Answer:
a) 32
b) 2 +5n
Step-by-step explanation:
Given the stick patterns shown, with 7, 12, 17 sticks, you want to know (a) the number of sticks in pattern 6, and (b) the number of sticks in pattern n.
SequenceThe numbers of sticks in the patterns shown are ...
7, 12, 17
The differences between these numbers are ...
12 -7 = 5
17 -12 = 5
That is, the first pattern has 7 and the common difference between patterns is 5. This indicates the sequence is arithmetic.
b) General termThe general term of an arithmetic sequence with first term a1 and common difference d is ...
an = a1 +d(n -1)
an = 7 +5(n -1) = 7 +5n -5
an = 5n +2 . . . . . . sticks in pattern n
a) Sixth termThe term when n=6 is ...
a6 = 5·6 +2 = 32 . . . . . . sticks in pattern 6
__
Additional comment
We find it easier to determine sticks in pattern 6 by first determining the formula for pattern n.
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Please Help Me With These Problems!!
4. The front wheels on DeMarius’ car are divided into sectors of equal area. The radius of each wheel is 8 inches. The area painted blue is twice the area painted green. The area painted green is half the area painted red. What is the area painted red on one of the front wheels? Round your answer to the nearest hundredth.
5. The rear wheels of DeMarius’ car complete 4/5 of a rotation for every full rotation of a front wheel. What is the radius, in feet, of a rear wheel on the car? Write your answer as a simplified fraction.
6. DeMarius’ original design for his car used rear wheels with a radius of 12 inches. What is the measure of the central angle of this rear wheel such that the arc length is equivalent to that of a full rotation of the rear wheel that is actually used on DeMarius’ car?
The area painted red on one of the front wheels on DeMarius’ car will be 80.42 inches².
How to calculate the area?From the information given, the The front wheels on DeMarius’ car are divided into sectors of equal area and the radius of each wheel is 8 inches. The area will be:
= 2/5 × πr²
= 0.4 × 3.14 × 8²
= 80.42 inches²
The radius, in feet, of a rear wheel on the car will be:
r1(2π) = r2(2π)
8(2π) = r2(8/5)(2π)
16 = r2(8/5)
r = 5/8 × 16
r = 10 inches
r = (5/6) feet
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Write an equation for a function whose graph has exactly two x-intercepts, one at x=-6 and the other at x=3.
Answer:
y = x^2 + 3x - 18
Step-by-step explanation:
A parabola with zeroes at x = - 6 and 3 would look like this:
(x+6)(x-3) = x^2 + 3x -18
QUESTION 13
An art student wants to enlarge a triangle with the sides 8, 8, and 14 cm. The new
triangle will have a measurement of 21 cm on its longest side. How long will the
other sides be on the new triangle?
O 12 cm
O24 cm
O 15 cm
21 cm
Answer:
12 c.m. and 12 c.m.
Step-by-step explanation:
model/actual = scale factor (same thing for dilation)
21/14 = 3/2
3/2*8 =4*3 =12
Which line will have no solution with the parabola y – x 2 = x2?
Step-by-step explanation:
y = –3x –3
y = –2x –3
y = 2x –3
y = 3x –3
Answer:
the correct answer is C.) y = 2x -3
Step-by-step explanation:
edge 2022
-(3/4)+1 7/8 divided by 1/2 =n
first off, let's convert the mixed fraction to improper fraction and then proceed, let's notice that by PEMDAS or order of operations, the multiplication is done first, and then any sums.
[tex]\stackrel{mixed}{1\frac{7}{8}}\implies \cfrac{1\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{15}{8}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{3}{4}~~ + ~~\cfrac{15}{8} \div \cfrac{1}{2}\implies -\cfrac{3}{4}~~ + ~~\cfrac{15}{8} \cdot \cfrac{2}{1}\implies -\cfrac{3}{4}~~ + ~~\cfrac{15}{4} \\\\\\ \cfrac{-3+15}{4}\implies \cfrac{12}{4}\implies 3[/tex]
The equation v=68t represents the number of views v for a video after t hours. Identify the independent and dependent variables.
Answer(s):
Dependent variable: vIndependent variable: tWhat is the dependent variable of an equation?
The dependent variable of an equation is the variable that is completely isolated on one side.
What is the independent variable of an equation?
