The two factors of the first number 28 that their sum is will be equal to the second number 16 are 2 and 14.
Factor of a numberFactor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.
The first number 28 have the following factors:
1, 2, 4, 7, 14, and 28.
the factors 2 and 14 are the factors we need because;
2 × 14 = 28
2 + 14 = 16
Therefore, 2 and 14 are the two factors of 28 that their product is the first number 28 and their sum is the second number 16.
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Following the steps below, what is the next step in constructing a line perpendicular to a segment? Start with a line and point K on that line. Set the compass's width to a medium setting. The actual width does not matter. Without changing the compass's width, mark a short arc on the line at each side of the point K, forming the points P and Q. These two points are the same distance from K because you did not change the width of the compass. ? Using the straight edge, draw a line from K to where the arcs cross. Without changing the compass's width, repeat from the point Q so that the two arcs cross each other, creating the point R. From P, mark off a short arc above K. Increase the compass to almost double the width (the exact setting is not important).
''Start with a line and point K on that line'' is the next step in constructing a line perpendicular to a segment
What is perpendicular line?
Whenever two lines cross at a right angle, they are perpendicular or orthogonal. All four of the angles created by two perpendicular lines are 90 degrees.
If and only if the slope product of two non-vertical lines is negative one, those lines are perpendicular. In other words, two perpendicular lines' slopes are the negative reciprocals of one another. A vertical line is perpendicular to only horizontal lines and has an infinite slope (which have slope 0).
This provides a way to determine if two lines are parallel by using their equations. Additionally, this enables us to discover the equations of lines that are perpendicular to another line.
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3x + 5 =− 7 solve for x
Answer:
x = -4
Step-by-step explanation:
3x + 5= -7
bring the 5 to the other side
3x = -12
divide both sides by 3
x = -4
Answer:
[tex] \sf \: x = - 4[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 3x + 5 = -7
Then the value of x will be,
→ 3x + 5 = -7
→ 3x = -7 - 5
→ 3x = -(7 + 5)
→ 3x = -12
→ x = -12 ÷ 3
→ [ x = -4 ]
Hence, the value of x is -4.
Explain why multiplying by 8/3 gives the same result as first multiplying by 8 and then multiplying by 1/3
Because by multiplying by 8/3, you're multiplying by 1/3, 8 times. (8*1/3=8/3)
A ball is rolled at a speed of 12m/sec after 40 seconds it comes to a stop . What is the acceleration of the ball ? Answer to nearest hundredth
Therefore , the solution of the given problem of speed comes out to be
the ball accelerates at 0.33 m/s2.
What is speed?Speed is a pace that is measured in terms of how far an object travels in a given amount of time. Speed can be measured in a wide range of ways, including in miles an hour, laps every minute, and meters a second. There are connections between the units of time, distance, and speed. Three ways of expressing the relationship are
d = rt, r = dt, and t = dr.
Given -
The ball's initial speed is 0 meters per second.
v = 12 m/s is the ball's final speed.
36 seconds were used.
Determine the ball's acceleration.
Solution:
=> A = (v-u)/t
=>A = (12-0)/36
=> A = 12/36
=> A =1 /3
=> A = 0.33 m/s²
Consequently, the ball accelerates at 0.33 m/s2.
Therefore , the solution of the given problem of speed comes out to be
the ball accelerates at 0.33 m/s2.
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(25 points) find x and y of the heptagon more info in the picture above
Answer:
x = 128.57°
y = 51.43°
Step-by-step explanation:
x = (n - 2) × 180°/n = (7 - 2) × 180°/7 = 900/7° = 128.57°
x + y = 180
y = 180° - 128.57°
y = 51.43°
The tallest tree in the world is in redwood California as of April 2019 if you’re standing on the trail 220 feet from the bottom of the tree you have to look up it is 60° angle to see the top how tall is the tree
Step-by-step explanation:
AB is the height of tree
angle is 60 degree
bc is the bottom of tree
A baker has three banana muffin recipes. Recipe A uses 3 bananas to make 12 muffins. Recipe B uses 5 bananas to make 24 muffins. Recipe C uses 11 bananas to make 48 muffins.
