For the first 3 images.
a) The linear equation is the one in option A:
y = x
b) The linear equation is the one in option B:
y = (1/2)*x + 3
c) The correct option is C, the slope of scenario 1 is 60
How to identify the linear equations?A general linear equation is:
y = a*x + b
So we have a polynomial of degree 1, this means that there can be at most two terms, one that depends of x, and other that is a constant.
From the first list the only linear equation is y = x.
none of the others depend linearly with x.
From the second list the only option that is a linear equation is B.
y = (1/2)*x + 3
Where you can see two terms, the first one depends linearly of x and the second one is a constant.
For the third image.
If you evaluate the equation for scenario 2 in x = 1, you get:
y = 50*1 = 50
So in one hour, you travel 50 miles.
While on scenario 1, on one hour you travel 60 miles.
Then the speed is greater on scenario 1, where the slope is 60, so the correct option is C.
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Out of the 25 families that Tod deliver magazines to on Friday, 10 families were home and the test were away. How is the fraction of magazines that were delivered to families who were home written as a decimal?
The fraction of magazines that were delivered to families who were at home is 0.4 if total number of families are 25 out of which 10 were at home and rest are away.
Total number of families = 25
Families at home = 10
So the ratio of the required families
= Families at home/total number of families
= 10/25
= 2/5
To convert the fraction into decimal form, we have to divide and we get
= 0.4
Hence, the number of families in decimal to which magazines got delivered are 0.4
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The height of a building is proportional to the number of floors. The figure shows the height of a building with 7 floors. Complete parts a and b.
well, the height of the building is 119 feet, as we can see right there on the picture. Now, there are 7 floors from the ground up, so the ratio is simply
[tex]\cfrac{\stackrel{overall~height}{119}}{\underset{floors}{7}}\implies \cfrac{17}{1}\implies \stackrel{unit~rate}{17}\hspace{5em}\cfrac{17~feet}{1~floor}\qquad \begin{array}{llll} \textit{each floor is}\\ \textit{17 feet high} \end{array}[/tex]
Tanvi and her friend Beth are making cookies for their school's cookie swap. Tanvi mixes 1
cup of chocolate chips and 3 cups of plain sugar cookie dough in a small bowl. Beth mixes 2
cups of chocolate chips and 6 cups of plain sugar cookie dough in a larger bowl. Once the
cookies are baked, the girls are ready for a chocolaty snack. Whose batch of cookies was
more chocolaty?
Correct statement for whose batch of cookies was more chocolaty is option (c) Neither, The batches were equally chocolaty
Consider Tanvi's cookies
Number of cups of chocolate chips = 1 cups
Number of cups of plain sugar = 3 cups
Total number of cups = 1 + 3 = 4 cups
Then the fraction of chocolate = 1 / 4
= 0.25
Consider Beth's cookies
Number of cups of chocolate chips = 2 cups
Number of cups of plain sugar = 6 cups
Total number of cups = 2 + 6 = 8 cups
Then the fraction of chocolate = 2 / 8
= 1 / 4
= 0.25
Hence, correct statement for whose batch of cookies was more chocolaty is option (c) Neither, The batches were equally chocolaty
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whats the answer
icl hurry up
The area of the circle in 2 decimal place is 394.13 cm².
How to find the area of a circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. The area of a circle is π multiplied by the square of the radius.
Therefore,
area of a circle = πr²
where
r = radius
Therefore,
area of a circle = πr²
r = 11.2 cm
area of a circle = 3.142 × 11.2²
area of a circle = 3.142 × 125.44
area of a circle = 394.13248
area of a circle = 394.13 cm²
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When solving: 1,175 ÷ 5, using partial quotients, how would you decide which power of 10, when multiplied by 5, should be subtracted first?
I need a step by step example please
Using partial quotient, the place value while subtracting is determined by the dividend.
