Answer:
[tex]x+y=27[/tex]
[tex]y=2x+6[/tex]
Step-by-step explanation:
Letting [tex]x[/tex] and [tex]y[/tex] represent the smaller and larger number, respectively we create these equations.
The greenhouse at the right is a regular octagonal pyramid with a height of 5 feet. The base has side lengths of 2 feet. What is the volume of the greenhouse?
Volume of a regular Octagon pyramid is = 96.55 [tex]feet^3[/tex]
In the given statement is:
The greenhouse at the right is a regular octagonal pyramid with a height of 5 feet. The base has side lengths of 2 feet.
To find the Volume of the greenhouse
We know that the :
Area of Regular Octagonal Pyramid is [tex]2a^{2}(1+\sqrt{2} )[/tex]
a = side of an octagonal
and, a= 2 feet
Let's find Area of Octagonal :
Now, putting the value of a in above formula:
[tex]2(2^{2} )(1+\sqrt{2} )\\\\8(1+\sqrt{2} )\\\\=19.31 feet^{2}[/tex]
Now, Volume of the green house
Volume of a regular Octagon pyramid is = Area of an Octagon x height
Height = 5 feet
Now, Volume of a regular Octagon pyramid is = 19.31×5
Volume of a regular Octagon pyramid is = 96.55 [tex]feet^3[/tex]
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An altitude is drawn to the base of equilateral triangle abc. if ac=13, find the length of the altitude.
The length of the altitude of the equilateral triangle ABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
Equilateral Triangle is defined as the triangle with all the sides equal and all the angles = 60 deg.
Altitude of a Triangle can be defined as the perpendicular drawn from the vertex of a triangle to the opposite side.
According to the question
In the figure given below
In ΔADC
Since ΔADC is a right angle triangle we can apply Pythagoras Theorem.
Let the sides of the equilateral triangle be "a". and "h" be the altitude.
Since the altitude is of equilateral triangle it divides the base i.e. DC=a/2
[tex](AC)^{2} =(AD)^{2}+(DC)^{2}[/tex]
[tex]a^{2} =h^{2}+(\frac{a}{2})^{2}\\ \\ h^{2}=\frac{4a^{2}-a^{2}}{4} \\ \\ h=\sqrt{3} *\frac{1}{2} *a[/tex]
Substituting the value of a=13 we get
Altitude [tex]h=\frac{13\sqrt{3} }{2}[/tex]
Therefore , The length of the altitude of the equilateral ΔABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
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In Algebra class, the average score on the second test is 76 points, all students scored within 5 points of the average. If x represents a student's score, write an equation that represents the minimum and maximum scores.
|x - 5| = 76
|x + 5| = 76
|x - 76| = 5
|x + 76| = 5
The equation to model the maximum and minimum scores is given by |x - 76| = 5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the student score. All students scored within 5 points of the average, hence:
|x - 76| = 5
The equation to model the maximum and minimum scores is given by |x - 76| = 5
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Order these numbers from least to greatest.
2.106, 1.1512, 2.1, 2.16
Answer:
1.1512, 2.1, 2.106, 2.16
Answer:
1.1512, 2.1, 2.106, 2.16
Step-by-step explanation:
1.1512 is the lowest cause it starts with 1
then 2.1 cause it has no more numbers to make it larger than the last two
then 2.106 because there is a 0 separating the 1 and 6 which makes the number smaller
which leaves you with 2.16 as the lasrgest
function 1, 2, 3, and 4
Label if 1-4 are linear or non linear
picture of function linked!
Answer:
1. Not Linear
2. Linear
3. Linear
4. Linear
Step-by-step explanation:
Linear means it follows the form y = mx + b
1. The x value increases by 2 each time, but the y value doubles each time. They are increasing at different rates, so they are not linear.
2. The x value is increasing by 3 each time, and the y value is deceasing by 1 each time. Slope (m) of this line would be -1/3
3. The x value is increasing by 4 each time, the y value is increasing by 3 each time. Slope (m) of this line would be 4/3
4. The x value is increasing by 1 each time, the y value is constantly -3. This means that the line is a horizontal line, which is linear with a slope of 0. So the equation of this line would be y = 0x -3 ----> y = -3
2³-2"=29
n=
Find the value of n
Answer:
[tex]2 + 2 + 2 - 2 = 29[/tex]
In a class of 30 students, 15 students have taken English, 10 students have taken English but not French. Find the number of students have taken: (i) French, and (ii) French but not English.