The independent variable is the variable that is not isolated. The independent variable can either have a cooeficient or has some operation (+ - × ÷) included on that side of the equation.
Determining the independent and dependent variable
In this equation, we can see that "v" is completely isolated on one side and "t" has a cooeficient of 68. Thus, the dependent variable is "v" and the independent variable is "t".
People with heart arrhythmia are known to have a resting pulse rate of 110 with a standard deviation of 5. With a new
experimental treatment, a group of 100 patients who suffer from heart arrhythmia has a resting pulse rate lowered to
108. Does this provide significant evidence that the experimental medication is effective at reducing resting pulse rate?
A. Yes, the test value is in the rejection region
B. No, the test value is not in the rejection region
C. Yes, the test value is not in the rejection region
OD. No, the test value is in the rejection region
The answer will be option A Yes, the test value is in the rejection region.
What is Z-score?A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
here the formula will be
[tex]Z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt {n}}}[/tex]
[tex]Z=\dfrac{100-110}{\dfrac{5}{\sqrt{100}}}[/tex]
[tex]Z=-20[/tex]
Z critical value =-1.645
Z calculated> Z critical value so we will reject.
Hence the answer will be option A Yes, the test value is in the rejection region.
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A group of doctors are conducting an experiment to test a new nutritional supplement. they randomly selected 600 subjects, assigning 300 subjects to receive the supplement and 300 subjects to receive a placebo. the doctors are unaware of which subjects are assigned to each treatment group. this experiment is because know which treatment group each subject is in.
This experiment is neither the subject nor the researcher because knows which treatment group each subject is in.
What is an experiment?A scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact.
A group of doctors are conducting an experiment to test a new nutritional supplement they randomly selected 600 subjects, assigning 300 subjects to receive the supplement and 300 subjects to receive a placebo.
The doctors are unaware of which subjects are assigned to each treatment group. this experiment is neither the subject nor the researcher because know which treatment group each subject is in.
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Just need the answer fast pls help
Answer:
Answer is D. [tex]\frac{121}{49}a^8b^2[/tex]
Step-by-step explanation:
We expand the powers.
[tex]\frac{11}{7}^2*(a^4)^2*(b)^2\\\frac{11}{7}*\frac{11}{7}*(a^4)(a^4)*(b*b)\\\frac{121}{49}*(a^8)*(b^2)[/tex]
when doing variable power you add them together.
a^4*a^4=a^(4+4) , b^1*b^1=b^(1+1)
HELP PLEASE FOR PRE-ALGEBRAIC
Answer:
Your answer is Vertical.
Step-by-step explanation:
help me im from VietNam
Answer:
Step-by-step explanation:
Adding and subtracting expressions:
a) M + (5x² -2xy) = 6x² +9xy - y²
M = 6x² + 9xy - y² - (5x² - 2xy)
Remove the parenthesis by mulplying each term of 5x² - 2xy by (-1) as (-1) is outside the parenthesis
= 6x² + 9xy - y² - 5x² + 2xy
Combine ( add or subtract) like terms.
= 6x² - 5x² + 9xy + 2xy - y²
= x² + 11xy - y²
Hint: Like terms have same variable with same power.
Here, like terms are (i) 6x² and (-5x²) (ii) 9xy and 2xy
b) (3xy - 4y²) - N = x² - 7xy + 8y²
3xy - 4y² = (x² - 7xy + 8y²) + N
3xy - 4y² - (x² - 7xy + 8y²) = N
3xy - 4y² - x² + 7xy - 8y² = N
3xy + 7xy -4y² - 8y² -x² = N
10xy -12y² - x² = N
Answer: N = 10xy - 12y² -x²
Write the equation of this line in slope-intercept form.
Answer:
Slope-Intercept Form: [tex]y = 2*x -3[/tex]
or
Point-intercept form: [tex]y-(-3)=2(x-0)[/tex]
Step-by-step explanation:
Method 1: Start from 1 point and then count the rise overrun.Slope-Intercept Form: [tex]y=mx+b[/tex]
Start from the Y-axis where [tex]b=-3[/tex] then rise/run to the next point. making that our slope.
Method 2: Using the point-intercept formPoint-intercept form: [tex]y-y_0=m(x-x_0)[/tex]
Solve the slope using the two points.