The place value should never be more than the dividend not up to a tens place value less than the dividend's place valueHow to perform division using partial quotientsdivisor dividend quotient multiplication subtraction new dividend
5 1175 200 200 * 5 = 1000 1175 - 1000 = 175
5 175 30 30 * 5 = 150 175 - 150 = 25
5 25 5 5 * 5 = 25 25 - 25 = 0
The quotient is then added as
= 200 + 30 + 5
= 235
Assuming the quotient was written 2. While subtracting, the dividend for the first value (1175) is in thousands. placing the the 2 in thousands makes it more than the dividend hence the 2 should be in hundreds
1175 - 2000 incorrect
1175 - 200 correct
for the second stage
175 - 150 correct (since 150 < 175)
last stage
25 - 25
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Find the distance between the point (5,12) and the line y = 5x + 12 (rounded to the nearest hundredth).
A. 1.36 units
B. 2.19 units
C. 4.81 units
D. 4.90 units
The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units
How to find the distance between a point and a line?
If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0
Then the distance of a point from the line is given by the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
Given: the point (5,12) and the line y = 5x + 12. The line can be written as
5x-y+12 = 0. Thus:
x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)
d = 25/√26 = 4.90 units
Therefore, the distance between the point and the line is 4.90 units. Option D is the answer
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Given the line below. a. Determine the slope of the line. Show all work on how you found the slope or determined the slope from the graph. b. In two or more complete sentences, explain why it is possible or it is not possible to write the equation of the given line in the traditional version of the point-slope form of a line.
The slope of the vertical line in the given graph is undefined.
The equation of the line is x = 2.
How to Write the Slope of a Vertical Line?The slope of a vertical line is usually undefined because the horizontal change (change in x) is equal to 0. Thus, we cannot divide a number by 0. Therefore, the slope of a vertical line is undefined.
The line given is a vertical line that intersects the x-axis at 2. Its slope is undefined. Since its slope is undefined, it is impossible to write the equation of the vertical line in the traditional version of the point-slope form. Hence, it is written as x = b, where b is the point where the x-axis is intersected by the line.
Slope of the line is undefined. The equation is x = 2.
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The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a
mean diameter of 22 mm and a standard deviation of 2.5 mm. What proportion of such tomatoes have a diameter
greater than 25 mm?
Find the z-table here.
O 0.1151
O 0.1539
0.8461
0.8849
Hi, that would be option 3 if I am correct.
Hope this helps.
Answer:
0.8461
To find the proportion of cherry tomatoes that have a diameter greater than 25 mm, we need to determine the proportion of the distribution that falls above this value. We can do this by converting the diameter of 25 mm to a z-score using the formula:
z-score = (value - mean) / standard deviation
For a diameter of 25 mm, the z-score is (3 - 22) / 2.5 = -2.8.
We can then use a z-table to find the proportion of the distribution that falls above this value. The z-table gives the area under the standard Normal curve to the left of a given z-score. To find the proportion of the distribution above the diameter of 25 mm, we need to find the area to the right of -2.8. From the z-table, we find that the area to the right of -2.8 is 0.8461. Therefore, approximately 84.61% of cherry tomatoes produced by the farm have a diameter greater than 25 mm.
[tex]f(x) = -x × -x - 2[/tex]
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x)=x²-18x+67
find the number of units manufactured at a cost of $8450.
The number of units manufactured at a cost of $8450 is x = 101.
What is a function?A function is a relation where every input is connected to only one possible output from a set of available inputs.
The given function is C(x) = x² - 18x + 67.
To find the number of units manufactured at a cost of $8450, substitute C(x) = 8450 into the given equation and solve for x:
8450 = x² - 18x + 67
x² - 18x + 67 - 8450 = 0
x² - 18x - 8383 = 0
x² - 101x + 83x - 8383 = 0
x(x - 101) + 83(x - 101) =0
(x + 83)(x - 101) = 0
(x + 83) = 0 or (x -101) = 0
x = -83 or x = 101
Since the number of manufactured units cannot be negative, it follows
x = 101.
Hence, the number of units manufactured at a cost of $8450 is x = 101.