By using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
What do you mean by arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Given:
Total no. of students is [tex]30[/tex]
Number of students taken English is [tex]15[/tex]
Number of students taken English but not French is [tex]10[/tex]
(i) Number of students taken French = Total no. of students - Number of students taken English but not French
[tex]= 30-10\\=20[/tex]
(ii) Number of students taken French not English = Number of students taken French - Number of students taken English
[tex]=20-15\\=5[/tex]
Therefore, by using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
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Answer:
By using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
What do you mean by arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Given:
Total no. of students is
Number of students taken English is
Number of students taken English but not French is
(i) Number of students taken French = Total no. of students - Number of students taken English but not French
(ii) Number of students taken French not English = Number of students taken French - Number of students taken English
Therefore, by using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
∠A and \angle B∠B are vertical angles. If m\angle A=(7x+22)^{\circ}∠A=(7x+22)
∘
and m\angle B=(8x+20)^{\circ}∠B=(8x+20)
∘
, then find the measure of \angle A∠A.
Based on the definition of vertical angles, m<A = 36°.
What are Vertical Angles?Two angles that are vertically opposite to each other are called vertical angles, and they have congruent angle measures. That is, vertical angles are equal.
Angles A and B are vertical angles, then, they are equal to each other.
m<A = (7x + 22)°
m<B = (8x + 20)°
m<A = m<B
Substitute
7x + 22 = 8x + 20
7x - 8x = -22 + 20
-x = -2
x = 2
m<A = 7x + 22
Plug in the value of x
m<A = 7(2) + 22
m<A = 14 + 22
m<A = 36°
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there is a 91% chance of seeing a shooting star in the next hour, what is the probability of seeing a shooting star in the next half hour?
136.5 percent chance.
91 percent in one hour
how much percent in 1.5 hour?
we need to find how much percentage is in 0.5 hour
91 divided by 2 = 45.5
91 + 45.5 = 136.5
Am i bad? pls tell
What is the answer to 3/10=15/50
Answer: 3/10 times 5 equals 15/50
Step-by-step explanation: First you do 3 times 5 which equals 15 and then 10 times 5 to get 50, which together make 15/50 and to make sure it's right check it by finding the greatest common factor they both have.
Answer:
5/5
Step-by-step explanation:
3 will enter 15, 5 times
n 10 will enter 50, 5 times
Please help!!
Here are Stages 1-4.
What stage will have closest to 1,000,000,000 circles?
Use a calculator if it helps you with your thinking.
Hence, at the stage [tex]1,073,741,824[/tex] it reached nearest to [tex]1,000,000,000[/tex].
What is the circle?
A circle is a round-shaped figure that has no corners or edges.
In geometry, a circle can be defined as a closed, two-dimensional curved shape.
So, the calculation is:-
Now, Multiplying by [tex]2[/tex]
[tex]2 * 2 = 4[/tex]
[tex]4 * 2 = 8[/tex]
[tex]8 * 2 = 16[/tex]
[tex]16 * 2 = 32[/tex]
[tex]32 * 2 = 64[/tex]
[tex]64 * 2 = 128[/tex]
[tex]128 * 2 = 256[/tex]
[tex]256 * 2 = 512[/tex]
[tex]512 * 2 = 1,024[/tex]
[tex]1,024 * 2 = 2,048[/tex]
[tex]2,048 * 2 = 4,096[/tex]
[tex]4,096 * 2 = 8,192[/tex]
[tex]8,192 * 2 = 16,384[/tex]
[tex]16,384 * 2 = 32,768[/tex]
[tex]32,768 * 2 = 65,536[/tex]
[tex]65,536 * 2 = 131,072[/tex]
[tex]131,072 * 2 = 262,144[/tex]
[tex]262,144 * 2 = 524,288[/tex]
[tex]524,288 * 2 = 1,048,576[/tex]
[tex]1,048,576 * 2 = 2,097,152[/tex]
[tex]2,097,152 * 2 = 4,194,304[/tex]
[tex]4,194,304 * 2 = 8,388,608[/tex]
[tex]8,388,608 * 2 = 16,777,216[/tex]
[tex]16,777,216 * 2 = 33,554,432[/tex]
[tex]33,554,432 * 2 = 67,108,864[/tex]
[tex]67,108,864*2 = 134,217,728[/tex]
[tex]134,217,728* 2 = 268,435,456[/tex]
[tex]268,435,456 * 2 = 536,870,912[/tex]
[tex]536,870,912* 2 = 1,073,741,824[/tex]
Hence, at the stage [tex]1,073,741,824[/tex] it reached nearest to [tex]1,000,000,000[/tex].