Rutendo tried to order the recipes from least to greatest by bananas per muffin, but he made a mistake. Here's his work:
\begin{aligned} \dfrac{12}{3}&=4\\\\ \dfrac{24}{5}&=4.8\\\\ \dfrac{48}{11}&\approx 4.36\\\\ \stackrel{\text{Least}}{\underbrace{4}_\text{Recipe A}} &< \underbrace{4.36}_\text{Recipe C} < \stackrel{\text{Greatest}}{\underbrace{4.8}_\text{Recipe B}} \end{aligned}
3
12
5
24
11
48
Recipe A
4
Least
=4
=4.8
≈4.36
<
Recipe C
4.36
<
Recipe B
4.8
Greatest
What was Rutendo's mistake?
Choose 1 answer:
Answer: Rutendo's mistake was ordering the recipes from least to greatest by bananas per muffin by comparing the number of bananas in each recipe rather than the number of bananas per muffin. ✅
Step-by-step explanation:
By dividing the number of bananas used in each recipe by the number of muffins, he would have been able to determine which recipe uses the least amount of bananas per muffin.
Recipe A: 3/12 = 0.25 bananas per muffin
Recipe B: 5/24 = 0.208 bananas per muffin
Recipe C: 11/48 = 0.229 bananas per muffin
So Recipe A uses the least amount of bananas per muffin, Recipe C uses the next least amount of bananas per muffin, and Recipe B uses the most amount of bananas per muffin.
Answer: The answer is C
Step-by-step explanation:
Because it is
A landlord plans to take out a $12,000 loan to cover the cost of a new roof for a rental home. If the loan has a 5% annual interest rate compounded continuously and the landowner plans to pay off the loan in 21 months, what is the total amount owed? $34,291.81 $24,600.00 $13,328.53 $13,097.31
Using compound interest formula, the final payment for a principal of $12000 compounded continuously at rate of 5% is $13,097.31
What is Compound InterestCompound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula of compound interest is given as;
A = P(1 + r/n)^nt
A = compound interestP = principalr = rate n = number times t = timeSubstituting the values into the formula
A = Pe^rt
This formula is only for continuously compounded
A = 12000e^(0.05 * 1.75)
A = $13,097.31
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What is the value of x
Answer:
x = 60
Step-by-step explanation:
x and 60 are alternate interior angles and since the lines are parallel, x = 60.
x = 60
Answer:
60°
Step-by-step explanation:
We know that, if two line are parallel, alternate angles are equal.
B D // X Y
Therefore,
x = 60°
Mason had 30 minutes to do a three-problem quiz. He spent 9 1/4 minutes on question A and 3 4/5 minutes on question B. How much time did he have left for question C?
Answer:
16 57/60 mins
Step-by-step explanation:
9 1/4 = 555 secs
3 4/5 = 228 secs
30.mins = 1800 secs
time for C = 1800 - 555 - 228
= 1017 sec
16 57/60 mins
Find the removable and non removable discontinuity.
F(x) = 2/x
The function F(x) = 2/x has a removable discontinuity at x = 0, and a non-removable discontinuity at x = 0.
What is the Function?
A function is a mathematical relation between a set of inputs, called the domain, and a set of possible outputs, called the range. The definition of a function is often written as "f: X → Y", where X is the domain and Y is the range, and "f" is the name of the function.
The function F(x) = 2/x has a removable discontinuity at x = 0, and a non-removable discontinuity at x = 0.
At x = 0, the function is not defined, so it has a removable discontinuity at x = 0.
However, since the function is not defined for x = 0, it is also a non-removable discontinuity at x = 0.
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Adding several variables to a regression analysis can help do which of the following?
A. Increase the statistical significance of the results
B. Control for several variables at once
C. Increase the construct validity of a study
D. Test for temporal precedence
Regression analysis is mostly used when you want to predict a continuous dependent variable from a several number of independent variables. If the dependent variable is dichotomous, then logistic regression can be used.
If the break between the two levels of the dependent variable is nearly to 50-50%, then we can use both logistic and linear regression will end up giving you similar results.
If you have inserted the data (rather than using an established dataset), it is a nice idea to check the accuracy and the consistence of the data entry.
If you do not want to re-check all the data point, you should at least check the minimum and maximum value for all the variable to ensure that all values for each variable are "valid" or not.
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Considering both dividends paid and capital gains, Dylan's pretax profit from his investment is $
Dylan's pretax return on investment (ROI) is
Type the correct answer in each box. Use numerals instead of words.