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need help pls thank you
The Venn diagram of visit to Paris is completed and attached
The probability is 22/30
How to complete the Venn diagramThe Venn diagram is completed using the principle of inclusion exclusive
let x be the number that visited both Eiffel tower and Notre-Dame Cathedral
The calculation is done by counting as the universal set is equal to the numbers of the people
30 = 13 - x + x + 16 - x + 7
30 = 13 + 16 + 7 - x
30 - 37 = -x
-7 = -x
x = 7
ET only = 13 - 7 = 6
NDC only = 16 - 7 = 9
The probability
= (6 + 9 + 7) / 30
= 22/30
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If you can do your homework at a rate of 9.3 minutes for every problem, how
many problems could be done after 8.13 hours? Round to a whole number.
Answer:
52 problems
Explanation:
8.13 hours
8.13 hours × 60 minutes = x minutes
487.8 minutes
487.8 minutes ÷ 9.3 minutes = 52.4516129 problems
Height (in.)
12
10
8642
Candle Height
0123456
Time (h)
12" candle:
8" candle:
12" candle
Step 1: Identify two points and 41
Step 2: Find the slope and simplify
Step 3: Label the answer with units
8" candle
Step 1: Identify two points and
Step 2: Find the slope and simplify
&
Step 3: Label the answer with units
By using the formula for slope of a line, it can be calculated that
For 12'' candle
Two points are (1, 10) and (4, 2)
Slope = [tex]-\frac{8}{3}[/tex]
For 8'' candle
Two points are (3, 4) and (6, 0)
Slope = [tex]-\frac{4}{3}[/tex]
What is slope of a line?
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta\\[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
Here,
For 12'' candle
Two points are (1, 10) and (4, 2)
Slope =
[tex]\frac{2-10}{4-1}\\-\frac{8}{3}[/tex]
For 8'' candle
Two points are (3, 4) and (6, 0)
Slope =
[tex]\frac{0-4}{6 - 3}\\-\frac{4}{3}[/tex]
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A circle in the x, y-plane has the equation x^2+y^2-10x+34y-527=0x. If the y-coordinate of a point on the circle is -38, what is the point's positive x-coordinate?
The Center of the circle is (5, -17) and radius of the circle is 29 units.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
We have given circle in the x, y-plane has the equation;
x² + y² -10x + 34y - 527 = 0
Now we will convert this equation to the standard form of the circle as;
x² -10x + y² + 34y = 527
[x² - 2(5)x] + [y² + 2(17)x] =527
[x² - 2(5)x + 5²] + [y² + 2(17)y + 17²] = 5² + 17² +527
(x - 5)² + (y + 17)² = 25 + 289 +527
(x - 5)² + (y + 17)² = 841
(x - 5)² + (y + 17)² = 29²
By comparing this equation with the standard equation of the circle →
That is; (x - h)² + (y - k)² = r²
The Center of the circle is (5, -17) and radius of the circle is 29 units.
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what expression is equivalent to cd√22
ONE OF THESE ANSWERS
a. √22c^d^
b. √22cd
c. √22c4d4
d. √22cd^
The expression equivalent to cd[tex]\sqrt{22}[/tex] is b)[tex]\sqrt{22}[/tex]cd.
What is expression?
Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it. a collection of symbols, numbers, and operators (like and) that represent the value of something. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
Here the given expression is ,
=> cd[tex]\sqrt{22}[/tex] which is ,
=> c×d×[tex]\sqrt{22}[/tex]
=>[tex]\sqrt{22}[/tex]cd.
Therefore the expression equivalent to cd[tex]\sqrt{22}[/tex] is b)[tex]\sqrt{22}[/tex]cd.
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Hey! Try to answer this for 15 points! It's urgent!
Substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place.
I=PRT; I=1920, P=24,000, R=0.04 (Simple interest formula)
The value of the unknown t, by susbtituting the values into the formula is 2
What is simple interest?Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit.