[tex](0,-3)[/tex] and [tex](2,1)[/tex] plug those values into the formula. Make [tex](x,y)=(0,-3)[/tex] and [tex](x_0,y_0)=(2,1)[/tex]
[tex]-3-1=m(0-2)[/tex]
[tex]-4=m(-2)[/tex]
[tex]m=-2[/tex]
[tex]y-(-3)=-2(x-0)[/tex]
ruben is buying bricks for a project. he knows that 5 bricks weigh 26 1/4. he wants to know the weight of 24 bricks
Answer:
the weight of 24 bricks is :
[tex]124\frac{4}{5}[/tex]
Step-by-step explanation:
[tex]26\frac{1}{4} =26+\frac{1}{4} =\frac{26\times 4}{4} +\frac{1}{4} =\frac{105}{4}[/tex]
It is clear that there is a proportional relationship between the number of bricks and their weights then :
[tex]\frac{26\frac{1}{4} }{5} =\frac{x}{24} \Longrightarrow \frac{\left( \frac{105}{4} \right) }{5} =\frac{x}{24} \Longrightarrow \frac{26}{5} =\frac{x}{24}[/tex]
[tex]\Longrightarrow x=\frac{26\times 24}{5} =\frac{624}{5} =124\frac{4}{5}[/tex]
What is the area of a rectangle that measures 4 meters wide and 6 meters long?
Answer:
The area of the rectangle is 24.
Step-by-step explanation:
To find the area it is Legth x Width
Therefore, 4 * 6 is 24
What is the measure of ∠3?
Question 2 options:
56°
73°
51°
107
Answer: The Answer for part 1 is 73 The answer for part 2 is 51
I hoped this helped also (im only 14 so if u see this ur doing great)
Step-by-step explanation:
Researchers at a drug company are testing the duration of a new pain reliever. The drug is normally distributed with a mean duration of 240 minutes (4 hours) and a standard deviation of 40 minutes. The drug is administered to a random sample of 10 people. (Round means, standard deviations, and z-scores to the nearest hundredth, if necessary.)
The population mean of the sampling by the researcher is 240, the standard deviation is 40 and the z score is -2.
What is a mean?It should be noted that the mean is the average of the numbers that are given in a population. The z score is -2 as it measures the relationship between the means.
The probability that the drug will wear off between 200 and 220 minutes will be:
= P(Z < -1.58) - P(Z < -3.16)
= 0.0571 - 0.0008
= 0.0563.
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Two Dimensional Shapes: Area
I really need help with this!!!
Answer:
area of the rectangle will be 175 square feet
Help!! I need the answer quick. Im really bad at fractions-
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
Let's evaluate ~
[tex]\qquad \tt \dashrightarrow \:6 \frac{5}{8} + 4 \frac{3}{4} [/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{53}{8} + \frac{19}{4} [/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{53 + 38}{8} [/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{91}{8} [/tex]
[tex]\qquad \tt \dashrightarrow \: 11\frac{3}{8} [/tex]
[tex]6 \frac{5}{8} + 4 \frac{3}{4} [/tex]
to find:the simplest form.
solution:[tex] \frac{53}{8} + \frac{19}{4} [/tex]
[tex] = \frac{(53 \times 4) + (19 \times 8)}{8 \times 4} [/tex]
[tex] = \frac{212 + 152}{32} [/tex]
[tex] = \frac{364}{32} [/tex]
[tex] = 11 \frac{3}{8} [/tex]
The most concise notation to use to define function parameters x and y as double is __________. Group of answer choices
HELP PLS HURRY!!!!!!
Answer:
The median of the data is 6
The Lower Quartile is 2
The upper quartille is 3
The mimimum value is 15
The maximum value is 9
the diameter of a semicircle is 24.6 feet. What is the semicircles radius?
Answer:
12.3 feet
Step-by-step explanation:
all you have to understand is that a radius is half the diameter....
24.6/2=12.3
( what’s the better deal ) please help me with this, i’ve been trying for a long time
Answer:
Brand A is the better deal!
Step-by-step explanation:
Let's start by comparing.
We know brand B has the following cost: 5 ounces = $3.75
10 ounces $7.50 and 16 ounces = $12
Now check the graph.
6 ounces cost $3
12 ounces cost $6
20 ounces cost $10
I don't think we need to look any further but brand A is the better deal!
