The classification of the numbers as counterexamples of the conjecture is given as follows:
12: no.19: no.22: yes.28: no.30: yes.The next number in the sequence is of 256.
Which numbers are counter example of the conjecture?The conjecture is defined as follows:
"Any number divisible by 2 is also divisible by 4"
Hence the counterexamples are the numbers that are divisible by 2 but not by 4, then they are classified as follows:
12: no. (divisible by both 2 and 4).19: no. (not divisible by 2, hence it cannot be a counterexample of the conjecture).22: yes. (divisible by 2 but not by 4).28: no. (divisible by both 2 and 4).30: yes. (divisible by 2 but not by 4).SequenceEach number in the sequence is given by the multiplication of the two previous terms, as:
1 x 2 = 2.2 x 2 = 4.4 x 2 = 8.8 x 4 = 32.Then the next number is calculated as follows:
32 x 8 = 256.
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you find a piece of bone that has a 14c/12c ratio that is 1/16 that of the atmospheric 14c/12c ratio. what is the approximate age of the bone?
The approximate age of the bone is 22920
The half-life of an isotope is characterized as the sum of time it takes for there to be half the beginning sum of the radioactive isotope present.
since we know for half time
N = N₀(1/2) n ..........1
where n is the new amount whereas N₀ is the initial amount and n is the number of half time
since the ratio of 14c:12c is 1/16
so the equation 1 gets converted to
N/No =(1/2)n
=>1/16 = (1/2)n
=>(1/2)4 = (1/2)n
=> n= 4
So the age of the bone will be 4* 5730 =22920
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You find a piece of bone that has a 14c/12c ratio that is 1/16 that of the atmospheric 14c/12c ratio. If the half-life of 14C is 57305730 years what is the approximate age of the bone?
May you guys/girls please help me I have to submit this befoer mid night and I do not fail because my parents will get me , so may y'all please help me out!?
Answer: 2/3
Step-by-step explanation:
1) First locate two points.
First, locate two points on the graph. For this example, I will choose (-2,0) and (1,2)
2) Find the distance between these two points.
We can find that from starting from (-2,0), we go right 3 and up 2. You can easily do this on paper by drawing a triangle.
3) Using the numbers we have before, find the rate.
To find the rate, we can use rise/run. Which will become 2/3.
Hello!
To find the slope of the line:
==> must find two points on the line
(x₁, y₁): (-2,0)
(x₂, y₂):(1,2)
[tex]Slope = \dfrac{2-0}{1--2} =\dfrac{2}{3}[/tex] <== Answer
Hope that helps!
0:3:4=9:y
Find y please
Based on the ratios given of 0.3 : 4 = 9 : y, the value of y can be found to be 120
How to find the value of y?From the given ratios of 0.3 : 4 = 9 : y, we can infer that these are equivalent ratios.
This means that y is to 9, what 4 is to 0.3.
The value of y can therefore be found by direct proportion:
0.3 : 4
9 : y
Cross multiplying gives:
0.3 y = 36
y = 36 / 0.3
y = 120
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The function y= (x - 4)^2 + 3 is a transformation of the function y = x^2 . How is the function’s vertex affected by the transformation?
The transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.
What do you mean by transformation of a function ?
The modification of a graphed function to create a different version of the parent function is known as transformation.
For the given condition :
The function is y = (x - 4)² + 3.
The above function is transformed from the parent function which is y = x².
We know that , the horizontal shift depends on the value of h. The horizontal shift and it is described as:
y = f (x + h)
Then , the graph of function will be shifted to left by h units.
and
y = f (x - h)
Then , the graph of function will be shifted to right by h units.
If we compare both functions i.e., y = (x - 4)² and y = f (x - h), their is a difference of -1 , it meant shift is right by 4 units.
Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:
y = f(x) + k
Then , the graph of function will be shifted up by k units.
and
y = f(x) - k
Then , the graph of function will be shifted down by k units.
Here , if we compare functions i.e., y = (x - 4)² + 3 and y = y = f(x) - k , we find out that the graph of function will be shifted upwards by 3 units.
Therefore , the transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.
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What pattern do you notice in these two
measurements,
10.3 cm and 103 mm?
Allison heads out on a three day sailing trip. On the first day, she sails 45 miles east and 15 miles north. On the second day,
she leaves from the exact location she ended the day before and makes it 35 miles east and 30 miles south. On the third
day, she gains another 15 miles east and 55 miles south. At the end of her final day, how far is she from her initial starting
point? Round your answer to the nearest whole number.