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a pesticide manufacturer is developing a new type of organic pesticide for a particular plant. to study the effectiveness of the new pesticide, a large sample of young plants is collected. the sample is then separated into many groups of two plants based upon age, size and soil type so that plants with similar characteristics are grouped together. one of the two plants in each group is randomly chosen and administered the pesticide, while both plants are placed in a controlled environment and are exposed to the possibility of attack from the target pests. the plants are inspected regularly over a 3 month period and the results are recorded for comparison.
According to the question, the study is based on the organic pesticide for a particular plant. The pesticide manufacturer is developing a new type of organic pesticide for the particular plants. To understand the application of a new organic pesticide, then perform one experiment where the members of plants have controlled the environment for the testing purpose. In this way, plants can be protected from pest attack. These types of experiments fall under matched pair experiments.
In the matched pair experiments, the samples are divided into two parts. The first part should be based on some controlled characteristics, whereas the other one should be based on randomly assigned characteristics.
What are matched pair experiments.?
Matched pair designs are experimental based designs. In this, one group is protected in a controlled environment whereas the other one is in a random environment.
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It costs $24.99 for a pizza
pasta for 4 people. Drinks are an
Extra$2.99 each. How much would it cost
for 4 people to eat and drink?
The final answer for this is $36.95.
Now, if we se the explanation
We have, the cost for pizza and pasta for four people is $24.99
and,
the cost of drink for single person is $2.99
Now, if we calculate the cost of drinks for all the four person,
it would be $2.99 × 4 = $11.96.
It is the cost of drinks only for four people.
we have already given the cost of eat I.e. $24.99
total cost for four people to eat and drink is
= $11.96 + $24.99
= $36.95
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the time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list, along with the five-number summary. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58
No, there is only one outlier at 58 minutes.
What are outliers in data?An observation that differs abnormally from other values in a population-based random sample is referred to as an outlier. In a way, this definition defers to the analyst's (or a consensus process') judgment as to what constitutes aberrant behavior. It is vital to define typical observations before distinguishing aberrant ones.
How do you calculate the outlier?A data point is considered an outlier if it is more than 1.5 times the IQR below the first quartile or more than 1.5 times the IQR above the third quartile, according to the general criterion for utilizing it to compute outliers. The first and third quartile percentiles must be known in order to compute the IQR.
Complete question -The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.
9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58
One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR rule for outliers, is there evidence to support the student's claim?
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Mandy has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will she have in 2 years
Amount after 2 years is $44.1
Compound interest formula
[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]
A= Amount after t years.
P= Principal amount.
r= Interest rate (decimal)
n=Period of compounding
t= Time
So ,
[tex]A=40(1+\frac{0.05}{1}) ^{1*2}\\ =40(1.05) ^{2}\\ = 40*1.1025\\ = 44.1[/tex]
Amount after 2 years is $44.1
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What is the area of the shades region below
Answer:
243m²
Step-by-step explanation:
work out 18x18=324
work out 9x9=81.
324-81= 243
Find the value of z.
X
7
Y
Z
3
Z = ✓[?]
Please helppppp
Answer:
z = [tex]\sqrt{30}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it) × ( whole hypotenuse) , so
z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )
z = [tex]\sqrt{30}[/tex]
Monthly Water Bills
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12
$40 $42 $40 $38 $48 $50 $58 $62 $56 $46 $44 $44
Write the formula for the mean water bill for the entire year using sigma notation.
The calculation for the average water bill for such entire year in sigma notation.
[tex]\bar{x}=\frac{1}{12} \sum_{i=1}^{12} x_i[/tex]
What is the sigma notation?To depict a series in a succinct format, summation or sigma symbols can be employed. The sum is denoted by the Greek capital letter ∑, The series 4+8+12+16+20+24 has the formula 6∑n=14n. As n increases from 1 to 6, the statement is read as the total of 4n.
