.Let v₁ represent the speed of Mattie's car.Let d₂ represent the distance covered by the turbopropeller plane.Let v₂ represent the speed of the turbopropeller plane.Translating the word problem into an algebraic equation, we have;
v₂ = v₁ + 200
Since Mattie and the turbopropeller plane travled at the same time, we have:
Time = distance/speed
Time = d₁/v₁ = d₂/v₂
Time = 140/v₁ = 540/v₁ + 200
Cross-multiplying, we have:
140(v₁ + 200) = 540v₁
140v₁ + 28,000 = 540v₁
Next, we would rearrange the equation by collecting like terms as follows:
540v₁ - 140v₁ = 28,000
400v₁ = 28,000
Speed of plane, v₁ = 28,000/400
Speed of plane, v₁ = 70 mph.
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Rectangle TUVW with vertices
T(-3,-1), U(0, -2), V(-2, -8), and
W(-5, -7): 90° counterclockwise
T':
U':
V':
W':
for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,
T': (1, -3)
U': (2, 0)
V': (8, -2)
W': (7, -5)
In this question, we have been given a rectangle TUVW with vertices
T(-3,-1), U(0, -2), V(-2, -8) and W(-5, -7)
We know that for 90° counterclockwise rotation is (x, y) becomes (-y, x)
so, the coordinates of T' would be,
T' = (1, -3)
the coordinates of U' would be,
U' = (2, 0)
the coordinates of V' would be,
V' = (8, -2)
the coordinates of W' would be,
W' = (7, -5)
Therefore, for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,
T': (1, -3)
U': (2, 0)
V': (8, -2)
W': (7, -5)
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The weight f a stack of standard 8.5*11 copier paper vs. number of sheets of paper
A. The weight of the copies and the quantity of papers are proportional.
B. There is no proportion between the number of books and their weight.
Given,
A. All versions of the document are 8.5 by 11 inches in size.
We can readily determine the quantity of papers using direct proportion because all the paper has the same dimensions and weight.
As a result, the weight of the copies and the quantity of papers are proportional.
B. Each book has a distinct weight, as we know.
Since each book varies in weight, it is difficult to calculate the quantity of papers using a direct percentage.
Therefore, there is no proportion between the number of books and their weight.
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NEEd HELP 9th grade asp
Answer:175/48
Step-by-step explanation:
Round 1.9541 to the nearest tenth
Answer:
2
Step-by-step explanation:
1.9541 lets only worry about 1.95 because it rounds to this rounding up because its five will be 2
If ADAB ACBA,
ZD = 132° and ZC = x + 18
Answer:
x = 114
Step-by-step explanation:
since the triangles are congruent then corresponding angles are congruent, then
∠ C = ∠ D , that is
x + 18 = 132 ( subtract 18 from both sides )
x = 114
Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.
In linear equation, R = 4c is an equation to represent the amount R Natalia and her friends raised after selling c cakes.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as .
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like
R = mc + b
We need to find the value of m and b, to get an equation to represent the situation.
The first point we have from the information given is (15, 60) => 15 cakes sold for $60.
The second point is (22, 88) => 22 cakes sold for $88.
Slope(m) = 88 - 60/22 - 15 = 28/7 = 4
To find b, substitute c = 15, R = 60 and m = 4, into R = mc + b
60 = 4(15) + b
60 = 60 + b
b = 0
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into R = mc + b to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
R = 4c + 0
R = 4c
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3. Suppose that the scores on a statewide standardized test are normally distributed with a mean of 69 and a standard deviation of 6. Estimate the percentage of scores that were(a) between 57 and 81. %(b) above 81. %(c) below 63. %(d) between 51 and 81. %
Answer:
a) 95%
b) 2%
c) 16%
d) 98%
Explanation:
We have the following:
This is a normal distribution
Mean = 69
Standard Deviation = 6
a) Between 57 and 81%
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x=57 \\ z=\frac{57-69}{6}=-\frac{12}{6} \\ z=-2 \\ \\ x=81 \\ z=\frac{81-69}{6}=\frac{12}{6} \\ z=2 \\ \end{gathered}[/tex]The probability that a score is between 57 & 81 is given by the Area between (z = -2) & (z = 2):
[tex]\begin{gathered} P=0.97725-0.02275 \\ P=0.9545 \\ P=95.45\approx95 \\ P=95\text{ \%} \\ \\ \therefore P=95\text{ \%} \end{gathered}[/tex]b) Above 81%
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x>81 \\ z=\frac{81-69}{6} \\ z=\frac{12}{6}=2 \\ z=2 \end{gathered}[/tex]The probability that a score is above 81% is given by the area of the graph greater than (z = 2):
[tex]\begin{gathered} P=0.02275 \\ P=2.275\approx2.3 \\ P=2.3\approx2 \\ P=2\text{ \%} \\ \\ \therefore P=2\text{ \%} \end{gathered}[/tex]c) Below 63%
[tex]\begin{gathered} x<63 \\ z=\frac{63-69}{6} \\ z=-\frac{6}{6}=-1 \\ z=-1 \end{gathered}[/tex]The probability that a score is below 63% is given by the area of the graph lesser than (z = -1):
[tex]\begin{gathered} P=0.15866 \\ P=15.866\approx16 \\ P=16\text{ \%} \end{gathered}[/tex]d) Between 51 and 81
[tex]\begin{gathered} 51\le x\le81 \\ z=\frac{51-69}{6} \\ z=-\frac{18}{6}=-3 \\ z=-3 \\ \\ z=\frac{81-69}{6} \\ z=\frac{12}{6}=2 \\ z=2 \end{gathered}[/tex]The probability that a score is between 51 & 81 is given by the Area between (z = -3 & (z = 2):
[tex]\begin{gathered} P=0.97725-0.00135 \\ P=0.9759 \\ P=97.59\approx98 \\ P=98\text{ \%} \end{gathered}[/tex]deltamath i need answers fast
Answer:
To stay within budget, she must use 3.9 gigabytes.