Answer:
118 miles
Step-by-step explanation:
Explanation in photo attached
I need to graph the line with slope 4 and y-intercept -4
The equation of a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. These values are given, then the equation of the line is:
[tex]y=4x-4[/tex]To graph it, we need to know the coordinates of at least two points on the line.
Whan x=0, then y is:
[tex]\begin{gathered} y=4\cdot0-4 \\ y=0-4 \\ y=-4 \end{gathered}[/tex]Thus, the first point is (0,-4).
When x=1, then y is:
[tex]\begin{gathered} y=4\cdot1-4 \\ y=4-4 \\ y=0 \end{gathered}[/tex]The second point on the line is (1,0).
If we draw these points in the coordinate plane, we can draw a line that passes through them, and this will be the graph of the line.
It looks like this:
Subject: Trigonometry, Evaluation of Functions
Hi, I only need help matching the graphs to the questions :) Brainly let's me attach a few graphs, this is 5/10, but i do have a similar question after this one with the rest of the graphs. Sorry!!
5. Given the following function, pick a graph with two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees. sin0 = 2/3
6. Given the following function, pick a graph with two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees. cos0 = -1/2
7. Given the following function, pick a graph with two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees. cot0 = 3/4
8. Given the following function, pick a graph with two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees. csc0 = 3/2
(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.
(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.
(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.
(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.
What is Quadrant?
A plane is split into four sections in the cartesian system by the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.A quadrant is an area or section of a cartesian plane that results from the intersection of two axes. It is employed to establish a point's location in a plane.(i) When sinФ=2/3
Ф=sin^(-1)(2/3)
Ф=41.81°,138.18°
So it lies in Ist and IInd quadrant.
A suitable graph is not provided here.
(ii) when cosФ=-1/2
Ф=cos^(-1)(-1/2)
Ф=120°,240°
So it lies in IInd and IIIrd quadrant.
A suitable graph is A and D.
(iii) when cotФ=3/4
Ф=cot^(-1)(3/4)
Ф=53.13°,233,13°
So it lies in Ist and IIIrd quadrant.
A suitable graph is E.
(iv) when cosecФ=3/2 or sinФ=2/3
Ф=sin^(-1)(2/3)
Ф=0.729°
So it lies in Ist quadrant.
A suitable graph is not provided here.
(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.
(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.
(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.
(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.
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If x=3yz^2, what is y in terms of x and z?
Two or more expressions with an Equal sign is called as Equation. y=x/3z^2 for equation x=3yz^2 in terms of x and z
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x equal to three y z square.
x=3yz²
We need to solve for y.
We need to separate y from other variables.
Divide both sides by 3z²
x/3z²=y
Hence y=x/3z² for equation x=3yz² in terms of x and z
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can someone please help solve this math problem with solution? thank u!
Answer:
the answer is 196
63^2-49^2
(7×9)^2 -(7×7)^2
7^2 (9-7)
7^2 ×2^2
49 × 4
196
Answer:
1568
Step-by-step explanation:
i simplified the expression
* 100 POINTS *
At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost
$2.35. One day, the receipts for a total of 172 cones and sundaes were
$294.20. How many cones were sold?
You purchase 8 gal of paint and 3 brushes for $152.50. The next day, you
purchase 6 gal of paint and 2 brushes for $113.00. How much does each
gallon of paint and each brush cost?
Two separate questions. 100 points for both answered. Brainliest if both answered.
Answer:
1.) 88 cones were sold
2.) $17.00 per gal of paint; $5.50 per brush
Step-by-step explanation:
1.) ($1.10(88)= $96.80) + ($2.35(84)= $197.40)= $294.20
2.) I have a really complicated process, and it's really late at night where I am
Answer:
For the first question, 88 cones were sold
For the second question, a gallon of paint costs 17 dollars and a brush costs 5.5 dollars (that is, 5 dollars and 50 cents).