The area of the regular hexagon is 10.4 in.2. a regular hexagon has side lengths of 2 inches and an area of 10.4 inches squared. an apothem is shown. what is the measure of the apothem, rounded to the nearest tenth of an inch? 1.3 in. 1.7 in. 2.0 in. 3.4 in.
Answer:
(b) 1.7 in
Step-by-step explanation:
The area of a regular polygon in terms of perimeter and apothem is given by the formula ...
A = 1/2Pa
For a hexagon, the perimeter is 6 times the side length, so this becomes ...
A = 1/2(6s)a = 3sa . . . . . for side length 's' and apothem 'a'
__
Solving for the apothem, we find ...
a = A/(3s)
For the given values of area and side length the apothem is ...
a = 10.4/(3·2) = 1.733... ≈ 1.7 . . . inches
The apothem, rounded to tenths, is 1.7 inches.
Answer:
1.7 in.
Step-by-step explanation:
E2020 Geometry B!! :3
Name the polynomial by degrees and the number of
terms.
7x^4+ 7x^3 +10x
Answer:
Fourth-degree trinomial
Step-by-step explanation:
7x⁴ + 7x³ + 10x
There are three terms, and the biggest degree (exponent) is 4. Therefore, this is a fourth-degree trinomial.
Note:
A polynomial with one term: monomialA polynomial with two terms: binomialA polynomial with three terms: trinomialA polynomial with four or more terms: polynomialHope this helps!
Please help!!! Eitan randomly selected volcanoes to travel to and study. After traveling, he had seen 13 cinder cone volcanoes,
18 shield volcanoes, and 6 stratovolcanoes.
Answer:
cinder cone: estimated probability = 0.35
shield: estimated probability = 0.49
stratovolcano: estimated probability = 0.16
Step-by-step explanation:
Given that he had seen 13 cinder cone volcanoes, 18 shield volcanoes, and 6 stratovolcanoes.
So the total number of volcanoes are 13 + 18 + 6 = 37
So the estimated probability of Cinder cone is \frac{13}{37}\approx 0.35
37
13
≈0.35
The estimated probability of Shield is \frac{18}{37}\approx 0.49
37
18
≈0.49
The estimated probability of Stratovolcano is \frac{6}{37}\approx 0.16
37
6
≈0.16
Below is the completed table
50pt:
You have 25 Hot Wheels vehicles. Your Hot Wheels race track has 5 lanes. What is the least amount of races needed to find the fastest Hot Wheels vehicle? What is the least amount of races needed to find the Top 3 fastest Hot Wheels vehicles?
the rectangular prism dimensione are in feet (ft). what is the volume, in cubic feet, of the rectangular prism?
Answer: 160
Step-by-step explanation: The formula for a rectangular prism is (Base)(Width)(Height). The length is 10 and the height and width are both 4 because it is a square.
jim has a dog. jim buys 6 bags of dog biscuits. there are 27 biscuits in each bag of dog biscuits. jims dog eats 5 dog biscuits each day. has jim brought enough dog biscuits for 4 weeks. you must show how you got your answer
Answer:
i will give it to you
Step-by-step explanation:
that's it for you dear
The relationship between food purchased and food eaten by dogs can be written as, 162 biscuits ≥ 80 biscuits
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
First, let's calculate the total number of dog biscuits that Jim has bought:
= 6 bags × 27 biscuits per bag
= 162 biscuits
Next, let's calculate how many biscuits the dog will eat in 4 weeks:
= 4 weeks × 5 biscuits per day
= 20 biscuits per week
20 biscuits per week × 4 weeks = 80 biscuits
So, Jim has bought 162 biscuits and his dog will eat 80 biscuits in 4 weeks. This means that Jim has brought enough dog biscuits for his dog for 4 weeks.
162 biscuits ≥ 80 biscuits
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PLEASE HELP!!
BRAINLIEST
Answer: 26 + 13 + 26 + 13 + x =180
Step-by-step explanation:
+
Write the equation of a line that passes through the points Which equations represent a line that passes through
shown in the table.
the points given in the table? Check all that apply.
y
B. y-2=-6(x + 10)
y-2=-1(x+10)
-10
2
y-1--2(x +4)
-4
1
y=-6x - 58
8
y=-x+
1
14
y=-2x+5
4
-1 -2
6
Answer:
2. y - 2 = -1/6(x + 10)
3. y - 1 = -1/6(x + 4)
5. y = -1/6x + 1/3
Step-by-step explanation:
hope this helps!