Caroline can use approximately 3.9 gigabytes of data while staying within her budget of $74 per month.
Let's assume the number of gigabytes of data Caroline can use while staying within her budget is represented by the variable "x."
The flat cost per month is $54.50, and Caroline pays an additional $5 per gigabyte.
If she wants to keep her bill at $74 per month, the equation can be set up as follows:
54.50 + 5x = 74
To solve for "x," we can isolate the variable on one side of the equation. First, subtract 54.50 from both sides:
5x = 74 - 54.50
5x = 19.50
Finally, divide both sides by 5:
x = 19.50 / 5
Simplifying the division gives us:
x = 3.9
Therefore, Caroline can use approximately 3.9 gigabytes of data while staying within her budget of $74 per month.
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How can this expression be written another way? 60x−24 Factor using the distributive property and the greatest common factor to write an equivalent expression.
The equivalent expression of the given expression 60x - 24 using distributive property and greatest common factor is 12(5x-2).
Distributive property is a property with which we multiply the sum or difference of two numbers with a number. For example:
a×(b+c) = a×b + a×c
a×(b-c) = a×b - a×c
The greatest common factor is a number which is common multiple of all the given numbers.
Now, solve the given expression 60x - 24
The factors of terms
60x = 12 × 5x
24 = 12 × 2
The greatest common factor is 12, so we take 12 common and the given expression can be written as
60x - 24
= 12 × 5x - 12 × 2
= 12(5x - 2)
Hence, the equivalent expression is 12(5x-24)
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6
Pens cost 20p each.
Rulers cost 60p each.
Saj buys some pens and some rulers.
He buys 8 rulers.
The total cost is £10
How many pens does he buy?
Answer:
26 pens
Step-by-step explanation:
Let P and R be the numbers of Pens and Rulers Saj purchases.
The cost of P Pens and R Rulers:
Pens = P(20p)
Rulers = R(60p)
P(20p) + R(60p) = £10
P(0.20) + R(0.60) = 10
R = 8
P(0.20) + (8)*(0.60) = 10
P(0.20) + 4.8= 10
P(0.20) = 5.2
P = (5.2/0.20)
P = 26 pens
CHECK:
8 Rulers = 8*(60p) = 480p
26 Pens = 26*(20p) = 520p
Total = £10
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP HELP
Answer:
a) 1.6×10∧-6
b)2×10∧7
Solven - 8 + n = 1 -4n
We will solve as follows:
[tex]n-8+n=1-4n\Rightarrow2n+4n=1+8[/tex][tex]\Rightarrow6n=9\Rightarrow n=\frac{3}{2}[/tex]The flag of Colombia is a rectangle that is 66 ft. long with three horizontal stripes
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Below is a scale illustration of the Colombian flag that ranges from 1 cm to 2 ft.
How are scale illustrations created?It is already stated that all measurements would be done using a fixed scale for a given scale drawing. Let the scale, for illustration, be K feet to s inches.
1ft ; s/k in
Thus, all foot measures will be multiplied by s/k to obtain the relevant lengths in the drawing.
Since the ratio is 2:1, there are 1 centimeter for every 2 feet.
This indicates that to reach 33, we must divide 66 by 2.
66/2 = 3
As a result, the scale drawing of the Colombian flag is attached below and has a scale of 1 cm to 2 ft.
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What is the volume of a triangular pyramid that is 10 in. tall and has a base area of 9 square in?
The volume of a triangular pyramid that is 10 in. tall and has a base area of 9 square inches is 30 cubic inches.
Volume of a triangular pyramidTetrahedrons are polyhedra made up of four triangular faces, six straight edges, and four vertex corners. They are also referred to as triangular pyramids.