The pretax rate of return is the profit or loss on an investment before taxes are subtracted.
What is the difference between taxable income and pretax income?Pretax financial income, on the other hand, is the amount a firm earns before taxes are taken into account. Taxable income is the amount of income that a corporation must pay taxes on.
Generally speaking, investment income includes, but is not limited to: interest, dividends, capital gains, rental and royalty income, non-qualified annuities, income from firms engaged in trading financial instruments or commodities, and enterprises that are passive for the taxpayer.
The profit or loss on an investment prior to deducting taxes is known as the pretax rate of return. Taxes on investment income are levied by the government on any additional income derived from purchasing or disposing of investments. Securities that are profitably sold are subject to capital gains taxes.
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Answer: Considering both dividends paid and capital gains, Dylan’s pretax profit from his investment is $30. Dylan’s pretax return on investment (ROI) is 24%.
Step-by-step explanation: To determine Dylan’s profit from his investment, add his dividends of $5 and his capital gains of $25.total profit = $25 + $5= $30Before taxes are applied, Dylan can calculate his return on investment (ROI) by dividing his profit by the cost of his investment:30125 = 0.24, or 24%.
Choose the better buy.
5 qt.: $2.25
5 liters: $2.35
There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.
How to calculate the value?5 Quarts =4.7317647 Liters
5 Liters =5.2834410 Quarts
The cost is In liter calculate
5 qt.: $2.25=4.7317647 liter
5 liters: $2.35=1000×5=5000
=5000-4.731
= 4,995.269 litter difference from 5 liter
5000 liter in liter $2.35 so each value 2,127.65957447
4.731 liter in of quarts $2.25 each value 2,102.66666667
1 qt = 2pt For every quart there are 5 qts = 10 pts two pints. So, multiply 5 x 2 = 10 pints. Example: If a pot has a capacity of 16 cups, how many quarts can it hold? 1 qt = 4c For every quart, there are 4 cups. The quart (symbol: qt) is an English unit of volume equal to a quarter gallon. Three kinds of quarts are currently used: the liquid quart and dry quart of the US customary system and the imperial quart of the British imperial system. All are roughly equal to one liter.
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Simplify
8!/(8-2)
A. 720
b. 0.018
C. 8
d. 56
e. 40320
f. 1.333
Answer:
D) 56
Step-by-step explanation:
[tex]\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56[/tex]
The function g is defined by g)2+bx, where b is a constant. If the line tangent to the graph of g at x 1 is parallel to the line that contains the points (0, -2) and (3, 4), what is the value of b ? (A) -1
(B) 2
(C) 5/2
(D) 4
Answer:
The cost per hour for renting the boat is $18 per hour.
A function is said to be linear if it is a straight line graph and it can be represented by the equation:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the total cost for renting the boat for x hours.
Given the equation:
y = 18x
Therefore the cost per hour for renting the boat is $18 per hour.
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What is the value of 2+b(a^2+4) when a = 2 and b = 4
[tex]2+b(a^2+4)[/tex] when a is 2 and b is 4
Substitute for variables with given values:
[tex]2+(4)((2)^2+4)[/tex]
[tex]=\fbox{34}[/tex]
explain how you know which number 1 15/16 17/8 63/32 is closest to 2
The closest number of 2 is 63/32. By using the subtraction operation, we can compute it.
What are numbers?
A number is a mathematical object that can be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original examples. Number words can be used to represent numbers in language.
Given numbers are [tex]1\frac{15}{16}[/tex], 17/8, 63/32
Now find the difference between the given numbers from 2.
The difference of [tex]1\frac{15}{16}[/tex] from 2 is
2 - [tex]1\frac{15}{16}[/tex]
= 2 - 31/16
= 1/16.
The difference of 17/8 from 2 is
|2 - 17/8|
= |(16 - 17)/8|
=| -1/8|
= 1/8
The difference of 63/32 from 2 is
2 - 63/32
= (64 - 63)/32
= 1/32
The numerator of the difference is the same. The greater denominator represents a less number.
Thus 63/32 is close to 2.
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a museum has three rooms, each with a motion sensor (m0,m1, and m2) that outputs 1 when motion is detected. at night, the only person in the museum is one security guard who walks from room to room. create a circuit that sounds an alarm (by setting an output a to 1) if motion is ever detected in more than one room at a time, meaning there must be at least one intruder. start with a truth table.