To calculate the unknown variable in the equation, we do substitution into the formula below.
Formula:
I = PRT............. Equation 1Given:
I = 1920R = 0.04P = 24000Substitute these values into equation 1
1920 = 0.04×24000×t1920 = 960tt = 1920/960t = 2Hence, the value of the unknown is 2.
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Identify the variable expression for “Two times the difference of x and the square of 7”
Answer:
Step-by-step explanation:
The square of 7 is:
[tex](7)^2=49[/tex]
The difference x and square of 7 is:
[tex]x-49[/tex]
Two times the difference of x and square of 7 is:
[tex]2(x-49)[/tex]
PLEASE HURRY
Statements. reasons
1. YW Perpendicular to XZ, 1. Given
YW bisects XZ.
2. XW congruent to ZW. 2. ______
3.
right angles, so
congruent to
4. YW is congruent to. 4. _____
YW
5. Triangle WXY is. 5. _____
congruent to triangle
WZY
6. XY is congruent to ZY. 6. ____
TRIANGLE BISECTORS
7. Fill in the missing statements and reasons in the proof. 4 points; 1 point each
Given: YW XZ XY bisects XZ
Prove: XY≅ZY
The missing reasons that completes the proof are:
2. Definition of bisection
4. Reflexive property
5. SAS
6. CPCTC
How to Fill in the Missing Statements and Reasons in a Proof?A proof usually contains the statements on one column, and the reason that justifies each of the statement on another column.
To prove that sides XY is congruent to side ZY, the following are the statements and reasons that completes the proof:
Statement Reason
1. Line YW ⊥ line XZ; YW bisects XZ. 1. Given
2. Side XW ≅ side ZW 2. Definition of bisection
3. Angles YWX and YWZ, 3. Definition of perpendicular
so ∠YWX ≅ ∠YWZ
4. Side YW ≅ Side YW 4. Reflexive property
5. Triangles WXY and WZY are 5. SAS postulate
Congruent
6. 6. XY ≅ ZY 6. CPCTC
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What function is being described Justify each part of your function, explaining how you determined it.
My function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2. It has end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity. The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.
What is the end behavior of a polynomial function?The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.
Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.
The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.
The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.
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2. Estimate the subtotal for a $14.00 shirt, a $27.00 pair of pants, and a $62.00 jacket.
Answer:
$100
Step-by-step explanation:
Round each price to the nearest 10 and add.
$10 + $30 + $60 = $100
Answer: $100
Convert 80.44 meters/seconds into miles/hour. Round to 1 decimal.
Answer: 80.44 meters/seconds/ to 179.9391553 miles/hours
Step-by-step explanation: Example: 80.44X2.2369362921=
1 m/s = 2.3469362921 that gives you the above answer.
Thomas has $1,300 to paint the figure below. If it costs $5 for every square unit of paint, will Thomas have enough money to paint the entire surface area (outside only) of the figure?
Using the dimensions of the figure, Thomas will have enough money to paint the surface area.
What are the dimensions of a figure?The dimensions of a two-dimensional figure are its lengths and widths.
The product of the length and width results in the surface area, which is stated in square units.
How is the conclusion reached?Since Thomas has $1,300, and the squared surface of the figure is equal to 260 square units, when $5 is multiplied into 260, the product is $1,300.
This amount is equal to the money available to Thomas for the painting.
If the dimensions produced a surface area of more or less than 260 square units, we can calculate Thomas' ability to complete the painting based on the information.
The length of the figure is given as 20 units.
The width of the figure is given as 13 units.
The surface area of the figure = 260 square units
The cost of paint per square unit = $5
The total cost for painting the figure = $1,300 ($5 x 260)
The amount available to Thomas for the painting = $1,300
Difference between the total cost and the available amount = $0.
Thus, we can assert that, given the dimensions of the figure, Thomas can complete the painting with the available funds.
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Question Completion:Length of the figure = 20 units
Width of the figure = 13 units
Help me please!!!!!!