Step-by-step explanation:
For the first question,
Let the number of ice cream cones be represented by the letter 'x'
And the number of sundaes be represented by the letter 'y'
[tex](1.10x + 2.35y) = 294.20 \: \: \: equ.2 \\ (x + y) = 172 \: \: \: equ.1[/tex]
Solving it simultaneously, subtract equ. 2 from equ. 1
[tex]0.10x - 1.35y = 122.20[/tex]
Making x the subject,
[tex]x = \frac{122.20 + 1.35y}{0.10} [/tex]
Substitute the value of x above in equ. 1
[tex] \frac{122.20 + 1.35y}{0.10} + y = 172[/tex]
L. C. M = 0.10
Multiply through by the L. C. M
[tex]122.20 + 1.35y + 0.10y = 17.2[/tex]
Collect like terms
122.20 - 17.2 = - 1.35y - 0.10y
105 = - 1.25y
[tex]y = \frac{105}{1.25} = 84[/tex]
Substituting the value of y in equ. 1
[tex]x + 84 = 172 \\ x = 172 - 84 \\ x = 88[/tex]
Therefore, 84 sundaes were sold and 88 ice-cream cones were sold.
For the second question, let paint represent 'p' and brush represent 'b'
[tex]8p + 3b = 152.5 \: \: \: equ2 \\ 6p + 2b = 113 \: \: \: equ1[/tex]
Solving simultaneously,
Subtract equ2 from equ 1
[tex]2p + b = 39.5 \\ b = 39.5 - 2p[/tex]
Substituting the value of b in equ1
[tex]6p + 2(39.5 - 2p) = 113 \\ 6p + 79 - 4p = 113[/tex]
Collect like terms
[tex]2p = 113 - 79 \\ 2p = 34 \\ p = 17[/tex]
Substituting the value of p in equ1
[tex]6(17) + 2b = 113 \\ 102 + 2b = 113[/tex]
Collect like terms
[tex]2b = 113 - 102 \\ 2b = 11 \\ b = 11 \div 2 \\ b = 5.5[/tex]
Therefore, a gallon of paint costs 17 dollars and a brush costs 5.5 dollars (i.e 5 dollars, 50 cents)
a pet store owner believes that dog owners spend more on average than cat owners on their pets. the owner randomly records the sales of 40 customers that said they only owned dogs and 40 customers that said they only owned cats. what is the correct decision and summary based on the excel output below? assume the populations are approximately normally distributed with unequal variances.
The correct decision and summary based on the excel output below is Standard Error =5.389361. and P-value=0.5364.
Two sample T summary hypothesis test:
[tex]u_{1[/tex] : Mean of Population 1
[tex]u_{2}[/tex] : Mean of Population 2
[tex]u_{1} -u_{2}[/tex] : Difference between two means
[tex]H_{0}[/tex] : [tex]u_{1} -u_{2}[/tex] = 0
[tex]H_{a}[/tex] : [tex]u_{1} -u_{2}[/tex]
0
(without pooled variances)
Hypothesis test results:
Difference = u1-u2
Sample Diff=3.34725
Standard Error =5.389361.
DF=77.988073
T-Stat=0.62108476
P-value=0.5364
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INSTANT HELP PLEASE PLEASE PLEASE
What is the absolute value of –8? Use the number line to help answer the question.
The absolute value of (-8) would be 8 on number line.
The absolute value of any number represented on number line is given as the distance of the number from zero on a number line, when counted on whichever side it is present that is either negative or positive. In mathematical notation, absolute value is defined as the modulus of the number, enclosed in two straight lines. For example: |-8| or |8| would have absolute value 8 even though both the numbers are represented on negative and positive side of zero respectively on the number line. The absolute value of any number which is also a real number is the non-negative value of that number irrespective of its sign. Number line figure is attached below.
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A savings account increases from 200$ to 208$. What is the percent increase of the savings account?
I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answer:
Step-by-step explanation:
To find the cost of the apples, simply multiply the cost by how much Derek buys. So: 3.8 * 1.35= 5.13.
So, For Part A the answer is A.
For Part B: We need to find the total cost of both apples and oranges. We already know the total cost of apples is 5.13. We need to find the cost of oranges.
We multiply:
5.2* 1.45= 7.54
Now, add the totals together: 7.54+5.13
The total is 12.67.
If Derek payed with a 20 dollar bill, we would subtract 20 with 12.67.
The answer is 7.33. So the answer is A.
You are given expression12^8/12^4 to simplify
Answer:
12^4
Step-by-step explanation:
because dividing exponent divide when the number in this case 12 don’t change so 8-4=4 so 12^4 or 20736
What’s 8(2y-6x)=4+2x as a sentence?