(a) Truth Table is attached.
(b) In canonical SOP form, A = ∑ m(3,5,6,7)
(c) Minimal form: A = m1m2 + m0m1 + m0m2
(b) Canonical SOP form: The canonical sum-of-products (sop) form of LPP in matrix notation is as follows: Boost Z = CX (objective function) AX b (restrictions) and X 0 (limitations) apply (non-negativity restrictions).
it will be A = ∑ m(3,5,6,7)
(c) Minimal form: The k-map can be defined as a map that provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. The Karnaugh map can also be described as a special arrangement of a truth table.
it will be A = m1m2 + m0m1 + m0m2
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The complete question is:
a museum has three rooms, each with a motion sensor (m0,m1, and m2) that outputs 1 when motion is detected. at night, the only person in the museum is one security guard who walks from room to room. create a circuit that sounds an alarm (by setting an output a to 1) if motion is ever detected in more than one room at a time, meaning there must be at least one intruder.
(a) Specify the truth table
(b) formulate canonical sum of products implementation for A
(c) Minimize A using K-maps and write the minimum implementation of A
What does it look like on a graph line
A horizontal x-axis and a vertical y-axis make up the line graph.
What does a graph line look like? These axes often cross around the bottom of the y-axis and the left end of the x-axis because the majority of line graphs only deal with positive numerical values. The intersection of the axes is always at (0, 0). To draw a graph line the following steps containStep 1: Identify the variables. Step 2: Determine the variable range. Step 3: Determine the scale of the graph.Step 4: Number and label each axis and title the graph.Step 5: Determine the data points and plot on the graph.Step 6: Draw the graph.To learn more about graph line refer to:
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Drag each symbol to the correct location on the equation. Not all symbols will be used.
A group of third-grade and fourth-grade students are taking a field trip. The group will fill a total of 4va
Each van seats 8students.
• There are 27third-grade students in the group.
• The rest of the students in the group are fourth-graders.
Complete the equation to show how to find f, the number fourth-grade students in the group.
X
4
+
8
27 = f
Answer:
The equation to find the number of fourth-grade students in the group (f) is:
(number of vans) x (number of students per van) + (number of third-grade students) = (number of fourth-grade students)
So, the equation would be:
4v x 8s + 27s = f
Where "v" stands for vans, "s" stands for students, and "f" stands for fourth-grade students.
To find the number of fourth-grade students, you would need to substitute in the given information:
4 x 8 + 27 = f
32 + 27 = f
So, there are 59 fourth-grade students in the group.
Step-by-step explanation:
[tex]\sqrt{144}[/tex]
Given m∠ABC=37°m∠ABC=37°and m∠CBD=165°m∠CBD=165°. According to the Angle Addition Postulate, what is the measure of ∠ABD∠ABD, that contains −−→BCBC→?
According to the Angle Addition Postulate, the measure of m∠ABD = 202°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
The angle measures:
m∠ABC=37°,
and m∠CBD= 165°.
So, according to the angle addition postulate;
m∠ABD = m∠ABC + m∠CBD
Substituting the values,
m∠ABD = 37° + 165°
m∠ABD = 202°
Therefore, the angle measure of m∠ABD = 202°.
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I need help with this math
Answer:
what your question tell me I will give you answer and also write down your name and question
14. Point B(4, -16) is dilated by a scale factor
3
of to create B'.
a. Write a rule for the transformation.
The rule for the transformation that dilates point B(4, -16) by a scale factor of 3 is: (x, y) --> (3x, 3y)
What is transformation?A transformation is a function that maps points in a given space to points in a different space. There are many types of transformations, including translations, rotations, dilations, and reflections.
What is coordinate?A coordinate is a set of numerical values that are used to specify the position of a point in a specific space. In two-dimensional space, a point is typically defined by an ordered pair of numbers (x, y), where x is the horizontal position and y is the vertical position. In three-dimensional space, a point is typically defined by an ordered triple of numbers (x, y, z), where x, y, and z are the positions in the three dimensions.
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Determine if each equation has one solution, no solution, or infinite solutions.