The digit in the ones place is 7, The digit in the tenths place is 6, and The digit in the tens place is 4.
What do you mean by place value?
In mathematics, each digit in an integer has a place value. Place value refers to the value that a digit in a number represents dependent on where it sits within the number.
For instance, 700 or 7 hundreds is the place value of the number 7. But 7,432 has a place value of 7,000, or 7,000. The place value of the digits changes despite the fact that they are the same in both numbers due to their position.
The chart is attached in the answer by which we can conclude that The digit in the ones place is 7, The digit in the tenths place is 6, and The digit in the tens place is 4.
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Simplify 4 – 8 × 2.
Question 18 options:
A)
–8
B)
–10
C)
–4
D)
–12
Answer:
D
Step-by-step explanation:
4 - 8 × 2 ← perform multiplication before doing subtraction
= 4 - 16
= - 12
2x2x2x2.5 divided 1.2+120
Answer:
i believe it's 136.666666667
Step-by-step explanation:
Two players A and B roll a pair of dice in turn, with A rolling first. A's objective is to obtain a sum of 5 and B's objective is to obtain a sum of 4. The game ends when either player reaches his or her objective and that player is declared the winner:
Calculate the probability that A is the winner.
Calculate the expected number of rolls of the dice
A probability is given by the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes when a pair of dice is rolled is given by:
6² = 36.
As each throw has six outcomes.
The outcomes with a sum of 5 are given as follows:
(1,4), (2,3), (3,2), (4,1).
Hence 4 outcomes, and the probability that player A wins is of:
p = 4/36 = 1/9.
The outcomes with a sum of 4 are given as follows:
(1,3), (2,2), (3,1).
Hence the probability that B wins is given by:
p = 3/36 = 1/12.
Then the probability that a player wins on each trial is given by:
p = 4/36 + 3/36 = 7/36.
Then the expected number of rolls is given as follows:
E(X) = 1/(7/36) = 36/7 = 5.1 rolls.
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What amount will Chris and Allison report for taxable interest on their Form 1040? The couple's partially completed Form 1040, page 1, is shown below. You may use the form to assist you in answering this question.
Answer:
Step-by-step explanation:
Write the standard form of the complex number
sqrt 108[cos(−30°) + i sin(−30°)]
Answer:
[tex]9-3\sqrt{3} i.[/tex]
Step-by-step explanation:
[tex]1. \ cos(-30)=\frac{ \sqrt{3}}{2}; \ sin(-30)=-0.5;[/tex]
[tex]2. \sqrt{108} (cos(-30)+isin(-30))=\frac{\sqrt{108} \sqrt{3}}{2}-i*\sqrt{108}*0.5=9-3\sqrt{3} i.[/tex]
A Chevrolet Sonic Hatchback costs $14,800.00. With a 12 % down payment, you can have an amortized loan for 6 years at a rate of 4.5%. What will the monthly payment be? car cost in total, money paid in interest
Based on the loan amount and the number of years, the monthly payment, total cost of the car, and amount of interest to be paid are as follows:
Payment each month: $206.74Total cost of the car was $14, 885.$1, 861.52 must be paid in interest.How do I calculate the required interest?Find the loan amount first:
= Car expense x ( 1 - down payment percent)
= 14, 800 x ( 1 - 12%)
= $13024
the monthly rate and the total number of periods, then:
Daily rate calculation:
= Annual Rate / Twelve-Month Period
= 4.5% / 12
= 0.375%
Counting periods:
= Years multiplied by Months per year
6 years times 12
72 months
These enable the following formula to determine the monthly payment:
= Loan Amount / 72-period Annuity Present Value Interest Factor of 0.375%
13024 / 62.995976235992
= $206.74
Total amount repaid on the auto loan:
= Amount Due Each Month x The Number of Months
= 206. 74 x 72
= $14, 885. 52
Accordingly, the total amount of interest paid was:
= Amount borrowed - Amount paid toward the car's cost
= 14, 885.52 - 13, 024
= $1, 861.52
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