The given shape is known as a triangular pyramid and the formula for calculating its volume is expressed as:
V = BH/3
where
B is the base area
H is the height of the prism
Determine the base area
B = 1/2 * base * height
B = 9 square inches
H = 10 inches
Substitute the given parameters into the formula
V = 9*10/3
V = 3*10
V = 30 cubic inches
This given the required volume of the prism
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Convert 41°F to degrees Celsius.
if necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer:
5°C
Step-by-step explanation:
hope this helps, i used your formula :D
The shortest side of a right triangle measures 6, and the longest side measures 10. Determine the measurement of the unknown side.
5
8
9
10
In a case whereby the the shortest side of a right triangle measures 6, and the longest side measures 10 the measurement of the unknown side is 8.
How can the measurement of the unknown side be calculated?We can use this expression from trigonometry to know the third side of the triangle as:
a^2 + b^2 = c^2
Then since the longest side measures 10 which is the c side of the triangle then the unknown side can be calculated as :
10^2 - 6^2
The we can simplify as
100-36=64
Then [tex]\sqrt{64}[/tex] = 8.
Therefore, the second option is correct.
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. Represent Real World Problems Lorena and Benita are saving
money. They began on the same day. Lorena started with $40. Each
week she adds $8. The graph describes Benita's savings plan. Which
girl will have more money in 6 weeks? How much more will she
have? Explain your reasoning.
We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.
We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.
amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88
Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.
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Linear equations
Which ordered pair is a solution of this equation, -2x+9y=-26
A. (4,4)
B. (-4,-4)
C. (-5,-4)
D. (-4,-5)
The ordered pair which is a solution to the given linear equation is (-5, -4)
What are linear equations?Linear equations are equations that has a leading degree of 1. The standard linear equation is given as Ax + By = C.
Given the linear equation below;
-2x+9y=-26
We need to determine the ordered pair that gives a solution to the linear expression.
For the coordinate point (4, 4)
-2(4) + 9y = -26
9y = -26 + 8
9y = -18
y = -18/9 = -2
This shows that (4, 4) is not a solution.
For the coordinate point (-4, -4)
-2(-4) + 9y = -26
9y = -26 - 8
9y = -34
y = -34/9
This shows that (-4, -4) is not a solution.
For the coordinate (-5, -4)
-2(-5) + 9y = -26
9y = -26 - 10
9y = -36
y = -4
This shows that (-5, -4) is a solution of the linear equation.
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suppose that a high school marching band has 108 members. of these 108 band members, 39 are seniors, 23 play the trumpet, and 8 are seniors who play the trumpet. what is the probability that a randomly selected band member is a senior given that he or she plays the trumpet? give your answer as a percentage, rounded to one decimal place.
The probability that a randomly selected band member is a senior given that he or she plays the trumpet is 34.78%.
Probability is defined as the likeliness of an event to happen. It can be calculated by dividing the total desired outcomes by the total outcomes.
P = desired outcomes / total outcomes
Of the 108 band members, if 23 play the trumpet, and 8 are seniors who play the trumpet, then the probability that a randomly selected band member is a senior given that he or she plays the trumpet is 8 divided by 23.
P = 8/23 x 100
P = 34.78%
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Angle JKL and angle MKQ are complementary angles. The measures of angle JKL is twice the measure of angle MKQ.• Write one equation to find x, the measure of angle MKQ• Solve for X
Answer : x = 30 degrees
< JKL and < MKQ are complementary
Let < MKQ = x
Angle JKL is twice the measure of angle MKQ
JKL = 2 x MKQ
Sum of a complementary angles = 90 degrees
< JKL + < MKQ = 90
< JKL = 2MKQ
Substitute the value of < jkl
2(<2MKQ + Since, Therefore,
2x + x = 90
3x = 90
Divide both sides by 3
3x / 3 = 90/3
x = 30 degrees
The longest side of a right angle triangle
is √46cm
One of the shorter sides has a length of
√7cm
What is the perimeter of the triangle?
Answer:
The exact answer would be:
[tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex] an approximate answer to the nearest whole number would be 7
Step-by-step explanation:
To find the missing side we would use the Pythagorean Theorem.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] =[tex]c^{2}[/tex]
[tex]\sqrt{7} ^{2}[/tex] + [tex]b^{2}[/tex] = [tex]\sqrt{46} ^{2}[/tex]
7 + [tex]b^{2}[/tex] = 46 Subtract 7 from both sides
[tex]b^{2}[/tex] = 39
[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{39}[/tex]
b = [tex]\sqrt{39}[/tex]
The perimeter, the distance around the triangle, is [tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex]
Which lines are perpendicular to 3x – y = 10? Select all that apply. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
What is the equation of a perpendicular line?Let the equation of the line be y = ma + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx +c is given as y = -(1/m)x + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
3x – y = 10
y = 3x – 10
Then the equation of the perpendicular line is given as,
y = –(1/3)x + d
The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.
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