1. -4g + 8 = 20
2. -3b = 2b - 5b
3. -3f = 2 - 3f
4. 2n - 12 = -12 + 2n
5. 7c - 4 = 3 + 7c
6. 3 - 5y = 2y + 24
7. 22 + w = 2(4w - 3)
8. 6h - 8 + 4h = 12 + 10h
9. 12j = 4(3j - 8)
10. 5(u-9) = -2u - 45 + 7u
11. 2 (4a - 7) - 3a = 19 - 6a
12. 3 - 11d = -6d + 3 - 5d
Answer:
Step-by-step explanation:
1. One solution. Solving for g gives g=2.
2. No solution. The equation is equivalent to -3b = -3b, which is always false.
3. One solution. Solving for f gives f=2/5.
4. Infinite solutions. The equation is equivalent to 2n-12 = 2n-12, which is always true for any value of n.
5. Infinite solutions. The equation is equivalent to 7c-4 = 7c+3, which is always true for any value of c.
6. One solution. Solving for y gives y = -3/7.
7. One solution. Solving for w gives w = -22
8. One solution. Solving for h gives h = 2
9. One solution. Solving for j gives j = -2
10. One solution. Solving for u gives u = -5
11. One solution. Solving for a gives a = -1/2
12. No solution. The equation is equivalent to 3-11d = -11d+3, which is always false.
Exit Slip: (5) The 6th grade class is competing in Field Day. There
are 32 girls and 40 boys. If each team must have the same
number of girls and boys, what's the greatest number of teams
that can be formed?
We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.
what is common factors ?The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM). A number that divides two or more numbers precisely is referred to as a common factor. For instance, because they are both even, 10 and 20 share a common factor of 2. The largest number that precisely divides two or more numbers is known as the greatest common factor (GCF).
given
32 girls and 24 boys
Additionally, we must divide them into groups in order to determine the number of groups that can be formed. To do this, we must determine the highest common factor between 24 and 32.
To obtain that, we can express both of these as a prime number product as follows:
24 = 2*2*2*3
32 = 2*2*2*2*2
The highest common factor between 24 and 32 is 2*2*2 = 8 since in all of these we have three times the factor 2.
Each squad will have the following number of boys 24/8 = 3
Each team will have four girls, or 32/8, total.
We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.
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A container can hold a maximum of 17.75 pounds. There are two objects in the container. The first object weighs 6.53 pounds and the second weighs 10.1 pounds. How many more pounds can the container hold? Write your answer as a decimal.
The container can hold 1.12 pounds
How to calculate the number of pounds that the container can hold?
A container can hold a maximum of 17.75 pounds
There are two objects in the container
The first object weights 6.53 pounds
The second object weight 10.1 pounds
The amounts of pounds that the container can hold is
6.53+10.1
= 16.63
17.75-16.63
= 1.12
Hence the container can hold 1.12 pounds
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2. If we want to find the volume of the child's toy shown below, what will the units be on our answer?
A cm^3
B cm
C cm^4
If we want to find the volume of the given toy, then the units of our answer will be (A) cm³.
What is volume?Volume is the amount of space a thing takes up, whereas capacity is the amount of solid, liquid, or gas that it can hold.
Volume is measured in cubic units, although capacity can be expressed in almost any other unit, such as liters, gallons, pounds, etc.
The capacity of an object is measured by its volume.
For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.
The quantity of space occupied by a three-dimensional object can also be used to describe volume.
So, in the description, it is stated that the value is measured in cubic units.
Therefore, if we want to find the volume of the given toy, then the units of our answer will be (A) cm³.
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Graph this on a line please
The last boxplot is the one that displays the values range of the distribution that is given.
What is the range?The range of a function in mathematics can refer to one of two ideas that are connected in some way: Codomain for the function an illustration of the action If there is precisely one y in Y and there are two sets X and Y, then a binary relation f between X and Y is a function that connects x and y.
Here ,Given information:
6,7,9,9,20,22,26,28,29,30
N = 10 observations were made.
The base number is 6. ( least value)
Quartile lower= n+1(0.25)
term = 0.25(13) = 3.25term = 13
Median equals 0.5 (n + 1)
term = 0.5(13) = 6.5 term = (20 + 24) /2 = 22
Upper quartile: 0.75 (13)
A term equals 9.75 a term equals 26.5
Interquartile Range (IQR) is equal to= Q3 - Q1= (26.5 - 13) = 13.5
The highest value is 30. (highest value in the distribution)
As a result, the Last boxplot is the one that shows the distribution that is given.
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