Answer:
8 times 2y minus 6x is equal to 4 plus 2x
PLS HELP ASAP (100 POINTS) The equation for the line of best fit for change in temperature, y, to amount of snow, s, is given by ŷ = − 2.6s + 1.1. On Friday, the observed amount of snow was 1.3 inches and the temperature change was 1.2 degrees. Find and interpret the residual.
1.08; The line of best fit underpredicts the temperature change.
−1.08; The line of best fit overpredicts the temperature change.
−3.48; The line of best fit overpredicts the temperature change.
3.48; The line of best fit underpredicts the temperature change.
residual = 3.48
The line of best fit underpredicts the temperature change.
============================================================
Explanation:
If s = 1.3, then ŷ is...
ŷ = -2.6s + 1.1
ŷ = -2.6*1.3 + 1.1
ŷ = -2.28
This is the estimated or predicted y value based on the input s = 1.3
Let's now compute the residual
e = residual error
e = (observed y value) - (predicted y value)
e = y - ŷ
e = 1.2 - (-2.28)
e = 1.2 + 2.28
e = 3.48 is the residual
A positive residual means that the predicted y value, aka ŷ, is an underestimate compared to the true observed value. In other words, the observed y value is higher than the ŷ value. Therefore, the line of best fit under-predicts the temperature change.
the vertices of PQR are P(-5,1), Q(-4,6), and R(-2,3), graph P"Q"R" after a composition of the transformations in the order they are listed.
SOLUTION
We are told to translate; (x, y) to (x -8, y). This means we have to add - 8 to each value of x in P(-5,1), Q(-4,6), and R(-2,3).
In P(-5,1), x = -5 and y = 1
In Q(-4,6), x = -4 and y = 6 and
In R(-2,3), x = -2 and y = 3
[tex]\begin{gathered} P(-5,\text{ 1) translates to (-5 -8, 1) }\rightarrow P^i(-13,\text{ 1)} \\ Q(-4,\text{ 6) translates to (-4 -8, 6) }\rightarrow Q^i(-12,\text{ 6)} \\ R(-2,\text{ 3) translates to (-2 -8, 3) }\rightarrow R^i(-10,\text{ 3)} \end{gathered}[/tex]For the dilation centered at the origin k =2, simply multiply the value of k, which is 2 into the translations.
[tex]\begin{gathered} At\text{ K = 2, }P^i(-13,\text{ 1) }\rightarrow\text{ }2(-13,\text{ 1) }\rightarrow\text{ }P^{ii}(-26,\text{ 2)} \\ Q^i(-12,\text{ 6) }\rightarrow\text{ }2(-12,\text{ 6) }\rightarrow\text{ Q}^{ii}(-24,\text{ 12)} \\ R^i(-10,\text{ 3) }\rightarrow\text{ }2(-10,\text{ 3) }\rightarrow\text{ R}^{ii}(-20,\text{ 6)} \end{gathered}[/tex]A rectangular park is 40 yards wide. Then a city planner designs a path that is 1 yard wide to run all the way around the park. Now the area of the park plus the path is 4200 yd.² how long is the park not counting the path?
The park is 98 yards long, not counting the path.
We are having a park that is rectangular in shape.The width of the rectangular park is 40 yards.The city planner designs a path that is 1 yard wide to run all the way around the rectangular park.The area of the rectangular park plus the path is 4200 square yards.Let the length of the rectangular park be "x".The width of the rectangular park, including the path, is 42 yards.The length of the rectangular park, including the path, is "x+2" yards.The area of the rectangular park, including the path, is the product of the length and its breadth.42*(x+2) = 4200x+2 = 100x = 98Thus, the length of the rectangular park is 98 yards.To learn more about area, visit :
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Please help
1: A rectangle has a length of 4.3 cm and a perimeter of 14.8 cm. Find the width of the rectangle.
Cm
2: Lanie has 33 total games downloaded on her phone and her laptop. Her laptop has 7 less than 3 times the number of games that are on her phone. How many games does Lanie have on her phone?