What is the purpose of sigma notations?Summation notation (also known as sigma notation) allows us to express a large sum in a single phrase.
What is the definition of a math term?The mean in mathematics and statistics is the average of a set of values. There are several methods for computing the mean, including the simple arithmetic mean, the geometric mean, and the harmonic mean.
According to the given data:x₁ x₂ x₃ x₄ x₅ x₆ x₇ x₈ x₉ x₁₀ x₁₁ x₁₂
$40 $42 $40 $38 $48 $50 $58 $62 $56 $46 $44 $44
The calculation for the average water bill for such entire year in sigma notation.
[tex]\bar{x}=\frac{1}{12} \sum_{i=1}^{12} x_i[/tex]
[tex]\bar{x}[/tex] = (40+42+40+38+48+50+58+62+56+46+44+44)/12
= 568/12
= 47
The calculation for the average water bill for such entire year in sigma notation.
[tex]\bar{x}=\frac{1}{12} \sum_{i=1}^{12} x_i[/tex]
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PLS HELP MARKING BRAINLIEST pls answer correctly
Answer:
24
Step-by-step explanation:
Let x be shirts.
Write an equation.
13x=321
Divide 13 from both sides.
x≈24.69
So, the soccer team can only buy 24 shirts, because it cannot go over the budget.
Hope this helps!
Please mark as brainliest if correct!
angle q and angle r are complementary. the measure of angle q is 26 degrees less than the measure of r. find the measure of each ang;e
Based on the definition of complementary angles, the measures are:
m<q = 32°
m<r = 58°
What are Complementary Angles?Tow angels are complementary if both angles give a sum of 90 degrees.
The sum of angle q and angle r would give 90 degrees because they are complementary angles. Therefore, we would have the following:
m<r = ?
m<q = m<r - 26
Plug in the values
m<r - 26 + m<r = 90
2(m<r) - 26 = 90
2(m<r) = 90 + 26
2(m<r) = 116
2(m<r)/2 = 116/2
m<r = 58°
m<q = m<r - 26 = 58 - 26
m<q = 32°
Therefore, based on the definition of complementary angles, the measures are:
m<q = 32°
m<r = 58°
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"If PQ+ RS = PS and RS = XY, then PQ + XY = PS"
Please
Help
Answer:
Substitution property.
Step-by-step explanation:
The substitution property is just like saying, "If a variable, b, equals c, then b will be substituted for c, and it goes for c being substituted as b, too."
➲ Hope this helps.
Write an indirect proof of each statement.
Given: x y is an odd integer.
Prove: x and y are both odd integers.
By assuming that one of the two integers is even we will reach an absurd, and in that way, prove the given statement.
How to prove the statement?
Remember that an odd integer number is written as:
A = (2n + 1)
While an even number would be written as:
B = 2n
Where n is a random integer.
Then if x times y is an odd integer we can write:
x*y = (2n + 1)
Where n, m ∈ Z.
Where Z is the set of integer numbers.
Now, let's do find an absurd. Let's suppose that one of the two numbers is even, then we can write:
x = 2m
And y can be even or odd, it does not matter, but it is an integer.
Replacing that we get:
x*y = (2m)*y
We can rewrite that as:
(2m)*y = 2*(m*y)
We know that integer numbers are closed under the product, and here m and y are integers, then m*y is also an integer.
Thus, 2*(m*y) is 2 times an integer, then that is an even number, which is absurd because we know that it should be odd. So, if at least one of the two integers is even, then the product will also be even.
Then if the product is odd, neither of the integers can be even, then we conclude that both of the integers are odd integers.
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Exspression 19- 11 is the amount by which
here are the exam grades of 15 students:88, 48, 60, 51, 57, 85, 69, 75, 97, 72, 71, 79, 65, 63, 73 use excel function to compute the quartiles and the interquartile range.the first quartile q1 is .the second quartile q2 is the third quartile q3 is .the interquartile range iqr is
Similarly, Q1 is obtained as the median of the lower half as (7+1)/2th = 4th observation i.e 60.
Similarly, Q3 is obtained for the upper half as 79 (4th upper half)
IQR (Interquartile Range) = Q3 - Q1 = 79 - 60 = 19
What is Interquartile Range?The interquartile range is a gauge for where a data set's "middle fifty" lies. An interquartile range (IQR) measures where most of the values lay, whereas a range measures where a set's start and finish are. For this reason, it is preferable when reporting things like academic performance or SAT scores over many other measures of spread.
The interquartile range IQR is 19
In ascending order we have: 48,51,57,60,63,65,69,71,72,73,75,79,85,88,97
Also, we get sample size (n) = 15 (odd)
So, Median = Q2 = (n+1)/2th observation
Median = (15+1)/2th term = 8th observation
Median = Q2 = 71
The formula for the interquartile range is the first quartile less the third quartile:
IQR = Q3 - Q1.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
For each function, what is the output of the given input?
For f(x) = 4x + 7, find f(4)
suppose your group measures the following three numbers in some experiment: 12.4,7.8,10.2. if you use half the range as an estimate of the standard deviation, what is the standard error on the mean of these numbers?
The standard error on the mean of these numbers is 1.08
For given question,
suppose your group measures the following three numbers in some experiment: 12.4,7.8,10.2
Mean of these numbers is:
[tex]\bar x=\frac{ 12.4+7.8+10.2}{3}\\\\ \bar x=10.13[/tex]
So the standard deviation would be,
[tex]\sigma=\sqrt{\frac{(12.4-10.13)^2+(7.8-10.13)^2+(10.2-10.13)^2}{3} }\\\\\sigma=1.88[/tex]
Now we find the standard error on the mean of these numbers.
[tex]\sigma_M=\frac{\sigma}{\sqrt{N} }[/tex]
where, [tex]\sigma_M[/tex] = standard error of the mean
σ = the standard deviation of the original distribution
N = the sample size
[tex]\sigma_M=\frac{1.88}{\sqrt{3} }\\\\\sigma_M=1.08[/tex]
Therefore, the standard error on the mean of these numbers is 1.08
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The Munchery Restaurant advertises that you
can have a different lunch combination every
day of the year. They offer 12 different kinds
of soups, 6 different sandwich meats and 4
different kinds of bread. Is their claim valid?
Explain.
brosse sit
There of 288 different kinds of lunch combination .
What is combination ?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.The Munchery Restaurant advertises that you can have a different lunch combination every day of the year.
types of soups = 12
types of sandwich = 4
types of bread = 4
find the number of combinations we multiply all the possible types we have
Number of combinations = 12 × 6 × 4 = 288
There of 288 different kinds of lunch combination .
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Rita bakes pies at a bakery. the number of pies she can bake, x, is limited by the ingredients they have in stock. this situation is represented by 2x - 3 < 7 and 5 - x < 8 solve the compound inequality and write the viable solutions.
The viables solutions for the given compound inequality are x ∈ (-3, 5).
According to the given question.
The number of pies baked by Rita is x which is limited by ingredients.
Also, the inequalities which represent the situation are
2x - 3 < 7
And, 5 - x < 8
Since, we have to solve the above inequality and find its solutions.
From the given inequality
2x - 3 <7 we can say that,
2x < 7 + 3
⇒ 2x < 10
⇒ x < 5 ..(i)
And, 5 - x < 8
⇒ 5 - 8 < x
⇒ - 3 < x
or, x < -3 ..(ii)
From i and ii we can say that the solution of the given compound inequality are the numbers which lies in between -3 and 5 or x ∈ (-3, 5).
Hence, the viables solutions for the given compound inequality are
x ∈ (-3, 5).
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The function f is defined as followed
f(x)=3x^2+1
More info linked please help with proper answer: find the expression for g(x)
(if you are good at this please help with the next two I will post soon after you answer)
Check the picture below, which is just a template for transformations.
so hmmm if we grab f(x) and move it downwards by 8 units, that means that the value for "D" gets a -8 added to it, so let's do that.
[tex]f(x)=3x^2+1\qquad \implies f(x)=\stackrel{A}{3}(\stackrel{B}{1}x+\stackrel{C}{0})^2+\stackrel{D}{1} \\\\\\ g(x)=3(1x+0)^2+1+(-8)\implies {\LARGE \begin{array}{llll} g(x)=3x^2-7 \end{array}}[/tex]
Can someone explain this im trying to get it but I can’t