Enter your answer in the box.
games
1. The width of the rectangle is 3.1cm
2. The number of games in Lanie's phone is 10
How to determine the valueThe formula for calculating the perimeter of a rectangle is expressed as;
Perimeter = 2(l + w)
Where;
L is the length of the rectanglew is the width of the rectangleGiven the values as length = 4.3cm and perimeter = 14. 8cm
Substitute the values into the formula
14. 8 = 2(4.3) + 2w
expand the bracket
14. 8 = 8. 6 + 2w
collect like terms
2w = 14. 8 - 8.6
2w = 6. 2
Divide through by the coefficient of w
w = 6.2/2
w = 3.1 cm
Let the number of games in Lanie's phone be x
x + 3x - 7 = 33
collect like terms
4x = 33 + 7
4x = 40
Divide both sides by 4
x = 40/4
x = 10 games
Hence, the width is 3.1cm
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what is the constant porpotionality of y=7.29x
Answer:
7.29
Step-by-step explanation:
the equation of proportionality is
y = kx ← k is the constant of proportionality
y = 7.29x ← is in this form with k = 7.29
Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
HELP PLEASE ILL MARK U BRAINLIEAST!!
this is for geometry can someone please help me find the missing angles?
Answer:
x = 50° , y = 40°
Step-by-step explanation:
x and 40° form a right angle and sum to 90° , that is
x + 40° = 90° ( subtract 40° from both sides )
x = 50°
x and y form a right angle and sum to 90° , then
x + y = 90°
50° + y = 90° ( subtract 50° from both sides )
y = 40°
Mr. Byars is buying a new tie from Macy's. It says the tie costs $15.00 but there is a sign above it that says 25% off. How much will the tie cost before taxes?
Before taxes, the tie will cost $11.25
What is a discount?Discounts are price cuts made by store owners on goods or services that would otherwise be sold for the indicated price. Usually, this portion of the rebate is given to increase sales or get rid of extra inventory. The List Price, sometimes referred to as the Marked Price, is the cost of a product as declared by the seller or manufacturer, excluding any discounts.
The final price at which a product is actually sold is the selling price, which includes any discounts or price drops from the list price. Off or reductions are frequent terms used to describe discounts. Note that the marked price of the item is always used to calculate the discount (list price).
Discount = List Price - Selling Price
Discount (%) = (Discount/List Price) × 100
According to the question,
List price = $15.00
Discount % = 25 %
Cost of the tie before taxes = [tex]List \: price \:\frac{ (100 - Discount \%)}{100}[/tex]
⇒ [tex]\text{\$15.00}\: \frac{(100-25)}{100}[/tex]
⇒ [tex]\text{\$15.00}\: \frac{75}{100}[/tex]
⇒ [tex]\text{\$15.00}\: \frac{3}{4} = \text\:{\$15.00 \times 0.75}[/tex]
⇒ $11.25
Therefore, before taxes, the tie will cost $11.25
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Each Marble bag sold by Rita's Marvel company contain two green marbles or every three orange marbles if a bag has 15 orange marbles how many green marbles does it contain
The number of green marbles in the bag is 10
How to determine the number of green marbles?From the question, we have the following parameters:
Green marble = 2Orange marble = 3Total number of orange marbles in a bag = 15The given parameters can be represented using the following ratio
Ratio = Green marble : Orange marble
So, we have
Green marble : Orange marble = 2 : 3
When there are a total number of 15 orange marbles in a bag, then we have
Green marble : 15 = 2 : 3
Multiply ratio by 5
Green marble : 15 = 10 : 15
By comparison, we have
Green marble = 10
Hence, there are 10 green marbles in the bag
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PLS HELP I REALLLY NEED IT ITS BEEN UP FOR SO LONG ITS ALMOST DUE PLEASE HELP
Answer:
400
Step-by-step explanation:
yw
Answer:
1. 26 2/3
2. 13/5
3. 2000,3000,4000
Mrs. Hull calculated the measure of central tendencies for the two plants in her science class. The measures are recorded below.Which measure of central tendency would be the best for Mrs. Hull to use if she wanted to argue that there is a difference between the plants?
The measure of central tendency that would be the best for Mrs. Hull to use if she wanted to argue that there is a difference between the plants is the median.
What is central tendency?The definition of central tendency is the statistical metric that identifies a single value as representative of a whole distribution. It strives to provide a complete explanation of the data. It is the single most representative number from the obtained data.
A measure of central tendency is a single value that seeks to represent a set of data by identifying the data's central position. The mode measurement is the one with the highest frequency.
When plants are placed in a circle, the median is the measurement of the middle plant provided in descending be order of sizes.
When there are a few extreme scores in the data distribution, the median is the recommended measure of the central tendency.
In conclusion, the correct option is the median.
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what is the y- intercept of y=4+x
Answer: the y-intercept of this equation is (0,4)
Step-by-step explanation: